DAMAIC Project Due
Data_Analysis_Tool_list_wDMAIC_3e_rev2.doc
Data Analysis Tools
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Tool |
What is it? |
When do I use it? |
Example |
DMAIC |
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Affinity Diagram |
A method to gather and organize brainstormed ideas (language data) into groupings based on the natural relationship between items. |
When you need to organize and consolidate large amounts of qualitative data in order to support a concept or solution. |
http://en.wikipedia.org/wiki/Affinity_diagram
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Measure, Analyze, Improve, Control |
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Box and Whisker Plot |
A graphical way to compare the medians and the variation between groups of data. It can also help to identify outliers. |
When you need a quick visual look at one or more sets of data. They graphically show different types of populations without any assumptions of the statistical distribution. |
Discovering Stats 3e – pg.173-176 |
Measure, Analyze, Improve |
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Cause and Effect / Fishbone / Ishikawa Diagram |
A structured problem solving technique that graphically displays / organize all possible brainstormed causes relating to a problem (focusing on causes, not symptoms). |
When you have a large number of factors that could influence your process and you need support for a resulting solution. |
Slides posted in Coursework
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Analyze
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Check Sheets |
Used for counting and accumulating data in a logical format during observation. This is a straightforward and easy way to answer the question, how often are certain events happening? |
When quantifying frequency / counting data on number of occurrences (eg. defects), information on variables (eg. weight, size, length, or defect location, etc.). |
http://web2.concordia.ca/Quality/tools/6cksheet.pdf
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Measure |
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Chi-Square – Test for Independence |
This is a procedure used to determine if two classifications variables are related, testing the statistical independence of two random variables. It compares the number of observed counts against the expected number of counts to determine if there is a difference in output counts.
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It is a good method to apply to before and after data to prove that a process improvement made an effective change. Use this method when you have nominal data in a table and you need to know if the output counts differ for two or more categories. |
Discovering Stats 3e – pg. 646-651 |
Analyze, Improve |
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Confidence Intervals |
A range of values in which we expect the population parameter to occur. A population parameter is likely to occur at a specified probability. It is constructed from sample data. |
Confidence intervals determine if a process is centered where it is expected. They are used to identify a shift or change in the process (mean) and to identify a difference in two populations (eg. does Vendor 1 and Vendor 2 give us the same dimensioned part?) |
Discovering Stats 3e – pg. 426-484 |
Measure, Analyze, Improve |
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Control Chart |
Can serve as a statistical tool for problem identification as well as, ongoing monitoring of a process (graphically) over time. It can assist in distinguishing random variation (noise) from assignable variation (signal). |
When you need to recognize and eliminate sources of variation in a process so that a process performs consistently and predictably. |
Understanding Variation by D.J. Wheeler |
Measure, Analyze, Improve, Control |
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Correlation Coefficient |
Correlation coefficient R is a measure of the strength and direction of the linear relationship between 2 random variables. R falls on or between the numbers -1 and 1. Coefficient of determination R2 is a measure representing the percent of variability in “y” that can be accounted for by the variable x. |
Although correlation does not explicitly imply causation, establishing a correlation between two variables is necessary (but not sufficient) to establishing a causal relationship. |
Discovering Stats 3e – pg. 192-199 |
Measure, Analyze, Improve |
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Fault Tree Analysis |
It is a visual tool that logically and graphically presents the various combinations of possible events or failures that could occur in a process or product. It is an inverted tree with the trunk (noting the failure or undesired event) of the tree at the top of the diagram and the branches are the contributing causes of the failure. |
When a simple visual is needed for determining (and presenting) the root cause of a failure. |
http://en.wikipedia.org/wiki/Fault_tree_analysis http://www.weibull.com/basics/fault-tree/
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Measure, Analyze, Improve |
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Force Field Analysis |
Method to present the “positives” and “negatives” of a situation so that they can be compared, the positives can be reinforced and the negatives can be eliminated. |
When the desired outcome is “making a change” in the midst of forces /barriers restraining movement towards the ideal state. |
http://www.mindtools.com/pages/article/newTED_06.htm
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Measure, Analyze, Improve |
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Histogram |
A graphical method of displaying the distribution of data by bar graphing the number of units of a particular category (illustrates process centering, spread and shape). |
When displaying large amounts of data that are difficult to interpret in tabular form. |
Discovering Stats 3e – pg. 65-66 |
Measure, Analyze, Improve |
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Hypothesis Testing |
Hypothesis testing is a process (inferential method) that uses sample data from a population to confirm or refute some statement or claim about that population. |
Hypothesis testing can tell us if two sets of data are really different from each other. Determines statistically whether or not there is a cause for concern or if our conclusion is simply due to random variation. It can be used to determine whether a population parameter (mean, variation, etc.) is statistically different than a standard or set value. |
Discovering Stats 3e – pg. 486-555, 574-629 |
Analyze, Improve
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Linear Regression Analysis |
This tool will help you to understand the relationship between the process output and any process input that could affect it. It is a way to model or predict the relationship between those variables. |
When you suspect there is a relationship between an input and output variable. It is especially useful when the output variable is difficult or expensive to measure and the input variables are not. |
Discovering Stats 3e – pg.186-237, 743-759 |
Analyze |
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Measurement System Analysis (MSA) |
A process that includes identifying, quantifying and reducing measurement errors. Measurement systems (a decision making tool) play a large part in process improvement activities. |
On every measurement system that a decision is based upon. |
http://www.6sigma.us/MeasurementSystemsMSA/measurement-systems-analysis-MSA-p1.html Slides posted in Coursework |
Measure, Analyze |
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Measures of Center (Descriptive Statistics -Measure of Location) |
The behavior of the middle (or central portion) of the population of process data. 3 measures are: Mean = arithmetic average Median = middle value Mode = most frequent value |
When you need a quantitative measure that summarizes an important characteristic of a population / process, the center of your data. |
Discovering Stats 3e – pg.108-117 |
Define, Measure, Analyze, Improve, Control |
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Measures of Variability (Descriptive Statistics -Measure of Dispersion or spread) |
A measure of how the data is spread around the mean. 3 Measures are: Range = difference between the largest and the smallest data point Standard Deviation = measure takes into account each data point and its distance from the mean Variance = standard deviation squared |
On any set of data - all populations and processes have some degree of variability. |
Discovering Stats 3e – pg.126-137 |
Define, Measure, Analyze, Improve, Control |
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Pareto Chart/Diagram |
A descending bar and cumulatively increasing line chart used to separate the vital few from the trivial many. The vital few are the few factors accounting for the largest part (%) of a problem or condition. Pareto Principle: 20% of the sources cause 80% of the problem. |
When you need to focus on the key problem(s) - when solved will have the greatest impact. |
Discovering Stats 3e – pg. 43-44 |
Define, Measure, Analyze, Improve
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Process Map (or Process Flow chart) |
A graphical tool for documenting a process. Each step or activity is mapped out as it occurs in the real-live process. |
When improving or creating a process |
http://en.wikipedia.org/wiki/Business_process_mapping
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Define, Measure Analyze, Improve, Control |
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Run Chart (Time Series Plot) |
A graphical tool that can show and track trends or patterns over a specified time period. |
When you need to do the simplest possible display of a trend over time. |
Discovering Stats 3e – pg.89-91 |
Measure, Analyze, Improve |
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Scatter Plot/Diagram |
A graphical tool to visualize the possible relationship between two variables and relative strength of that relationship. |
When you need to display what happens to one variable when another variable changes (visualize a relationship between two variables). |
Discovering Stats 3e – pg.188-192 |
Measure, Analyze, Improve |
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SIPOC (Supplier / Input / Process / Output / Customer) |
A simple way to document (or map) a process in the “as is” (current) state by listing the suppliers, inputs, outputs and customers. The “process” should be identified by a high level flow chart. This sets the scope for the value-stream map. |
This is a quick way to document your process (and start to analyze) when parts of the process are not clear or consistent (ie. Who supplies inputs to the process? Who are the true customers of the process? Is there a customer for each output? What are the requirements of customers?) |
Slides posted in Coursework http://www.isixsigma.com/library/content/c010429a.asp
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Define, Measure |
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Stem and Leaf plot (Stemplot) |
A graphical technique that shows the shape (distribution) of the data like a histogram but displays all of the individual values within an interval rather than just the frequency for each interval. |
When evaluating the shape of the data with the ability to maintain visibility to the original raw data points. |
Discovering Stats 3e – pg.68-71 |
Measure, Analyze, Improve |
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Solution Selection Matrix |
A matrix that helps identify the best solution among several solutions by weighting the impact of each solution on established criteria (ie. cost, time to implement, impact on quality, etc.), hence measuring the effectiveness of solving the problem with that solution. |
Use this when you have a couple solutions to choose from and want to make your decision fact based, taking more factors into consideration. |
http://www.whatissixsigma.net/six-sigma-dmaic-improve-phase/
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Improve |
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Thought Process Map (TPM) |
A logical, visual representation or map of someone’s thought process flow (of questions, tools used to help answer the question, related actions and related decisions) that shows how a process or problem was/is attacked / addressed. |
Use this for any situation. This is an “evergreen” document that can be used as a communication tool for where you are, where you’ve been and where you are going. |
Slides posted in Coursework |
Define, Control |
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EXAMPLE_storyboard_example_students.ppt
MBC638
Data Analysis
DEFINE
MEASURE
Web Metrics Cost Reduction
Team
Launch
Define
Measure
Analyze
Control
Improve
Key Dates --->
ANALYZE
IMPROVE
Process owner: John
CONTROL
Joe, Pat and Dave
8/28
Fee for web
Analytics Service up over 20%
$
Annual Budget
is at risk of overrun
Cpk = 0.382
9/3
9/5
9/7
9/7
Invoice cost increasing
Page view volume increasing
Page view volume increase
starts with data collector changes
One data
collector
per page
Invoice cost lowered 15%
10/15
- Data collector tag instructions
added to operational definitions
- Page view volumes are reviewed
Monthly
- Invoices are reviewed monthly
- Control charts are maintained
More than one data collector found on some pages
*
DEFINE
MEASURE
Process Improvement Project – Cycle Time Reduction
Team Launch
8/23
Define
9/08
Measure
10/16
Analyze
10/24
Control
On-Going
Improve
10/31
Key Dates --->
ANALYZE
IMPROVE
Process owner: Dan
CONTROL
PROJECT TEAM: Dan Mary Karen Linda Peter
BUSINESS CASE: $54,000 in annual processing costs
It takes 43 days to process a grant application. Only 8% of applications are being processed within 30 days of receipt. The time to process the application has lead to unhappy applicants and staff who are finding more and more of their daily work time being devoted to “grant administration.” The funding levels available to applicants and the number of applications are expected to increase in the near future, which has the potential to compound the problem.
Defects/delays are inherent in the current process. Current SQL is 1.9
The Number of applications received is increasing.
The time to complete a process cycle is also increasing.
Problem: Incomplete and inaccurate applications were identified as the primary factor leading to defects in the process cycle.
Solution: New Application process incorporating drop down menus
New Application Procedure =
Less Mistakes & Quicker Cycle Time
The defect rate reduced from 93% to 32%
Monthly monitor and review procedure is in place. Out of control signal = action plan.
↑ Number of Applications + ↑ Cycle Process Time __Tough Times Ahead
*
DEFINE
MEASURE
Closing the Gap in Incoming Material Analysis
Team Launch
Define
Measure
Analyze
Control
Improve
Key Dates --->
ANALYZE
IMPROVE
Process owner: Bob
CONTROL
Buyer (myself), Vendor, Quality, Accounting, Manufacturing
September 8
October 10
November 10
January 10
September 14
January 15
Longer lead time for vendor payment.
Additional time reconciling invoices.
Increased inventory levels waiting for third party analysis.
Animosity in relationship.
25% discrepancies between Receiving & Vendor lead to:
reproducibility
= .0022
Precision-to-total ratio = .4315
Capability ratio = .66
Unacceptable
Measurement
System
Define how much discrepancy is defined by the process
Create clearer operational definitions
Modified Process Map to catch defects
Create Standard Operating Procedures
Expand improvements to other vendors
Compare analysis on identical samples (DOE)
Maintain lot identity
Standardize sampling and analysis
The “variation” Receiving found
FY08 high volume vendors
*
Chart4
| BS261/191 | BS261/191 |
| BS261/192 | BS261/192 |
| BS261/193 | BS261/193 |
| BS261/194 | BS261/194 |
| BS261/195 | BS261/195 |
| BS261/196 | BS261/196 |
| BS261/197 | BS261/197 |
| BS261/198 | BS261/198 |
| BS261/199 | BS261/199 |
| BS261/200 | BS261/200 |
| BS261/201 | BS261/201 |
| BS261/202 | BS261/202 |
| BS261/203 | BS261/203 |
| BS261/204 | BS261/204 |
| BS261/205 | BS261/205 |
| BS261/206 | BS261/206 |
| BS261/207 | BS261/207 |
| BS261/208 | BS261/208 |
| BS261/209 | BS261/209 |
| BS261/210 | BS261/210 |
| BS261/211 | BS261/211 |
| BS261/212 | BS261/212 |
| BS261/213 | BS261/213 |
| BS261/214 | BS261/214 |
| BS261/215 | BS261/215 |
| BS261/216 | BS261/216 |
| BS261/217 | BS261/217 |
| BS261/218 | BS261/218 |
| BS261/219 | BS261/219 |
| BS261/220 | BS261/220 |
| BS261/221 | BS261/221 |
| BS261/222 | BS261/222 |
| BS261/223 | BS261/223 |
| BS261/224 | BS261/224 |
| BS261/225 | BS261/225 |
| BS261/226 | BS261/226 |
| BS261/227 | BS261/227 |
| BS261/228 | BS261/228 |
| BS261/229 | BS261/229 |
| BS261/230 | BS261/230 |
| BS261/231 | BS261/231 |
| BS261/232 | BS261/232 |
| BS261/233 | BS261/233 |
| BS261/234 | BS261/234 |
| BS261/235 | BS261/235 |
| BS261/236 | BS261/236 |
| BS261/237 | BS261/237 |
| BS261/238 | BS261/238 |
| BS261/239 | BS261/239 |
| BS261/240 | BS261/240 |
| BS261/241 | BS261/241 |
| BS261/242 | BS261/242 |
| BS261/243 | BS261/243 |
| BS261/244 | BS261/244 |
| BS261/245 | BS261/245 |
| BS261/246 | BS261/246 |
| BS261/247 | BS261/247 |
| BS261/248 | BS261/248 |
| BS261/249 | BS261/249 |
| BS261/250 | BS261/250 |
| BS261/251 | BS261/251 |
Suppliers FY08
| Supplier | STUs | Cumulative % | % | ||
| Beralt | 121.9 | 23.11% | 23.11% | ||
| DLA | 111.2 | 44.20% | 21.08% | 65.21% | |
| Spot | 80 | 59.37% | 15.17% | ||
| Cantung | 72.3 | 73.08% | 13.71% | ||
| Dynacor | 71.4 | 86.61% | 13.54% | ||
| Heemskirk | 46.8 | 95.49% | 8.87% | ||
| KMT | 16.8 | 98.67% | 3.19% | ||
| Other | 7 | 100.00% | 1.33% | ||
| 527.4 | |||||
| Pareto |
Suppliers FY08
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
Dynacor
| lot | Dynacor Analysis | OSI Analysis | Difference | Population | Sample of last 20 lots | ||
| 1 | 73.50% | 74.50% | 1.00% | ||||
| 2 | 75.36% | 75.10% | -0.26% | ||||
| 3 | 75.78% | 75.20% | -0.58% | Dynacor | |||
| 4 | 75.68% | 75.20% | -0.48% | ||||
| 5 | 75.23% | 75.20% | -0.03% | Mean | 0.7531547619 | ||
| 6 | 75.15% | 75.60% | 0.45% | Standard Error | 0.0005393807 | ||
| 7 | 75.39% | 75.70% | 0.31% | Median | 0.7535 | ||
| 8 | 74.69% | 75.50% | 0.81% | Mode | 0.7549 | ||
| 9 | 75.49% | 75.60% | 0.11% | Standard Deviation | 0.0034955862 | ||
| 10 | 75.71% | 75.60% | -0.11% | Sample Variance | 0.0000122191 | ||
| 11 | 75.40% | 75.30% | -0.10% | Kurtosis | 17.8674511313 | ||
| 12 | 75.27% | 75.60% | 0.33% | Skewness | -3.6031269153 | ||
| 13 | 75.34% | 75.60% | 0.26% | Range | 0.0228 | ||
| 14 | 75.34% | 75.60% | 0.26% | Minimum | 0.735 | ||
| 15 | 74.96% | 75.10% | 0.14% | Maximum | 0.7578 | ||
| 16 | 75.01% | 75.40% | 0.39% | Sum | 31.6325 | ||
| 17 | 75.28% | 75.50% | 0.22% | Count | 42 | ||
| 18 | 75.49% | 75.40% | -0.09% | ||||
| 19 | 75.31% | 75.30% | -0.01% | ||||
| 20 | 75.30% | 75.60% | 0.30% | ||||
| 21 | 75.40% | 75.00% | -0.40% | OSI | |||
| 22 | 75.08% | 75.20% | 0.12% | ||||
| 23 | 75.28% | 75.50% | 0.22% | Mean | 0.7530238095 | ||
| 24 | 75.27% | 75.50% | 0.23% | Standard Error | 0.000464148 | ||
| 25 | 75.49% | 75.60% | 0.11% | Median | 0.7535 | ||
| 26 | 75.46% | 75.70% | 0.24% | Mode | 0.756 | ||
| 27 | 75.20% | 75.10% | -0.10% | Standard Deviation | 0.0030080226 | ||
| 28 | 75.28% | 75.30% | 0.02% | Sample Variance | 0.0000090482 | ||
| 29 | 75.29% | 75.50% | 0.21% | Kurtosis | -0.1311559736 | ||
| 30 | 75.48% | 74.80% | -0.68% | Skewness | -0.7805090956 | ||
| 31 | 75.35% | 74.90% | -0.45% | Range | 0.012 | ||
| 32 | 75.31% | 75.60% | 0.29% | Minimum | 0.745 | ||
| 33 | 75.52% | 75.50% | -0.02% | Maximum | 0.757 | ||
| 34 | 75.57% | 74.80% | -0.77% | Sum | 31.627 | ||
| 35 | 75.43% | 75.50% | 0.07% | Count | 42 | ||
| 36 | 75.33% | 74.90% | -0.43% | ||||
| 37 | 75.35% | 74.70% | -0.65% | ||||
| 38 | 75.41% | 75.30% | -0.11% | ||||
| 39 | 75.49% | 74.90% | -0.59% | ||||
| 40 | 75.39% | 75.30% | -0.09% | ||||
| 41 | 75.58% | 75.40% | -0.18% | ||||
| 42 | 75.61% | 75.10% | -0.51% | ||||
| 43 | -0.01% | ||||||
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Dynacor
| 0.735 | 0.745 |
| 0.7536 | 0.751 |
| 0.7578 | 0.752 |
| 0.7568 | 0.752 |
| 0.7523 | 0.752 |
| 0.7515 | 0.756 |
| 0.7539 | 0.757 |
| 0.7469 | 0.755 |
| 0.7549 | 0.756 |
| 0.7571 | 0.756 |
| 0.754 | 0.753 |
| 0.7527 | 0.756 |
| 0.7534 | 0.756 |
| 0.7534 | 0.756 |
| 0.7496 | 0.751 |
| 0.7501 | 0.754 |
| 0.7528 | 0.755 |
| 0.7549 | 0.754 |
| 0.7531 | 0.753 |
| 0.753 | 0.756 |
| 0.754 | 0.75 |
| 0.7508 | 0.752 |
| 0.7528 | 0.755 |
| 0.7527 | 0.755 |
| 0.7549 | 0.756 |
| 0.7546 | 0.757 |
| 0.752 | 0.751 |
| 0.7528 | 0.753 |
| 0.7529 | 0.755 |
| 0.7548 | 0.748 |
| 0.7535 | 0.749 |
| 0.7531 | 0.756 |
| 0.7552 | 0.755 |
| 0.7557 | 0.748 |
| 0.7543 | 0.755 |
| 0.7533 | 0.749 |
| 0.7535 | 0.747 |
| 0.7541 | 0.753 |
| 0.7549 | 0.749 |
| 0.7539 | 0.753 |
| 0.7558 | 0.754 |
| 0.7561 | 0.751 |
Beralt
| Lot | Beralt | OSI | Difference | Rec'd date | |
| BS261/191 | 72.15% | 73.30% | 1.15% | 9-Feb | |
| BS261/192 | 72.89% | 74.10% | 1.21% | 9-Feb | |
| BS261/193 | 72.98% | 73.50% | 0.52% | 16-Feb | |
| BS261/194 | 73.10% | 71.50% | -1.60% | 27-Feb | |
| BS261/195 | 73.18% | 72.00% | -1.18% | 27-Feb | |
| BS261/196 | 73.12% | 71.10% | -2.02% | 2-Mar | |
| BS261/197 | 72.95% | 72.60% | -0.35% | 16-Mar | |
| BS261/198 | 73.10% | 73.40% | 0.30% | 16-Mar | |
| BS261/199 | 73.05% | 73.30% | 0.25% | 15-Mar | |
| BS261/200 | 72.80% | 73.10% | 0.30% | 23-Mar | |
| BS261/201 | 73.10% | 72.80% | -0.30% | 27-Mar | |
| BS261/202 | 73.00% | 71.20% | -1.80% | 30-Mar | |
| BS261/203 | 72.95% | 71.90% | -1.05% | 2-Apr | |
| BS261/204 | 73.00% | 72.70% | -0.30% | 2-Apr | |
| BS261/205 | 73.15% | 72.60% | -0.55% | 13-Apr | |
| BS261/206 | 72.85% | 72.90% | 0.05% | 20-Apr | |
| BS261/207 | 73.18% | 73.30% | 0.12% | 19-Apr | |
| BS261/208 | 73.10% | 72.70% | -0.40% | 2-May | |
| BS261/209 | 73.12% | 71.40% | -1.72% | 17-May | |
| BS261/210 | 72.92% | 72.50% | -0.42% | 10-May | |
| BS261/211 | 72.72% | 72.70% | -0.02% | 10-May | |
| BS261/212 | 72.78% | 72.90% | 0.12% | 16-May | |
| BS261/213 | 72.69% | 73.50% | 0.81% | 21-May | |
| BS261/214 | 72.80% | 73.40% | 0.60% | 21-May | |
| BS261/215 | 72.78% | 72.80% | 0.02% | 29-May | |
| BS261/216 | 72.70% | 73.00% | 0.30% | 7-Jun | lots that were sent to run twice in random order: |
| BS261/217 | 73.20% | 73.40% | 0.20% | 12-Jun | |
| BS261/218 | 73.12% | 73.40% | 0.28% | 13-Jun | |
| BS261/219 | 73.25% | 73.10% | -0.15% | 19-Jun | |
| BS261/220 | 73.18% | 73.30% | 0.12% | 19-Jun | |
| BS261/221 | 73.28% | 74.10% | 0.82% | 27-Jun | |
| BS261/222 | 73.22% | 73.70% | 0.48% | 28-Jun | |
| BS261/223 | 73.35% | 73.60% | 0.25% | 9-Jul | |
| BS261/224 | 73.50% | 72.80% | -0.70% | 9-Jul | |
| BS261/225 | 73.56% | 73.30% | -0.26% | 23-Jul | |
| BS261/226 | 73.42% | 72.70% | -0.72% | 23-Jul | |
| BS261/227 | 73.45% | 73.80% | 0.35% | 26-Jul | |
| BS261/228 | 73.38% | 72.90% | -0.48% | 2-Aug | |
| BS261/229 | 73.48% | 73.70% | 0.22% | 2-Aug | |
| BS261/230 | 73.65% | 73.40% | -0.25% | 14-Aug | |
| BS261/231 | 73.90% | 73.60% | -0.30% | 15-Aug | |
| BS261/232 | 73.82% | 72.20% | -1.62% | 16-Aug | |
| BS261/233 | 73.75% | 73.20% | -0.55% | 16-Aug | |
| BS261/234 | 73.62% | 72.50% | -1.12% | 22-Aug | |
| BS261/235 | 73.58% | 73.40% | -0.18% | 22-Aug | |
| BS261/236 | 73.60% | 74.10% | 0.50% | 24-Sep | |
| BS261/237 | 73.48% | 73.40% | -0.08% | 3-Oct | |
| BS261/238 | 73.40% | 73.40% | 0.00% | 2-Oct | |
| BS261/239 | 73.30% | 73.40% | 0.10% | 15-Oct | |
| BS261/240 | 73.35% | 73.00% | -0.35% | 15-Oct | |
| BS261/241 | 73.22% | 73.10% | -0.12% | 17-Oct | |
| BS261/242 | 73.28% | 74.00% | 0.72% | 23-Oct | |
| BS261/243 | 73.25% | 73.80% | 0.55% | 22-Oct | |
| BS261/244 | 73.29% | 73.10% | -0.19% | 7-Nov | |
| BS261/245 | 72.61% | 73.90% | 1.29% | 19-Nov | |
| BS261/246 | 73.15% | 74.00% | 0.85% | 19-Nov | |
| BS261/247 | 73.00% | 73.60% | 0.60% | 20-Nov | |
| BS261/248 | 73.50% | 73.90% | 0.40% | 20-Nov | |
| BS261/249 | 73.10% | 74.10% | 1.00% | 3-Dec | |
| BS261/250 | 73.12% | 73.80% | 0.68% | 4-Dec | |
| BS261/251 | 73.20% | 73.20% | 0.00% | 30-Nov | |
| -0.06% |
Beralt
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Process Map
Stratification
| Data Stratification Tree | ||||
| Questions About Process | Stratification factors | Measurements | ||
| X Variables | ||||
| Can the reconciliation process be eliminated? | ||||
| How can discrepancies be tracked? | Supplier W content | |||
| Is the supplier performing the same analysis to determine tungsten content? | Osram W content | * Discrepancy between W content from supplier, | ||
| How much of a discrepancy would constitute a third party analysis? | Payment based on W content | Third Party W content | Osram and third party by lot. | |
| Can the tungsten concentrate be held if a discrepancy evolves? | (output y1) | Invoice | ||
| Would going to strictly third party analysis resolve the pain in the process? | Credit/Debit Memo | |||
| Could a pre-sample be air shipped to shorten the lead time in determining a discrepancy? | Purchase Order | |||
| Which analysis is more advantageous to use for future contracts? |
DEFINE
MEASURE
Process Improvement Project – Graphing Time Reduction
Mike – MBC 638
Team Launch
5/11/08
Define
5/19/08
Measure
5/26/08
Analyze
6/6/08
Control
On-Going
Improve
7/4/08
Key Dates --->
ANALYZE
IMPROVE
BUSINESS CASE: $18,943 Annual Cost Reduction if Implemented in Engineering Department
Extensive graphing is required for good data analysis of lab qualification testing
350 Engineer hours in the department are spent on repetitive graphing procedures within Excel. This equates to $52,471/year
A 30% reduction in graphing time could result in a $15,741 annual savings.
$
=
Sigma Quality Level
Increased from 1.72
to 3.26
$18,943 annual cost reduction!
$
Eliminated wasteful, repetitive steps that can be automated with Excel Macros
Pareto showed that 80% of graphs consisted of 8 variables or less
95% confidence interval that true graphing time is 57 +/- 5.16 seconds
Hypothesis test indicates 88% confidence that new process meets the goal of at least a 30% improvement in graphing time
Identified Critical Inputs and Outputs to Measure
Measurement Systems Analysis using X-bar, R Charts and Precision-To-Total Ratio
R Charts in control.
Xbar Charts show ability to
measure differences
PTR = 0.22
Control
Maintain Revision Control on original spreadsheet macros
Provide to Engineering Department
Survey engineers for usage in 3 months
*
Chart1
| 1 | 1 | 1 | 1 |
| 2 | 2 | 2 | 2 |
| 3 | 3 | 3 | 3 |
| 4 | 4 | 4 | 4 |
| 5 | 5 | 5 | 5 |
DataStratification
| Data Stratification Tree | ||||||||
| Questions about Process | Output | Stratification Factors | Measurements | |||||
| X | Output | |||||||
| Is y affected by the number of data points recorded in a test? | X1 = Total Data points collected | Number of data points collected | ||||||
| Is y affected by the total number of columns graphed? | Y = Graphing Time = f (X) | Number of different variables measured | ||||||
| Is y affected by the person creating the graphs? | Name of engineer | |||||||
| Is y affected by the quality of the graph required? | Title, labels, presentation ready | |||||||
| Is y affected by additional graphs required for comparison? | Number of graphs | |||||||
| Is y affected by the total number of columns of data available? | Total number of available variables |
Costs
| Cost Reduction | ||
| Current | Improved | |
| Tests/month/engineer | 60 | 60 |
| Tests/year/engineer | 11100 | 11100 |
| Engineers | 4 | 4 |
| Total tests/year | 44400 | 44400 |
| $/hour | 150 | 150 |
| Graphs/test | 1 | 1 |
| Graphs/year | 22200 | 22200 |
| Time per graph (sec) | 57 | 36 |
| Time spent graphing/year (hr) | 350 | 224 |
| Annual Cost Reduction | $ 52,471 | $ 33,529 |
| % Percent Annual Cost Reduction | 36% | |
| $ 15,741.41 |
Initial Data Collection
| Run | Number of Data Points Collected | Total Number of Different Variables Included in Graphs | Total number of available variables | Name of Operator | Title, Labels, Presentation | Number of Graphs | Time (sec) | Time per Graph (sec) | Number of data points collected | ||||||||
| 1 | 308 | 4 | 129 | MB | Yes | 1 | 51 | 51 | Column1 | Number of different variables measured | |||||||
| 2 | 31 | 4 | 160 | MB | Yes | 1 | 58 | 58.0 | Name of engineer | ||||||||
| 3 | 820 | 8 | 160 | MB | Yes | 2 | 158 | 79.0 | Mean | 56.7258064516 | Title, labels, presentation ready | ||||||
| 4 | 31 | 1 | 155 | MB | Yes | 1 | 43 | 43.0 | Standard Error | 2.6336276364 | Number of graphs | ||||||
| 5 | 820 | 7 | 160 | MB | Yes | 1 | 95 | 95.0 | Median | 53 | Total number of available variables | ||||||
| 6 | 760 | 7 | 160 | MB | Yes | 1 | 83 | 83.0 | Mode | 51 | |||||||
| 7 | 61 | 24 | 155 | MB | Yes | 1 | 53 | 53.0 | Standard Deviation | 14.663418099 | |||||||
| 8 | 362 | 4 | 162 | MB | Yes | 1 | 56 | 56.0 | Sample Variance | 215.0158303465 | |||||||
| 9 | 362 | 6 | 162 | MB | Yes | 2 | 109 | 54.5 | Kurtosis | 0.5911961314 | |||||||
| 10 | 482 | 16 | 131 | MB | Yes | 2 | 140 | 70.0 | Skewness | 1.0232211831 | |||||||
| 11 | 308 | 8 | 129 | MB | Yes | 3 | 174 | 58.0 | Range | 57 | |||||||
| 12 | 743 | 3 | 160 | MB | Yes | 1 | 70 | 70.0 | Minimum | 38 | |||||||
| 13 | 30 | 2 | 164 | MB | Yes | 1 | 54 | 54.0 | Maximum | 95 | |||||||
| 14 | 30 | 29 | 164 | MB | Yes | 1 | 69 | 69.0 | Sum | 1758.5 | |||||||
| 15 | 30 | 8 | 125 | MB | Yes | 1 | 43 | 43.0 | Count | 31 | |||||||
| 16 | 31 | 6 | 159 | MB | Yes | 3 | 119 | 39.7 | Confidence Level(95.0%) | 5.3785796423 | |||||||
| 17 | 30 | 3 | 164 | MB | Yes | 1 | 52 | 52.0 | n= | 31 | |||||||
| 18 | 30 | 4 | 168 | MB | Yes | 1 | 67 | 67.0 | x bar (sec) = | 56.7 | 39.7080645161 | ||||||
| 19 | 173 | 6 | 156 | MB | Yes | 2 | 118 | 59.0 | s = | 14.7 | |||||||
| 20 | 30 | 4 | 168 | MB | Yes | 1 | 44 | 44.0 | 1- alpha = | 0.95 | |||||||
| 21 | 31 | 6 | 129 | MB | Yes | 2 | 112 | 56.0 | alpha = | 0.05 | |||||||
| 22 | 143 | 2 | 30 | MB | Yes | 1 | 48 | 48.0 | alpha/2 = | 0.025 | |||||||
| 23 | 31 | 12 | 123 | MB | Yes | 2 | 105 | 52.5 | |||||||||
| 24 | 31 | 13 | 123 | MB | Yes | 2 | 79 | 39.5 | U= | 61.89 | |||||||
| 25 | 362 | 8 | 162 | MB | Yes | 2 | 87 | 43.5 | L= | 51.56 | |||||||
| 26 | 30 | 8 | 168 | MB | Yes | 1 | 51 | 51.0 | 95% Confidence Interval for the true average graphing time | ||||||||
| 27 | 451 | 4 | 218 | MB | Yes | 1 | 88 | 88.0 | 51.56 <= Population Mean <= 61.89 | ||||||||
| 28 | 121 | 6 | 218 | MB | Yes | 3 | 156 | 52.0 | 57 +/- 5.16 seconds | ||||||||
| 29 | 31 | 6 | 218 | MB | Yes | 2 | 105 | 52.5 | |||||||||
| 30 | 175 | 4 | 218 | MB | Yes | 2 | 76 | 38.0 | |||||||||
| 31 | 141 | 13 | 218 | MB | Yes | 3 | 118 | 39.3 | Find SQL | ||||||||
| SQL Baseline | |||||||||||||||||
| Population Mean = | 56.7 | ||||||||||||||||
| Std Deviation = | 14.7 | ||||||||||||||||
| The sample size I chose for my initial baseline estimate of the population statistics was based on time constraints and the Central Limit Theorem. For almost all populations, the sampling distribution of the mean can be approximated closely by a normal d | X2 (Upper Spec Limit) | 60 | |||||||||||||||
| Z2 = | 0.223 | ||||||||||||||||
| P(X>60) = | 0.412 | ||||||||||||||||
| P(X is out of spec) = | 0.412 | ||||||||||||||||
| DPM = | 411655 | ||||||||||||||||
| SQL = | 1.72 | ||||||||||||||||
| Number of Variables | 1 to 4 | 5 to 7 | 8 to 10 | 11 to 13 | >13 | ||||||||||||
| Total | 12.0 | 8.0 | 5.0 | 3.0 | 3.0 | ||||||||||||
| % | 38.7% | 25.8% | 16.1% | 9.7% | 9.7% | ||||||||||||
| Cumul Freq | 38.7% | 64.5% | 80.6% | 90.3% | 100.0% |
Initial Data Collection
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
Process Improved Data
| Run | Number of Data Points Collected | Total Number of Different Variables Included in Graphs | Total number of available variables | Name of Operator | Title, Labels, Presentation | Number of Graphs | Time (sec) | Time per Graph (sec) | |||||||
| Determine Sample Size That would be required | 1 | 308 | 4 | 129 | MB | Yes | 1 | 33 | 33 | ||||||
| 2 | 31 | 4 | 160 | MB | Yes | 1 | 25 | 25.0 | |||||||
| Before process improvement | 3 | 820 | 8 | 160 | MB | Yes | 2 | 54 | 27.0 | ||||||
| U / L = | 86.48 +/- 13.05 | 4 | 31 | 1 | 155 | MB | Yes | 1 | 14 | 14.0 | |||||
| After process Improvement | 5 | 820 | 7 | 160 | MB | Yes | 1 | 54 | 54.0 | ||||||
| Desire 95% confidence interval that produces an interval half width of only 5 seconds | 6 | 760 | 7 | 160 | MB | Yes | 1 | 53 | 53.0 | ||||||
| 7* | 61 | 24 | 155 | MB | Yes | 1 | 53 | 53.0 | |||||||
| Z = | 95% | 8 | 362 | 4 | 162 | MB | Yes | 1 | 29 | 29.0 | |||||
| 1- alpha = | 0.95 | 9 | 362 | 6 | 162 | MB | Yes | 2 | 62 | 31.0 | |||||
| 1- alpha/2 = | 0.975 | 10* | 482 | 16 | 131 | MB | Yes | 2 | 140 | 70.0 | |||||
| Confidence = Z(.975) = | 1.96 | 11 | 308 | 8 | 129 | MB | Yes | 3 | 79 | 26.3 | |||||
| Est Pop Std Deviation = | 13.48 | 12 | 743 | 3 | 160 | MB | Yes | 1 | 35 | 35.0 | |||||
| n = | 28 | 13 | 30 | 2 | 164 | MB | Yes | 1 | 25 | 25.0 | |||||
| 14* | 30 | 29 | 164 | MB | Yes | 1 | 69 | 69.0 | |||||||
| 15 | 30 | 8 | 125 | MB | Yes | 1 | 40 | 40.0 | |||||||
| Column1 | 16 | 31 | 6 | 159 | MB | Yes | 3 | 71 | 23.7 | ||||||
| 17 | 30 | 3 | 164 | MB | Yes | 1 | 34 | 34.0 | |||||||
| Mean | 36.247311828 | 18 | 30 | 4 | 168 | MB | Yes | 1 | 45 | 45.0 | |||||
| Standard Error | 2.4214650296 | 19 | 173 | 6 | 156 | MB | Yes | 2 | 56 | 28.0 | |||||
| Median | 33 | 20 | 30 | 4 | 168 | MB | Yes | 1 | 36 | 36.0 | |||||
| Mode | 25 | 21 | 31 | 6 | 129 | MB | Yes | 2 | 59 | 29.5 | |||||
| Standard Deviation | 13.4821466974 | 22 | 143 | 2 | 30 | MB | Yes | 1 | 22 | 22.0 | |||||
| Sample Variance | 181.7682795699 | 23* | 31 | 12 | 123 | MB | Yes | 2 | 105 | 52.5 | |||||
| Kurtosis | 0.6312076295 | 24* | 31 | 13 | 123 | MB | Yes | 2 | 79 | 39.5 | |||||
| Skewness | 1.003498986 | 25 | 362 | 8 | 162 | MB | Yes | 2 | 69 | 34.5 | |||||
| Range | 56 | 26 | 30 | 8 | 168 | MB | Yes | 1 | 47 | 47.0 | |||||
| Minimum | 14 | 27 | 451 | 4 | 218 | MB | Yes | 1 | 29 | 29.0 | |||||
| Maximum | 70 | 28 | 121 | 6 | 218 | MB | Yes | 3 | 76 | 25.3 | |||||
| Sum | 1123.6666666667 | 29 | 31 | 6 | 218 | MB | Yes | 2 | 61 | 30.5 | |||||
| Count | 31 | 30 | 175 | 4 | 218 | MB | Yes | 2 | 47 | 23.5 | |||||
| Confidence Level(95.0%) | 4.9452862403 | 31* | 141 | 13 | 218 | MB | Yes | 3 | 118 | 39.3 | |||||
| n= | 31 | * Graphs calling for # variables > 8 used previous recorded time. Process fix works on up to 8 variables | |||||||||||||
| x bar = | 36.2 | ||||||||||||||
| s = | 13.5 | ||||||||||||||
| 1- alpha = | 0.95 | ||||||||||||||
| alpha = | 0.05 | ||||||||||||||
| alpha/2 = | 0.025 | ||||||||||||||
| U= | 40.99 | ||||||||||||||
| L= | 31.50 | ||||||||||||||
| 95% Confidence Interval for the true average graphing time | |||||||||||||||
| 31.5 <= Population Mean <= 40.99 | |||||||||||||||
| 36 +/- 4.7 sec | |||||||||||||||
| ` | |||||||||||||||
| SQL Improved Process | |||||||||||||||
| Population Mean = | 36.2 | ||||||||||||||
| Std Deviation = | 13.5 | ||||||||||||||
| X2 (Upper Spec Limit) | 60 | ||||||||||||||
| Z2 = | 1.762 | ||||||||||||||
| P(X>60) = | 0.039 | ||||||||||||||
| P(X is out of spec) = | 0.039 | ||||||||||||||
| DPM = | 39052 | ||||||||||||||
| SQL = | 3.26 |
Hypothesis Testing
| The goal of the project is to reduce the time it takes to create graphs by 30%. This means we want to reduce the estimated population mean from 57 seconds to 40 seconds. This forms the bases of a One-Sided, One-Sample Hypothesis test of the mean. | |||
| H0: mu >= | 40 | ||
| H1: mu < | 40 | ||
| Acceptable Level of Risk= | 10% | ||
| alpha = | 0.10 | ||
| n = | 31 | ||
| New Process Mean = | 36.2 | ||
| New Process Variance = | 181.8 | ||
| Zo = | -1.549759392 | ||
| P = 2* Z() | 0.12 | 0.2423986059 | |
| Confidence = | 87.9% | ||
| Since [P =b24] < [alpha = .10] reject Ho and conclude H1) with (1-b24)*100% confidence. We can be X % confident that the new process has reduced the time it takes to create graphs by 50%. |
Measurement System Analysis
| 1. Establish operational Definitions | ||||||||||||||||||||||||
| An operational definition is a clear concise, unambiguous definition of what time start and stop means. | ||||||||||||||||||||||||
| Start - Time starts when the operator clicks on the spreadsheet to open it. | ||||||||||||||||||||||||
| Stop - Time stops when the closes the file indicating that all graphs are complete. | ||||||||||||||||||||||||
| Completed Graph: A Completed graph includes a title and labeled x and y axis. | ||||||||||||||||||||||||
| 2. Kappa technique to assess Measurement system within the operator | ||||||||||||||||||||||||
| Choose 10 different graphs. Do each graph twice. | ||||||||||||||||||||||||
| Use Kappa technique to assess measurement system capability | Column1 | Day 1 | ||||||||||||||||||||||
| Day 1 | Day 2 | # graphs | variables | Xbar line | UCL | LCL | R bar line | R- UCL | ||||||||||||||||
| Run # | M1 | M2 | xbar | R | M1 | M2 | xbar | R | Mean | 57.1 | 1 | 59.1 | 66.2 | 52.0 | 3.8 | 12.4 | ||||||||
| 1 | 36.0 | 34.0 | 35.0 | 2.0 | 34.0 | 33.0 | 33.5 | 1.0 | 1 | 2 | Standard Error | 4.6111421122 | 2 | 59.1 | 66.2 | 52.0 | 3.8 | 12.4 | ||||||
| 2 | 59.0 | 60.0 | 59.5 | 1.0 | 56.0 | 58.0 | 57.0 | 2.0 | 2 | 4 | Median | 58 | 3 | 59.1 | 66.2 | 52.0 | 3.8 | 12.4 | ||||||
| 3 | 96.0 | 90.0 | 93.0 | 6.0 | 87.0 | 93.0 | 90.0 | 6.0 | 3 | 8 | Mode | 58 | 4 | 59.1 | 66.2 | 52.0 | 3.8 | 12.4 | ||||||
| 4 | 48.0 | 45.0 | 46.5 | 3.0 | 37.0 | 35.0 | 36.0 | 2.0 | 1 | 4 | Standard Deviation | 20.6216544336 | 5 | 59.1 | 66.2 | 52.0 | 3.8 | 12.4 | ||||||
| 5 | 58.0 | 65.0 | 61.5 | 7.0 | 60.0 | 58.0 | 59.0 | 2.0 | 2 | 6 | Sample Variance | 425.2526315789 | ||||||||||||
| Xbar2 = | 59.1 | Xbar2 = | 55.1 | Kurtosis | -0.5588580019 | |||||||||||||||||||
| Rbar = | 3.8 | Rbar = | 2.6 | Skewness | 0.657122154 | Day 2 | ||||||||||||||||||
| Range | 63 | Xbar line | UCL | LCL | R bar line | R -UCL | ||||||||||||||||||
| Xbar UCL | 66.2 | Xbar UCL | 60.0 | Minimum | 33 | 1 | 55.1 | 60.0 | 50.2 | 2.6 | 8.5 | |||||||||||||
| Xbar LCL | 52.0 | Xbar LCL | 50.2 | Maximum | 2 | 55.1 | 60.0 | 50.2 | 2.6 | 8.5 | ||||||||||||||
| R UCL | 12.426 | R UCL | 8.502 | Sum | 1142 | 3 | 55.1 | 60.0 | 50.2 | 2.6 | 8.5 | |||||||||||||
| R LCL | 0 | R LCL | 0 | Count | 20 | 4 | 55.1 | 60.0 | 50.2 | 2.6 | 8.5 | |||||||||||||
| Confidence Level(95.0%) | 9.6512343576 | 5 | 55.1 | 60.0 | 50.2 | 2.6 | 8.5 | |||||||||||||||||
| Average of Average Ranges = | 3.20 | 0.22 > 0.10, measurement system not capable? Need to explore why. | ||||||||||||||||||||||
| Repeatability Std Deviation= | 2.83 | |||||||||||||||||||||||
| Reproducibility Std Deviation= | 3.54 | |||||||||||||||||||||||
| Measurement Variance= | 20.55 | |||||||||||||||||||||||
| Measurement Std Dev = | 4.53 | |||||||||||||||||||||||
| Total Variance (All 20 Meas.)= | 425.25 | |||||||||||||||||||||||
| Total Standard Deviation = | 20.62 | |||||||||||||||||||||||
| Precision to Total Ratio = Measurement Std Dev / Total Std Dev = | 0.22 | |||||||||||||||||||||||
| A Rule of thumb used to determine if the measurement system is capable is to see if the precision to total ratio is less than 10%. In this case, 0.27 is greater than .10, so the measurement system is a little out of control. Sigma reproducibility is the | ||||||||||||||||||||||||
| R charts are in control both days, but on Day 1 I exhibited more repeatability variability as evidenced by an average range of 5.2 vs a range of 2.8 on Day 2. Possible reasons might be that on day 2 I had made the graphs before and was more familiar wher |
Measurement System Analysis
Data Stratification Tree
Questions About Process
Stratification factors
X Variables
Measurements
Handicap Index
Ball (Titleist, Nike)
Putter (Titleist, Callaway)
Tempo (Normal, Slow)
(ULTIMATE
Output Y
1
)
Does Tempo impact my performance?
Does equipment impact my performance on
putting green and consequently my USGA
handicap index?
Stance (Open like Jack N., Normal)
FiskarRuler
Does my stance affect the putting result?
•# of feet to hole
What % of my putts are within 2 feet?
Does music (sounds) impact
performance on the putting green?
Does the distance from the hole matter?
Will randomization show different results?
Is there variability in the measurement?
What is the average distance from the hole from
10, 20 and 40 feet?
Measuring Tape
•# of inches from hole after putt
•Measure variation with music, tempo,
stance from each distance
•% of putts within 2 feet
•repeatability
•reproducibility
•average distance from 10 feet
•Average distance from 20 feet
•Average distance from 40 feet
Putter and ball combination?
Music (On, None)
•Average change in inches further from hole
Is there a financial impact on the result?
Handicap Index as Measure
•Compare USGA index before and after
Inches from Hole
(Output Y
2
)
Percentage
Within 2 feet
(from 20 feet
And further)
Percentage
Of putts made
(from 10 feet and
Closer)
(Output Y
3
)
(Output Y
4
)
HOW DO I IMPROVE MY GOLF GAME
AND LOWER MY HANDICAP?
Questions about ProcessOutputStratification FactorsMeasurements
X
Is y affected by the number of
data points recorded in a test?
X1 = Total Data points collectedNumber of data points collected
Is y affected by the total number
of columns graphed?
X
2
= Variables included in graphNumber of different variables measured
Is y affected by the person
creating the graphs?
X
3
= OperatorName of engineer
Is y affected by the quality of the
graph required?
X
4
= Graph qualityTitle, labels, presentation ready
Is y affected by additional graphs
required for comparison?
X
5
= Number of graphsNumber of graphs
Is y affected by the total number
of columns of data available?
X
6
= Total number of available variablesTotal number of available variables
Data Stratification Tree
Y = Graphing Time = f (X)
Y = f(X
1
,X
2
,X
3
,X
4
,X
5
,X
6
)
Questions about ProcessOutputStratification FactorsMeasurements
X
Is y affected by the number of
data points recorded in a test?
X1 = Total Data points
collected
Number of data points
collected
Is y affected by the total number
of columns graphed?
X
2
= Variables included in
graph
Number of different
variables measured
Is y affected by the person
creating the graphs?
X
3
= OperatorName of engineer
Is y affected by the quality of the
graph required?
X
4
= Graph quality
Title, labels,
presentation ready
Is y affected by additional graphs
required for comparison?
X
5
= Number of graphsNumber of graphs
Is y affected by the total number
of columns of data available?
X
6
= Total number of
available variables
Total number of
available variables
Data Stratification Tree
Y =
Graphing
Time =
f (X)
Y = f(X
1
,X
2
,X
3
,X
4
,X
5
,X
6
)
Chart2
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 3 | 3 | 3 |
| 4 | 4 | 4 |
| 5 | 5 | 5 |
DataStratification
| Data Stratification Tree | ||||||||
| Questions about Process | Output | Stratification Factors | Measurements | |||||
| X | Output | |||||||
| Is y affected by the number of data points recorded in a test? | X1 = Total Data points collected | Number of data points collected | ||||||
| Is y affected by the total number of columns graphed? | Y = Graphing Time = f (X) | Number of different variables measured | ||||||
| Is y affected by the person creating the graphs? | Name of engineer | |||||||
| Is y affected by the quality of the graph required? | Title, labels, presentation ready | |||||||
| Is y affected by additional graphs required for comparison? | Number of graphs | |||||||
| Is y affected by the total number of columns of data available? | Total number of available variables |
Costs
| Cost Reduction | ||
| Current | Improved | |
| Tests/month/engineer | 60 | 60 |
| Tests/year/engineer | 11100 | 11100 |
| Engineers | 4 | 4 |
| Total tests/year | 44400 | 44400 |
| $/hour | 150 | 150 |
| Graphs/test | 1 | 1 |
| Graphs/year | 22200 | 22200 |
| Time per graph (sec) | 57 | 36 |
| Time spent graphing/year (hr) | 350 | 224 |
| Annual Cost Reduction | $ 52,471 | $ 33,529 |
| % Percent Annual Cost Reduction | 36% | |
| $ 15,741.41 |
Initial Data Collection
| Run | Number of Data Points Collected | Total Number of Different Variables Included in Graphs | Total number of available variables | Name of Operator | Title, Labels, Presentation | Number of Graphs | Time (sec) | Time per Graph (sec) | Number of data points collected | ||||||||
| 1 | 308 | 4 | 129 | MB | Yes | 1 | 51 | 51 | Column1 | Number of different variables measured | |||||||
| 2 | 31 | 4 | 160 | MB | Yes | 1 | 58 | 58.0 | Name of engineer | ||||||||
| 3 | 820 | 8 | 160 | MB | Yes | 2 | 158 | 79.0 | Mean | 56.7258064516 | Title, labels, presentation ready | ||||||
| 4 | 31 | 1 | 155 | MB | Yes | 1 | 43 | 43.0 | Standard Error | 2.6336276364 | Number of graphs | ||||||
| 5 | 820 | 7 | 160 | MB | Yes | 1 | 95 | 95.0 | Median | 53 | Total number of available variables | ||||||
| 6 | 760 | 7 | 160 | MB | Yes | 1 | 83 | 83.0 | Mode | 51 | |||||||
| 7 | 61 | 24 | 155 | MB | Yes | 1 | 53 | 53.0 | Standard Deviation | 14.663418099 | |||||||
| 8 | 362 | 4 | 162 | MB | Yes | 1 | 56 | 56.0 | Sample Variance | 215.0158303465 | |||||||
| 9 | 362 | 6 | 162 | MB | Yes | 2 | 109 | 54.5 | Kurtosis | 0.5911961314 | |||||||
| 10 | 482 | 16 | 131 | MB | Yes | 2 | 140 | 70.0 | Skewness | 1.0232211831 | |||||||
| 11 | 308 | 8 | 129 | MB | Yes | 3 | 174 | 58.0 | Range | 57 | |||||||
| 12 | 743 | 3 | 160 | MB | Yes | 1 | 70 | 70.0 | Minimum | 38 | |||||||
| 13 | 30 | 2 | 164 | MB | Yes | 1 | 54 | 54.0 | Maximum | 95 | |||||||
| 14 | 30 | 29 | 164 | MB | Yes | 1 | 69 | 69.0 | Sum | 1758.5 | |||||||
| 15 | 30 | 8 | 125 | MB | Yes | 1 | 43 | 43.0 | Count | 31 | |||||||
| 16 | 31 | 6 | 159 | MB | Yes | 3 | 119 | 39.7 | Confidence Level(95.0%) | 5.3785796423 | |||||||
| 17 | 30 | 3 | 164 | MB | Yes | 1 | 52 | 52.0 | n= | 31 | |||||||
| 18 | 30 | 4 | 168 | MB | Yes | 1 | 67 | 67.0 | x bar (sec) = | 56.7 | 39.7080645161 | ||||||
| 19 | 173 | 6 | 156 | MB | Yes | 2 | 118 | 59.0 | s = | 14.7 | |||||||
| 20 | 30 | 4 | 168 | MB | Yes | 1 | 44 | 44.0 | 1- alpha = | 0.95 | |||||||
| 21 | 31 | 6 | 129 | MB | Yes | 2 | 112 | 56.0 | alpha = | 0.05 | |||||||
| 22 | 143 | 2 | 30 | MB | Yes | 1 | 48 | 48.0 | alpha/2 = | 0.025 | |||||||
| 23 | 31 | 12 | 123 | MB | Yes | 2 | 105 | 52.5 | |||||||||
| 24 | 31 | 13 | 123 | MB | Yes | 2 | 79 | 39.5 | U= | 61.89 | |||||||
| 25 | 362 | 8 | 162 | MB | Yes | 2 | 87 | 43.5 | L= | 51.56 | |||||||
| 26 | 30 | 8 | 168 | MB | Yes | 1 | 51 | 51.0 | 95% Confidence Interval for the true average graphing time | ||||||||
| 27 | 451 | 4 | 218 | MB | Yes | 1 | 88 | 88.0 | 51.56 <= Population Mean <= 61.89 | ||||||||
| 28 | 121 | 6 | 218 | MB | Yes | 3 | 156 | 52.0 | 57 +/- 5.16 seconds | ||||||||
| 29 | 31 | 6 | 218 | MB | Yes | 2 | 105 | 52.5 | |||||||||
| 30 | 175 | 4 | 218 | MB | Yes | 2 | 76 | 38.0 | |||||||||
| 31 | 141 | 13 | 218 | MB | Yes | 3 | 118 | 39.3 | Find SQL | ||||||||
| SQL Baseline | |||||||||||||||||
| Population Mean = | 56.7 | ||||||||||||||||
| Std Deviation = | 14.7 | ||||||||||||||||
| The sample size I chose for my initial baseline estimate of the population statistics was based on time constraints and the Central Limit Theorem. For almost all populations, the sampling distribution of the mean can be approximated closely by a normal d | X2 (Upper Spec Limit) | 60 | |||||||||||||||
| Z2 = | 0.223 | ||||||||||||||||
| P(X>60) = | 0.412 | ||||||||||||||||
| P(X is out of spec) = | 0.412 | ||||||||||||||||
| DPM = | 411655 | ||||||||||||||||
| SQL = | 1.72 | ||||||||||||||||
| Number of Variables | 1 to 4 | 5 to 7 | 8 to 10 | 11 to 13 | >13 | ||||||||||||
| Total | 12.0 | 8.0 | 5.0 | 3.0 | 3.0 | ||||||||||||
| % | 38.7% | 25.8% | 16.1% | 9.7% | 9.7% | ||||||||||||
| Cumul Freq | 38.7% | 64.5% | 80.6% | 90.3% | 100.0% |
Initial Data Collection
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
Process Improved Data
| Run | Number of Data Points Collected | Total Number of Different Variables Included in Graphs | Total number of available variables | Name of Operator | Title, Labels, Presentation | Number of Graphs | Time (sec) | Time per Graph (sec) | |||||||
| Determine Sample Size That would be required | 1 | 308 | 4 | 129 | MB | Yes | 1 | 33 | 33 | ||||||
| 2 | 31 | 4 | 160 | MB | Yes | 1 | 25 | 25.0 | |||||||
| Before process improvement | 3 | 820 | 8 | 160 | MB | Yes | 2 | 54 | 27.0 | ||||||
| U / L = | 86.48 +/- 13.05 | 4 | 31 | 1 | 155 | MB | Yes | 1 | 14 | 14.0 | |||||
| After process Improvement | 5 | 820 | 7 | 160 | MB | Yes | 1 | 54 | 54.0 | ||||||
| Desire 95% confidence interval that produces an interval half width of only 5 seconds | 6 | 760 | 7 | 160 | MB | Yes | 1 | 53 | 53.0 | ||||||
| 7* | 61 | 24 | 155 | MB | Yes | 1 | 53 | 53.0 | |||||||
| Z = | 95% | 8 | 362 | 4 | 162 | MB | Yes | 1 | 29 | 29.0 | |||||
| 1- alpha = | 0.95 | 9 | 362 | 6 | 162 | MB | Yes | 2 | 62 | 31.0 | |||||
| 1- alpha/2 = | 0.975 | 10* | 482 | 16 | 131 | MB | Yes | 2 | 140 | 70.0 | |||||
| Confidence = Z(.975) = | 1.96 | 11 | 308 | 8 | 129 | MB | Yes | 3 | 79 | 26.3 | |||||
| Est Pop Std Deviation = | 13.48 | 12 | 743 | 3 | 160 | MB | Yes | 1 | 35 | 35.0 | |||||
| n = | 28 | 13 | 30 | 2 | 164 | MB | Yes | 1 | 25 | 25.0 | |||||
| 14* | 30 | 29 | 164 | MB | Yes | 1 | 69 | 69.0 | |||||||
| 15 | 30 | 8 | 125 | MB | Yes | 1 | 40 | 40.0 | |||||||
| Column1 | 16 | 31 | 6 | 159 | MB | Yes | 3 | 71 | 23.7 | ||||||
| 17 | 30 | 3 | 164 | MB | Yes | 1 | 34 | 34.0 | |||||||
| Mean | 36.247311828 | 18 | 30 | 4 | 168 | MB | Yes | 1 | 45 | 45.0 | |||||
| Standard Error | 2.4214650296 | 19 | 173 | 6 | 156 | MB | Yes | 2 | 56 | 28.0 | |||||
| Median | 33 | 20 | 30 | 4 | 168 | MB | Yes | 1 | 36 | 36.0 | |||||
| Mode | 25 | 21 | 31 | 6 | 129 | MB | Yes | 2 | 59 | 29.5 | |||||
| Standard Deviation | 13.4821466974 | 22 | 143 | 2 | 30 | MB | Yes | 1 | 22 | 22.0 | |||||
| Sample Variance | 181.7682795699 | 23* | 31 | 12 | 123 | MB | Yes | 2 | 105 | 52.5 | |||||
| Kurtosis | 0.6312076295 | 24* | 31 | 13 | 123 | MB | Yes | 2 | 79 | 39.5 | |||||
| Skewness | 1.003498986 | 25 | 362 | 8 | 162 | MB | Yes | 2 | 69 | 34.5 | |||||
| Range | 56 | 26 | 30 | 8 | 168 | MB | Yes | 1 | 47 | 47.0 | |||||
| Minimum | 14 | 27 | 451 | 4 | 218 | MB | Yes | 1 | 29 | 29.0 | |||||
| Maximum | 70 | 28 | 121 | 6 | 218 | MB | Yes | 3 | 76 | 25.3 | |||||
| Sum | 1123.6666666667 | 29 | 31 | 6 | 218 | MB | Yes | 2 | 61 | 30.5 | |||||
| Count | 31 | 30 | 175 | 4 | 218 | MB | Yes | 2 | 47 | 23.5 | |||||
| Confidence Level(95.0%) | 4.9452862403 | 31* | 141 | 13 | 218 | MB | Yes | 3 | 118 | 39.3 | |||||
| n= | 31 | * Graphs calling for # variables > 8 used previous recorded time. Process fix works on up to 8 variables | |||||||||||||
| x bar = | 36.2 | ||||||||||||||
| s = | 13.5 | ||||||||||||||
| 1- alpha = | 0.95 | ||||||||||||||
| alpha = | 0.05 | ||||||||||||||
| alpha/2 = | 0.025 | ||||||||||||||
| U= | 40.99 | ||||||||||||||
| L= | 31.50 | ||||||||||||||
| 95% Confidence Interval for the true average graphing time | |||||||||||||||
| 31.5 <= Population Mean <= 40.99 | |||||||||||||||
| 36 +/- 4.7 sec | |||||||||||||||
| ` | |||||||||||||||
| SQL Improved Process | |||||||||||||||
| Population Mean = | 36.2 | ||||||||||||||
| Std Deviation = | 13.5 | ||||||||||||||
| X2 (Upper Spec Limit) | 60 | ||||||||||||||
| Z2 = | 1.762 | ||||||||||||||
| P(X>60) = | 0.039 | ||||||||||||||
| P(X is out of spec) = | 0.039 | ||||||||||||||
| DPM = | 39052 | ||||||||||||||
| SQL = | 3.26 |
Hypothesis Testing
| The goal of the project is to reduce the time it takes to create graphs by 30%. This means we want to reduce the estimated population mean from 57 seconds to 40 seconds. This forms the bases of a One-Sided, One-Sample Hypothesis test of the mean. | |||
| H0: mu >= | 40 | ||
| H1: mu < | 40 | ||
| Acceptable Level of Risk= | 10% | ||
| alpha = | 0.10 | ||
| n = | 31 | ||
| New Process Mean = | 36.2 | ||
| New Process Variance = | 181.8 | ||
| Zo = | -1.549759392 | ||
| P = 2* Z() | 0.12 | 0.2423986059 | |
| Confidence = | 87.9% | ||
| Since [P =b24] < [alpha = .10] reject Ho and conclude H1) with (1-b24)*100% confidence. We can be X % confident that the new process has reduced the time it takes to create graphs by 50%. |
Measurement System Analysis
| 1. Establish operational Definitions | ||||||||||||||||||||||||
| An operational definition is a clear concise, unambiguous definition of what time start and stop means. | ||||||||||||||||||||||||
| Start - Time starts when the operator clicks on the spreadsheet to open it. | ||||||||||||||||||||||||
| Stop - Time stops when the closes the file indicating that all graphs are complete. | ||||||||||||||||||||||||
| Completed Graph: A Completed graph includes a title and labeled x and y axis. | ||||||||||||||||||||||||
| 2. Kappa technique to assess Measurement system within the operator | ||||||||||||||||||||||||
| Choose 10 different graphs. Do each graph twice. | ||||||||||||||||||||||||
| Use Kappa technique to assess measurement system capability | Column1 | Day 1 | ||||||||||||||||||||||
| Day 1 | Day 2 | # graphs | variables | Xbar line | UCL | LCL | R bar line | R- UCL | ||||||||||||||||
| Run # | M1 | M2 | xbar | R | M1 | M2 | xbar | R | Mean | 57.1 | 1 | 59.1 | 66.2 | 52.0 | 3.8 | 12.4 | ||||||||
| 1 | 36.0 | 34.0 | 35.0 | 2.0 | 34.0 | 33.0 | 33.5 | 1.0 | 1 | 2 | Standard Error | 4.6111421122 | 2 | 59.1 | 66.2 | 52.0 | 3.8 | 12.4 | ||||||
| 2 | 59.0 | 60.0 | 59.5 | 1.0 | 56.0 | 58.0 | 57.0 | 2.0 | 2 | 4 | Median | 58 | 3 | 59.1 | 66.2 | 52.0 | 3.8 | 12.4 | ||||||
| 3 | 96.0 | 90.0 | 93.0 | 6.0 | 87.0 | 93.0 | 90.0 | 6.0 | 3 | 8 | Mode | 58 | 4 | 59.1 | 66.2 | 52.0 | 3.8 | 12.4 | ||||||
| 4 | 48.0 | 45.0 | 46.5 | 3.0 | 37.0 | 35.0 | 36.0 | 2.0 | 1 | 4 | Standard Deviation | 20.6216544336 | 5 | 59.1 | 66.2 | 52.0 | 3.8 | 12.4 | ||||||
| 5 | 58.0 | 65.0 | 61.5 | 7.0 | 60.0 | 58.0 | 59.0 | 2.0 | 2 | 6 | Sample Variance | 425.2526315789 | ||||||||||||
| Xbar2 = | 59.1 | Xbar2 = | 55.1 | Kurtosis | -0.5588580019 | |||||||||||||||||||
| Rbar = | 3.8 | Rbar = | 2.6 | Skewness | 0.657122154 | Day 2 | ||||||||||||||||||
| Range | 63 | Xbar line | UCL | LCL | R bar line | R -UCL | ||||||||||||||||||
| Xbar UCL | 66.2 | Xbar UCL | 60.0 | Minimum | 33 | 1 | 55.1 | 60.0 | 50.2 | 2.6 | 8.5 | |||||||||||||
| Xbar LCL | 52.0 | Xbar LCL | 50.2 | Maximum | 2 | 55.1 | 60.0 | 50.2 | 2.6 | 8.5 | ||||||||||||||
| R UCL | 12.426 | R UCL | 8.502 | Sum | 1142 | 3 | 55.1 | 60.0 | 50.2 | 2.6 | 8.5 | |||||||||||||
| R LCL | 0 | R LCL | 0 | Count | 20 | 4 | 55.1 | 60.0 | 50.2 | 2.6 | 8.5 | |||||||||||||
| Confidence Level(95.0%) | 9.6512343576 | 5 | 55.1 | 60.0 | 50.2 | 2.6 | 8.5 | |||||||||||||||||
| Average of Average Ranges = | 3.20 | 0.22 > 0.10, measurement system not capable? Need to explore why. | ||||||||||||||||||||||
| Repeatability Std Deviation= | 2.83 | |||||||||||||||||||||||
| Reproducibility Std Deviation= | 3.54 | |||||||||||||||||||||||
| Measurement Variance= | 20.55 | |||||||||||||||||||||||
| Measurement Std Dev = | 4.53 | |||||||||||||||||||||||
| Total Variance (All 20 Meas.)= | 425.25 | |||||||||||||||||||||||
| Total Standard Deviation = | 20.62 | |||||||||||||||||||||||
| Precision to Total Ratio = Measurement Std Dev / Total Std Dev = | 0.22 | |||||||||||||||||||||||
| A Rule of thumb used to determine if the measurement system is capable is to see if the precision to total ratio is less than 10%. In this case, 0.27 is greater than .10, so the measurement system is a little out of control. Sigma reproducibility is the | ||||||||||||||||||||||||
| R charts are in control both days, but on Day 1 I exhibited more repeatability variability as evidenced by an average range of 5.2 vs a range of 2.8 on Day 2. Possible reasons might be that on day 2 I had made the graphs before and was more familiar wher |
Measurement System Analysis
Data Stratification Tree
Questions About Process
Stratification factors
X Variables
Measurements
Handicap Index
Ball (Titleist, Nike)
Putter (Titleist, Callaway)
Tempo (Normal, Slow)
(ULTIMATE
Output Y
1
)
Does Tempo impact my performance?
Does equipment impact my performance on
putting green and consequently my USGA
handicap index?
Stance (Open like Jack N., Normal)
FiskarRuler
Does my stance affect the putting result?
•# of feet to hole
What % of my putts are within 2 feet?
Does music (sounds) impact
performance on the putting green?
Does the distance from the hole matter?
Will randomization show different results?
Is there variability in the measurement?
What is the average distance from the hole from
10, 20 and 40 feet?
Measuring Tape
•# of inches from hole after putt
•Measure variation with music, tempo,
stance from each distance
•% of putts within 2 feet
•repeatability
•reproducibility
•average distance from 10 feet
•Average distance from 20 feet
•Average distance from 40 feet
Putter and ball combination?
Music (On, None)
•Average change in inches further from hole
Is there a financial impact on the result?
Handicap Index as Measure
•Compare USGA index before and after
Inches from Hole
(Output Y
2
)
Percentage
Within 2 feet
(from 20 feet
And further)
Percentage
Of putts made
(from 10 feet and
Closer)
(Output Y
3
)
(Output Y
4
)
HOW DO I IMPROVE MY GOLF GAME
AND LOWER MY HANDICAP?
Questions about ProcessOutputStratification FactorsMeasurements
X
Is y affected by the number of
data points recorded in a test?
X1 = Total Data points collectedNumber of data points collected
Is y affected by the total number
of columns graphed?
X
2
= Variables included in graphNumber of different variables measured
Is y affected by the person
creating the graphs?
X
3
= OperatorName of engineer
Is y affected by the quality of the
graph required?
X
4
= Graph qualityTitle, labels, presentation ready
Is y affected by additional graphs
required for comparison?
X
5
= Number of graphsNumber of graphs
Is y affected by the total number
of columns of data available?
X
6
= Total number of available variablesTotal number of available variables
Data Stratification Tree
Y = Graphing Time = f (X)
Y = f(X
1
,X
2
,X
3
,X
4
,X
5
,X
6
)
Questions about ProcessOutputStratification FactorsMeasurements
X
Is y affected by the number of
data points recorded in a test?
X1 = Total Data points
collected
Number of data points
collected
Is y affected by the total number
of columns graphed?
X
2
= Variables included in
graph
Number of different
variables measured
Is y affected by the person
creating the graphs?
X
3
= OperatorName of engineer
Is y affected by the quality of the
graph required?
X
4
= Graph quality
Title, labels,
presentation ready
Is y affected by additional graphs
required for comparison?
X
5
= Number of graphsNumber of graphs
Is y affected by the total number
of columns of data available?
X
6
= Total number of
available variables
Total number of
available variables
Data Stratification Tree
Y =
Graphing
Time =
f (X)
Y = f(X
1
,X
2
,X
3
,X
4
,X
5
,X
6
)
DEFINE
MEASURE
Team Launch:
Define:
Measure:
Analyze:
Control:
Improve:
Key Dates
ANALYZE
IMPROVE
Process owner: Landon
CONTROL
September 10
September 17
September 24
October 29
November 19
Landon, Engineering Project Managers, Finance Office, Stakeholders
September 6
Problem Statement
Cycle time for a signature sheet averaged 11.25 days with each project manger spending about 11.25 hours for each purchase over $100,000.
Business Impact
The average wage a project manager earns is $35/hr, therefore it costs $393.75 per project in just gathering signatures! At 144 projects a year this process costs $56,700 annually.
- Finance Office will not accept old version of signature sheet.
- Purchases tracked in SharePoint
- Appraisal rated on compliance
High man-hours
High cycle time
Too many steps!
Need to take PM out of all these steps
Cycle time reduced to 2.88 days!
Man-hours reduced to 0.20 hours!
Cost savings $55,692 annually!
SQL raised from 2.3 to 3.6 and rising!
SQL = 2.3
Hypothesis Test
Ho: mu ≥ 11.25 hr Ha: mu < 11.25 hr
P-value ≈ 0
Electronic Signature Sheet
No
No
Project manager signs form
Obtain engineering supervisor’s signature
Submit to Finance
Obtain production supervisor’s signature
Obtain engineering director’s signature
Obtain group director’s signature
Submit form to Finance Department
Wait for Thursday
Obtain finance supervisor’s signature
Is it Thursday?
Is project over $100,000?
*
DEFINE – 5/15/11
MEASURE - 6/1/11
Finding the Skinny on Thin Film Sensor Reject Rates
Control
Improve
ANALYZE - 7/1/11
IMPROVE - 8/1/11
1) Problem Statement:
Production reject rate of thin film sensors increases after process change.
3) Business Impact:
Reducing/eliminating frequency rejects will prevent reworking of part, extra inventory and labor from 100% testing which could potentially save
The r2 shows that the amount of raw material used from Vendor A explains 46.6 % of the change in reject rate.
8) Probable Cause 2 – Evaporation Fixture Geometry
7) Probable Cause 1 - Raw Material Supply
The sensors are held in a fixture positioned over a evaporation source that coats them with metal. I performed a test run to measure baseline performance. The data revealed that the metallic coating has too much variation in thickness w/ a mean of 2235 Å, but the range should be 500 Å. This could be caused by the position of the source, size of mask or angle of the holding fixture.
2) Work on largest category of defect for MAXIUM IMPACT
Before
After
4) Out-of-Control:
Process is highly variable to begin w/ but much worse after change.
DPMO of 31,934,Ouch!
5) Change of Focus
The change did cause an increase in variability, but the process is not very good to start w/ a DPMO of 19,263! Finding the root cause of the inherent process variability should solve the new issue.
6) Identify Primary Inputs (Y)
Separated wheat from chaff
A second run was done to test if a centered evaporation source would decrease thickness variability (Ha). A
one-tail test was performed & the P value was high,
thus it did not significantly improve the process. This points to the mask size & fixture as the root cause of
the variation.
Z=
Z = -1.19 P = 1-Z = 1-1.19 =0.86 =86%
=
Ho: Test 1 thickness variability ≤ Test 2
- Receipt of material from Vendor A
was halted. A comparison of their measurements vs. ours found a 7.6 KHz difference!
They recalibrated their instruments & next shipment was markedly improved with a mean very close to the center of our specification range of 6.055 as shown on this histogram.
9) Solution to Probable Cause 1
10) Solution to Probable Cause 2
I’m working with engineering to
develop a new fixture that will
improve the geometry.
Scatter plot reveals that using raw materials from Vendor A has a strong positive correlation of 0.7 with the reject rate.
Constructing a control chart of measurements taken by QC of frequency illustrates that the vendors process is out of control.
10) Changes to be Made:
QC technician does acceptance testing of raw materials w/ zero tolerance.
Vendor supplies Certificate of Analysis w/ test statistics.
Control chart created for raw materials.
New fixture for more uniform thickness to prevent any frequency rejects.
Control – 8/8/11
Box Plot
Pareto Chart
C&E Matrix
Control Chart
Scatter Plot
Hypothesis Test
Histogram
Rick, Steve & Production Staff
| Cause & Effect Matrix | ||||
| Scoring:1=low, 3 = med, 5=high, Importance to Customer (sensors w/ correct frequency) = 1 | ||||
| Process Inputs (X) | Effect | Rating | Probability | Score |
| Vendor frequency sorting quality | Allow accurate calculation of thickness | 5 | High, makes adjustments when providing thickness data to techs | 25 |
| Fixture Geometry | Even coating thickness | 5 | High, location determines the thickness of the coating. | 25 |
34
35
36
Invoice Cost Increase
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
Jun-07Jul-07Aug-07
Invoice Cost
Invoice (X)
Mean
UNPL
LNPL
Page Views Increase
8,000,000
9,000,000
10,000,000
11,000,000
12,000,000
13,000,000
14,000,000
15,000,000
16,000,000
17,000,000
18,000,000
May-07Jun-07Jul-07
Pageviews
Mean
UNPL
LNPL
Invoice Cost After Improvement
$9,500
$9,700
$9,900
$10,100
$10,300
$10,500
$10,700
$10,900
$11,100
$11,300
$11,500
Aug-07
Sep-07
Oct-07
Number of Complete Applications
5
7
888
7
9
1111
12
1313
14
0
5
10
15
Jul, 2006
Sept
Nov
Jan
Mar
May
Jul, 2007
Date
Number
Series1
Linear (Series1)
Time to Complete Proccess Cycle
28
33
38
43
48
53
58
Jul-06AugSeptOct NovDecJanFebMarchAprilMayJuneJul-07
Date/Time/Period
Time (Days)
Data 1
Median
Goal
Total Application Errors by Type
132
21
14
9
75.0%
86.9%
94.9%
0
20
40
60
80
100
120
140
160
Incomplete/Incorrect ApplicationsStalled Approvals In The Log-in
Phase,
Stalled Approval At The
Managerial Level
Reworks
Type
Defects
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
Base Group
62.06UCL
42.50CL
22.94LCL
16
21
26
31
36
41
46
51
56
61
66
16111621263136414651566166717681869196101106111116121126
Units
Cycle Time- Days
New "Improved" Process
UCL 44.59
CL 28.56
LCL 12.53
7
12
17
22
27
32
37
42
47
12345678910111213141516171819202122232425
Units
Cycle Time
Beralt - OSI Ore Comparison
69.50%
70.00%
70.50%
71.00%
71.50%
72.00%
72.50%
73.00%
73.50%
74.00%
74.50%
BS261/191
BS261/195
BS261/199
BS261/203
BS261/207
BS261/211
BS261/215
BS261/219
BS261/223
BS261/227
BS261/231
BS261/235
BS261/239
BS261/243
BS261/247
BS261/251
Beralt
OSI
Tungsten Ore Suppliers FY08
0
20
40
60
80
100
120
140
Beralt
DLA
Spot
CantungDynacor
Heemskirk
KMT
Other
STUs
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
STUs
Cumulative %
Questions about Process
Output
Stratification Factors
Measurements
X
Is y affected by the number of
data points recorded in a test?
X1 = Total Data points
collected
Number of data points
collected
Is y affected by the total number
of columns graphed?
X
2
= Variables included in
graph
Number of different
variables measured
Is y affected by the person
creating the graphs?
X
3
= Operator
Name of engineer
Is y affected by the quality of the
graph required?
X
4
= Graph quality
Title, labels,
presentation ready
Is y affected by additional graphs
required for comparison?
X
5
= Number of graphs
Number of graphs
Is y affected by the total number
of columns of data available?
X
6
= Total number of
available variables
Total number of
available variables
Data Stratification Tree
Y =
Graphing
Time =
f (X)
Y = f(X
1
,X
2
,X
3
,X
4
,X
5
,X
6
)
Day 1/Operator 1 - Xbar Chart
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
0123456
Run #
Xbar
Day 1/Operator 1 - R Chart
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
0123456
Run #
R
Pareto Diagram of Number of Variables Graphed
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
1 to 4
5 to 7
8 to 10
11 to 13
>13
Number Variables
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
Cumulative Frequency
Current
Improved
Time per graph (sec)
57
36
Time spent
graphing/year (hr)
350
224
Annual Cost Reduction
52,471
$
33,529
$
% Percent Annual Cost
Reduction
Cost Reduction
36%
Population Mean =
56.7
Std Deviation =
14.7
X2 (Upper Spec Limit)
60
Z2 =
0.223
P(X>60) =
0.412
P(X is out of spec) =
0.412
DPM =
411655
SQL =
1.72
SQL Baseline
Population Mean =
36.2
Std Deviation =
13.5
X2 (Upper Spec Limit)
60
Z2 =
1.762
P(X>60) =
0.039
P(X is out of spec) =
0.039
DPM =
39052
SQL =
3.26
SQL Improved Process
H0: mu >=
40
H1: mu <
40
Acceptable Level of Risk=
10%
alpha =
0.10
n =
31
New Process Mean =
36.2
New Process Variance =
181.8
Zo =
-1.55
P = 2* Z()
0.12
Confidence =
87.9%
n=
31
x bar (sec) =
56.7
s =
14.7
1- alpha =
0.95
alpha =
0.05
alpha/2 =
0.025
U=
61.89
L=
51.56
95% Confidence Interval for the true average graphing time
51.56 <= Population Mean <= 61.89
57 +/- 5.16 seconds
7
.
240
24
/
23
.
0
5
.
11
2
.
0
/
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Rubric_Process Improvement Project.xlsx
Blank
| Process Improvement Project – Feedback – | |||
| Content Requirements | Possible Points | Points Earned | Comments |
| Project | |||
| A) An executive summary is provided in the storyboard format including: Is the storyboard presented in 1 PowerPoint slide? Follows DMAIC? Are tools/graphs/charts used and clearly visible? Do they support findings and conclusions Are arrows, call-out boxes, etc. used to summarize, highlight questions and key learnings? Are expected results clear? And next steps noted? | 5 | ||
| B)Is it a cohesive presentation opening with the business process and problem statement? The submission is 5-15 slides. | 2 | ||
| C) Was the success measure clearly identified, operationally defined and baseline identified? (Was the data identified as continuous or discrete, includes SQL?) | 3 | ||
| D) Was the data measurement plan or data stratification tree included? | 1 | ||
| E) Was the data collection method identified? | 1 | ||
| F) Was there rationale for the sample size taken? Use of the formula? Is there any reference to measurement error and how to minimize? | 2 | ||
| G) Are at least 5 different tools and techniques clearly identified? Are the tools linked/ pertinent to the data analysis? | 4 | ||
| H) Does the data analysis clearly tie to the problem conclusion? Is the “discovery” clear to the reader? | 2 | ||
| Total possible 100 points | 20 | 0.00 |
storyboard_template_2.ppt
DEFINE
MEASURE
Name of your project
Team
Launch
Define
Measure
Analyze
Control
Improve
Key Dates --->
ANALYZE
IMPROVE
Process owner: your Name
EXAMPLE
CONTROL
*
DMAIC_courseflow_.pptx
Description:
Clearly identify the business problem / performance gap (output measure), customer, scope, goals and resources.
Key Concepts:
y = f(x)
Types of data
Descriptive statistics and soft tools
Project:
Complete Problem Definition Worksheet
Tools:
Process map
SIPOC
Descriptive statistics
Thought process map
Affinity diagram
Sigma Quality Level (SQL)
Description:
Validate your measurement system and collect baseline data.
Key Concepts:
Mapping a process/value-stream, forms of waste, measurement error, reproducibility, repeatability
Project:
Identify potential inputs, develop operational definitions, develop data measurement/collection plan, validate measurement system, collect baseline data, calculate SQL.
Tools:
Operational definitions
Kappa
Process map (detailed)
Data measurement plan
Data stratification tree
Histogram
Trend/ line chart
Pareto chart
Fishbone (cause/effect) diagram
DMAIC
Week 1
Week 2
LM:MBC638
1
Define
Measure
Key Concepts:
Inferential statistics, common distributions, developing a hypothesis, determining the likelihood some event happens based on a sample (calculating probabilities), Using the normal distribution as the “go to” distribution.
Project:
Write a null and alternative hypothesis statement.
Tools:
Hypothesis testing
Chi-square test for independence
Week 3 & 4
Week 5
Week 6 &7
Key Concepts:
Collecting sample data, how confidence intervals and sample size are related.
Project:
Utilize the sample size formula.
Tools:
Confidence intervals.
Key Concepts:
Determining input’s (x) impact on the output (y).
Project:
Use regression to identify relationships between the output (y) and inputs (x’s).
Tools:
Correlation
Simple linear regression
Multiple regression
Scatterplot
Trend/ line chart
Pareto chart
Fishbone (cause/effect) diagram
Description:
Analyze, describe, and present the data to discover the root cause(s), identify/prioritize critical inputs (x’s), determine the inputs impact on the output.
LM:MBC638
Analyze
Description:
Develop potential solutions, select best solution, pilot solutions, measure results, document new process.
Key Concepts:
Discover y= f(x)
Project:
Implement a solution, run a pilot, evaluate the results, complete a hypothesis test.
Tools:
Affinity diagram
Fishbone cause/effect diagram
Pareto
Control charts
Hypothesis testing
Process map
Solution selection matrix
Description:
Implement process changes and controls. Verify expected performance was achieved, monitor performance to sustain new levels.
Key Concepts:
Xbar/R and ImR control charts, Different control charts applicable to different processes, time series forecasting methods predict future performance.
Project:
Utilize an appropriate control chart and /or time series forecasting method
Tools:
Control charts
Time series analysis
Operational definitions
Process map
Sigma Quality Level (SQL)
Week 9
Week 8
LM:MBC638
Improve
Control
Process_Improvement_Project_Requirements_122017.ppt
Process Improvement Project
Project Selection Criteria:
- Select an issue or opportunity that can be written as a problem statement.
- Must be within your sphere of influence.
- Is not an attempt to solve world hunger.
- Uses data that is accessible to you or can be collected in a reasonable amount of effort/time.
- You have the ability to measure the current and future state. You have access to baseline data or can collect it.
- Preferably uses more continuous data (rather than all discrete data).
- Fixing this problem will provide value. You should develop a business case to support working this issue (consider your time and others when calculating ROI.)
Examples:
Improve product quality
Reduce expenses
Improve the output of your organization
Decrease wait time
Page 1
1) Executive Summary :: Storyboard (should be presented in 1 PowerPoint slide)
Follow the DMAIC steps
Include the problem statement and baseline
Utilize at least 5 different tools/techniques (present relevant key tools to best tell your story).
Be readable; summarize and condense exhibits where necessary
Use arrows, call out boxes, and balloons to highlight questions and key learnings
Display data/charts supporting your findings and conclusions
Show results or expected results
Process Improvement Project
-Requirements-
Page 2
The final submission should be 1 file, in slide format, created in PowerPoint.
It should include 2 parts:
- Executive summary slide – 1 slide Storyboard (specific requirements below).
2) Back-up slides – additional 5-15 slides (specific requirements pgs. 3-4). This is not a repeat/copy of your storyboard. The back-up slides should detail and support the content of your storyboard.
*************************************************************************************************************
*
2) Back-up slides - following the Storyboard include 5-15 slides containing the answers to the following questions.
DEFINE
- What is your goal? How will you know if you’ve been successful?
- Have clear operational definitions been established for your inputs and outputs?
- What is the process you’re trying to improve? What are the current steps of the process?
MEASURE
- Include your Data Measurement Plan or Data Stratification Tree (examples on pgs. 5-6).
- What type of data did you collect (cost, cycle time, changeover time, yield, machine utilization, scrap, rework, defects, inventory)?
- Was that data continuous or discrete?
- Did you collect your own data or did you use existing data?
- How much data did you collect and why? What is your ideal sample size using the sample size formula? What is the risk if you collected fewer samples?
- How was your data collected? Describe the methods you used to collect it.
- Where could you have measurement error? How much measurement error do you have? What could you do to minimize your measurement error?
Process Improvement Project
-Requirements-
Page 3
*
2) Back-up slides continued:
ANALYZE
- What tools did you use to analyze the data? (Utilize at least 5 different tools/techniques and show evidence and detail of the tool/technique).
- What is the data telling you? What did you discover?
- What is the SQL for the old and new process?
IMPROVE
- What solutions did you propose and/or implement? Did you successfully improve your process? What did you learn about your process?
CONTROL
- How will you use this information to “hold the gains” of your improvement or make the next round of improvements in your process?
Process Improvement Project
-Requirements-
Page 4
*
Data Stratification Tree
Questions About Process
Stratification factors
X Variables
Measurements
New Orders
Time of year (mo.)
Training
Skill level
Wait time
(Output Y)
Does the Sales Rep have the right skills to improve selling more orders?
Are orders impacted by the sales rep skill-levels (systems, product, pricing, listening, ability to follow the process)?
Pricing Issue
Customer attitude
No.of backorders
Do new orders vary by month ?
- % of orders per Sales Rep by skill level type
- average & range of Sales Rep skill levels
What % of the calls are order related?
Do new orders change by the receptiveness of the customer?
Are orders impacted by call wait time?
Are orders impacted by pricing issues?
Are orders impacted by whether or not the Sales Rep follows the written process?
Do new orders vary by the availability of the product (not on backorder)?
Type of call
Written process
- % type of call
- wait time for each call
- customer attitude rating by order type
- % of calls transferred to OB due to pricing issues
- mystery call /silent monitoring results (points per call)
- % of orders resulting in backorders
- total orders placed by month
- % new orders are of total orders
- % new order revenue of total revenue by month
- no. of hours of training per month
Are orders impacted by call duration?
Call duration
- Average call duration for xyz order vs. other orders
Do the current targets impact orders?
Target settings (calls, orders, revenue)
- calls, orders, total rev, rev per mo. per Sales Rep
Page 5
*
Data Measurement Plan
Performance Measure
Data Source and Location
Target
Sample
Size
Who Will Collect
Data
When Will Data Be Collected
How Will Data Be Collected
- % type of call
- No. of inbound calls per day
- order revenue per Sales Rep per month
- Total revenue per month
- Revenue per month by product type
- Manual data collection
- Susie
- Develop rating scale & assess performance
- John’s training spreadsheet
- Use data collection form
- Manual data collection
- Manual data collection
- Manual data collection
- IB performance reports
- Susie
- Use data collection form
- Use data collection form
- Use data collection form
- Use data collection form
- All
- All
- John
- All
- All
- All
5/11-6/2
5/20
5/12
1000 calls
1000 calls
500 orders
500 orders
- Pull from report
- Leanne
By 6/3
28 mo
5/11 - 6/2
tbd
5/11 - 6/2
5/11 - 6/2
5/11 - 6/2
- Manual data collection
- Manual data collection
tbd
- Monthly mystery call results
- Leanne
By 6/3
- Compile Pamela’s data
30
500 orders
12 mo
28 mo
28mo
28 mo
- Leanne
ytd
- Obtain from other team
- Aspect reports
- Leanne
- % of orders per Sales Rep by skill level type
- average & range of Sales Rep skill levels
- wait time for each call
- customer attitude rating by order type
- % of calls transferred to OB due to pricing issues
- mystery call /silent monitoring results (points per call)
- % of orders resulting in backorders
- total orders placed by month
- % new orders are of total orders
- % order revenue of total revenue by month
- no. of hours of training per month
- Average call duration for new order vs. other
- calls, orders, total rev, per Sales Rep per month
N/A
- IB performance reports
- Pull from report
- Susie
By 6/3
28 mo
- IB performance reports
- Pull from report
- IB performance reports
- Pull from report
- IB performance reports
- Pull from report
- SN report
- Pull from report
By 6/3
By 6/3
By 6/3
- Susie
- Susie
- Susie
By 6/3
Page 6
*
DEFINE
MEASURE
Name of your project
Team
Launch
Define
Measure
Analyze
Control
Improve
Key Dates --->
ANALYZE
IMPROVE
Process owner: or your Name
Storyboard
template
CONTROL
Page 7
*
Process Improvement Project
-Rubric-
Page 8
| Content Requirements | Possible Points |
| A) An executive summary is provided in the storyboard format including: Is the storyboard presented in 1 PowerPoint slide? Follows DMAIC? Are tools/graphs/charts used and clearly visible? Do they support findings and conclusions Are arrows, call-out boxes, etc. used to summarize, highlight questions and key learnings? Are expected results clear? And next steps noted? | 5.0 |
| B)Is it a cohesive presentation opening with the business process and problem statement? The back-up slides (5-15) detail and support the storyboard content. | 2.0 |
| C) Was the success measure clearly identified, operationally defined and baseline identified? (Was the data identified as continuous or discrete, includes SQL?) | 3.0 |
| D) Was the data measurement plan or data stratification tree included? | 1.0 |
| E) Was the data collection method identified? | 1.0 |
| F) Was there rationale for the sample size taken? Use of the formula? Is there any reference to measurement error and how to minimize? | 1.0 |
| G) Are at least 5 different tools and techniques clearly identified? Are the tools linked/ pertinent to the data analysis? | 5.0 |
| H) Does the data analysis clearly tie to the problem conclusion? Is the “discovery” clear to the reader? | 2.0 |
| Total | 20 |
03GoodEXAMPLEs_storyboard_students.pdf
DEFINE MEASURE
Process Improvement Project – Graphing Time Reduction Mike – MBC 638
Team Launch
5/11/08
Define
5/19/08
Measure
5/26/08
Analyze
6/6/08
Control
On-Going
Improve
7/4/08Key Dates --->
ANALYZE IMPROVE
BUSINESS CASE: $18,943 Annual Cost Reduction if Implemented in Engineering Department
Extensive graphing is
required for good data
analysis of lab qualification
testing
350 Engineer hours in the
department are spent on
repetitive graphing
procedures within Excel.
This equates to
$52,471/year
A 30% reduction in
graphing time could result in
a $15,741 annual savings.
$=
Questions about Process Output Stratification Factors Measurements
X Is y af f ected by the number of
data points recorded in a test?
X1 = Total Data points
collected
Number of data points
collected
Is y af f ected by the total number
of columns graphed?
X2 = Variables included in
graph
Number of dif f erent
variables measured
Is y af f ected by the person
creating the graphs? X3 = Operator Name of engineer
Is y af f ected by the quality of the
graph required?
X4 = Graph quality Title, labels,
presentation ready
Is y af f ected by additional graphs
required f or comparison? X5 = Number of graphs Number of graphs
Is y af f ected by the total number
of columns of data available?
X6 = Total number of
available variables
Total number of
available variables
Data Stratification Tree
Y =
Graphing
Time =
f (X)
Y = f(X1,X2,X3,X4,X5,X6)
Day 1/Operator 1 - Xbar Chart
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
0 1 2 3 4 5 6
Run #
X b
a r
Day 1/Operator 1 - R Chart
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
0 1 2 3 4 5 6
Run #
R
Pareto Diagram of Number of Variables Graphed
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
1 to 4 5 to 7 8 to 10 11 to 13 >13
N u
m b
e r
V a ri
a b
le s
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
C u
m u
la ti
v e
F re
q u
e n
c y
Current Improved
Time per graph (sec) 57 36
Time spent
graphing/year (hr) 350 224
Annual Cost Reduction 52,471$ 33,529$
% Percent Annual Cost
Reduction
Cost Reduction
36%
Population Mean = 56.7
Std Deviation = 14.7
X2 (Upper Spec Limit) 60
Z2 = 0.223
P(X>60) = 0.412
P(X is out of spec) = 0.412
DPM = 411655
SQL = 1.72
SQL Baseline
Population Mean = 36.2
Std Deviation = 13.5
X2 (Upper Spec Limit) 60
Z2 = 1.762
P(X>60) = 0.039
P(X is out of spec) = 0.039
DPM = 39052
SQL = 3.26
SQL Improved Process
H0: mu >= 40
H1: mu < 40
Acceptable Level of Risk= 10%
alpha = 0.10
n = 31
New Process Mean = 36.2
New Process Variance = 181.8
Zo = -1.55
P = 2* Z() 0.12
Confidence = 87.9%
Sigma Quality Level
Increased from 1.72
to 3.26
$18,943 annual cost
reduction! $
Eliminated wasteful, repetitive
steps that can be automated
with Excel Macros
Pareto showed that 80% of
graphs consisted of 8
variables or less
n= 31
x bar (sec) = 56.7
s = 14.7
1- alpha = 0.95
alpha = 0.05
alpha/2 = 0.025
U= 61.89
L= 51.56
95% Confidence Interval for the true average graphing time
51.56 <= Population Mean <= 61.89
57 +/- 5.16 seconds 95% confidence interval that
true graphing time is 57 +/-
5.16 seconds
Hypothesis test indicates 88%
confidence that new process
meets the goal of at least a 30%
improvement in graphing time
Identified Critical Inputs and
Outputs to Measure
Measurement Systems Analysis
using X-bar, R Charts and
Precision-To-Total Ratio
R Charts in control.
Xbar Charts show ability to
measure differences
PTR = 0.22
Control
Maintain Revision Control on
original spreadsheet macros
Provide to Engineering Department
Survey engineers for usage in 3
months
DEFINE MEASURE
Process Improvement Project – Cooking Optimization
Define
Feb
Measure
March Analyze
March
Control
May Improve
April Key Dates --->
ANALYZE IMPROVE
Process owner: Neil
CONTROL
• Optimize the governing
factors of cooking, with
considerations being the
taste and cost.
• 2 types of dishes- A & B
• A & B have a fixed amount
of chicken, carrots,
tomatoes, capsicum, onion.
• Chilies and Garlic also, but
varying quantity.
Taste of Dish A
When Y = cost, all ingredients are
significant; but when Y = Taste above
inputs are significant
S- Money (Myself) & Wegmans (Ingredients)
I- Ingredients, Utensils, Electric Stove
P-Cooking Process
O- Dish A & B
C- Volunteers
Taste of Dish B
DISH A
DISH B
Dish B>Dish A, avg. means
(even with less ingredients)
Keeping the ingredients which
have significance to cost and taste
in mind, with preferences to taste; I
run the test again with less quantity
of salt, garlic, siracha, soy sauce,
sugar and vinegar.
We can see from the new t-test
that the mean cost of the dish A
& B now have lower avg. means
and only chili & garlic are in
excess (acceptable).
DISH A
& B
average
savings
$15.2
BUSINESS IMPACT
To save money while
still maintaining taste
of the dishes
$
DEFINE MEASURE
Team Launch: Define: Measure: Analyze: Control:Improve: Key Dates
ANALYZE IMPROVE
Process owner: Landon
CONTROL
September 10 September 17 September 24 October 29 November 19
Landon, Engineering Project Managers, Finance Office, Stakeholders
September 6
Problem Statement
Cycle time for a signature
sheet averaged 11.25 days
with each project manger
spending about 11.25 hours
for each purchase over
$100,000.
Business Impact
The average wage a project
manager earns is $35/hr,
therefore it costs $393.75 per
project in just gathering
signatures! At 144 projects a
year this process costs
$56,700 annually.
- Finance Office will not accept old
version of signature sheet.
- Purchases tracked in SharePoint
- Appraisal rated on compliance
0
1
2
3
4
5
6
7
8
1 3 5 7 9 11 13 15 17
F r e q
u e n
c y
Cycle Time (Days)
0
2
4
6
8
10
12
1 3 5 7 9 11 13 15 17
F r e q
u e n
c y
Cycle Time (Days)
New Old S
ig n
a tu
re S
h e
e t
C y
cl e
T im
e (m
a n
-h o
u rs
)
Past man-hours
4 11
6 11
6 11
7 11
9 12
9 12
9 13
10 13
10 14
11 14
11 17
11 28
Mean= 11.25
Std dev= 4.57
Median= 11.0
High man-
hours High cycle
time
No
No
Project manager signs form
Obtain engineering supervisor’s signature
Submit to Finance
Obtain production supervisor’s signature
Obtain engineering director’s signature
Obtain group director’s signature
Submit form to Finance Department
Wait for Thursday
Obtain finance supervisor’s signature
Is it
Thursday?
Is project over
$100,000?
Too many steps!
Need to take
PM out of all
these steps • Cycle time reduced to 2.88 days!
• Man-hours reduced to 0.20 hours!
• Cost savings $55,692 annually!
• SQL raised from 2.3 to 3.6 and rising!
SQL = 2.3 Hypothesis Test Ho: mu ≥ 11.25 hr
Ha: mu < 11.25 hr
7.240 24/23.0
5.112.0
/
ns
x t
P-value ≈ 0
Electronic Signature Sheet
SQL = 3.6
R = 0.78
between no. of
steps and time
EV 7.21
AV 3.65
R&R 10.86
PV 89.14
Percent of Total
Variance Ratios
DEFINE MEASURE
Process Improvement Project - for Widget Assembly
Team
Launch
Define
2/02/2017
Measure
2/16/2017
Analyze
03/23/2017
Control
04/20/2017
Improve
04/13/2017 Key Dates --->
ANALYZE IMPROVE
Nelson
CONTROL
Problem statement: Due to high cycle
times we cannot get the desired amount of
throughput for the Widget assembly. The
average cycle time for each part is less than
44 seconds. Defects are inherent because of
improper line balancing and bottleneck in
the system.
SQL = 2.752
Ho :Mean cycle time for part >= 44 seconds
Ha :Mean cycle time for part < 44 seconds
Sample size 36
Sample mean 45.036
Standard Deviation 2.681
Hypothesized mean 44
Test Statistic (Z) 2.318537859
P-value 0.989789946
From the above result P-value is greater
than 0.05 thus we do not reject the Null
hypothesis and thus the Mean cycle time is
greater than 44 seconds. Hence we need to
analyze what’s wrong
1 2 2 1.5 1
Easy to implement Resources Cost Process impact Complexity Total Rank
Solution 1 5 3 3 1 5 23.5 3
Solution 2 1 1 1 5 1 13.5 4
Solution 3 3 3 5 3 3 26.5 2
Solution 4 3 3 5 5 3 29.5 1
Solution 1
Solution 2
Solution 3
Solution 4 To implemet Solution 1 and Solution 3 together
To reduce number of activites at station 5 and distribute them equally
Increase one more station and equally dstirubte the activites at station 5
Reduce one station form the process line and combine two stations
SQL = 3.545
Mean 47.94 45.30
Known Variance 10.37 3.57
Observations 36.00 44.00
Hypothesized Mean Difference 0.00
z 4.36
P(Z<=z) one-tail 0.00
z Critical one-tail 1.64
P(Z<=z) two-tail 0.00
z Critical two-tail 1.96
Here the p-value = 0.00 < 0.05. Hence we reject the null hypothesis and we
can say the Cycle time before is greater then the cycle time after
improvement. Hence we have improved our process considerably.
We have finalized
fourth proposed
solution from the
matrix and thus
we need to
improve the
process based
upon the selected
solution.
Here we have selected the R chart and Xbar chart for the
control of the process because the sub group size is
only two for my process. Now as we can see the R chart seems to be under
control. Only some of the points on Xbar chart are out of control for the process. Thus we need to double
check what wrong at those points and figure out a way
to get the process under control.
Also from the Cp and Cpk values we can see that our
process is capable to be undertaken but there is still scope of improvement to
make it more capable.
Cp = 1.16
Cpk = 1.08
Why is SQL less?
What can be done better?
What factors shall we
measure, analyze and
improve?
R&R =10.86% < 30 %,
Measurement plan is okay
Because the Station 5 has the highest
number of activities being done and thus it
takes the highest time. So we need to
equally divide the number of activities
hence to reduce cycle time
> 44 seconds
DEFINE MEASURE
Process Improvement Project – Cycle Time Reduction
Team Launch
8/23
Define
9/08
Measure
10/16
Analyze
10/24
Control
On-Going
Improve
10/31 Key Dates --->
ANALYZE IMPROVE
Process owner: Dan
CONTROL
PROJECT TEAM: Dan Mary Karen Linda Peter
BUSINESS CASE: $54,000 in annual processing costs
It takes 43 days to process a
grant application. Only 8% of
applications are being
processed within 30 days of
receipt. The time to process
the application has lead to
unhappy applicants and staff
who are finding more and more
of their daily work time being
devoted to “grant
administration.” The funding
levels available to applicants
and the number of applications
are expected to increase in the
near future, which has the
potential to compound the
problem.
Number of Complete Applications
5 7
8 8 8 7
9 11 11 12
13 13 14
0
5
10
15
Ju l, 20
0 6
S ep
t N o v
Ja n
M ar
M ay
Ju l, 20
0 7
Date
N u
m b
e r
Series1
Linear (Series1)
The Number of applications
received is increasing.
The time to complete a process
cycle is also increasing.
Total Application Errors by Type
132
21
14 9
75.0%
86.9%
94.9%
0
20
40
60
80
100
120
140
160
Incomplete/Incorrect ApplicationsStalled Approvals In The Log-in
Phase,
Stalled Approval At The
Managerial Level
Reworks
Type
D e fe
c ts
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
Problem:
Incomplete and inaccurate
applications were identified as
the primary factor leading to
defects in the process cycle.
Solution:
New Application process
incorporating drop down menus
New Application Procedure =
Less Mistakes & Quicker Cycle Time
Base Group
62.06UCL
42.50CL
22.94LCL
16
21
26
31
36
41
46
51
56
61
66
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126
Units
C y
c l e
T
i m
e - D
a y
s
New "Improved" Process
UCL 44.59
CL 28.56
LCL 12.53
7
12
17
22
27
32
37
42
47
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Units
C y
c le
T im
e
The defect rate reduced from 93% to 32%
Monthly monitor and review procedure is in
place. Out of control signal = action plan.
↑ Number of Applications
+ ↑ Cycle Process Time __Tough Times Ahead
Time to Complete Proccess Cycle
28
33
38
43
48
53
58
Jul-06 Aug Sept Oct Nov Dec Jan Feb March April May June Jul-07
Date/Time/Period
T im
e (
D a
y s
)
Data 1
Median
Goal
43 days
29 days
SQL=3
DEFINE MEASURE
Increase Monthly Income of Check Cashing Business
Project Launch
2/2
Define
2/3
Measure
2/11
Analyze
3/16
Control
4/15 Improve
4/6 Key Dates --->
ANALYZE IMPROVE
Process owner: Yanni
CONTROL
Problem Statement
Revenue varies by month.
Weekly average of check
Cashed amount= $80k
Variability:
Cashed amount= $45-50k
Business Impact
Increase yearly cashed
amount by $60K-70K
by reducing the
variability per month
by.
That will improve
monthly average
income.
Feb Mar
0
20000
40000
60000
80000
100000
1 16 31 46 61 76
C a sh
e d
A m
o u n t
Date
RUN Chart
Cashed Amount
Linear (Cashed Amount)
Multiple Linear Regression
Analysis
• Advertisements
• Money Lost due to Fraud
Checks
• Monitor the Run chart weekly.
• Implement advanced check
cashing equipment and keep
track of Bounced checks.
• Increase newspaper and flyer
advertising.
Weekend
spikes
After ChangeBefore Change
1000
800
600
400
200
0
# o
f R
e je
c t s p
e r D
a y
Frequency Rejects Before Change & After Change
DEFINE – 5/15/11 MEASURE - 6/1/11
Finding the Skinny on Thin Film Sensor Reject Rates
Control
Improve
ANALYZE - 7/1/11 IMPROVE - 8/1/11 1) Problem Statement:
Production reject rate of thin film
sensors increases after process
change.
3) Business Impact:
Reducing/eliminating frequency
rejects will prevent reworking of
part, extra inventory and labor
from 100% testing which could
potentially save
Cause & Effect Matrix Scoring:1=low, 3 = med, 5=high,
Importance to Customer (sensors w/ correct frequency) = 1
Process
Inputs
(X)
Effect Rating Probability Score
Vendor
frequency
sorting
quality
Allow accurate
calculation of
thickness
5 High, makes adjustments
when providing thickness
data to techs
25
Fixture
Geometry
Even coating
thickness
5 High, location determines
the thickness of the
coating.
25
0
200
400
600
800
1 /5
/2 0
1 0
1 /2
6 /2
0 1
0 2
/2 3
/2 0
1 0
3 /3
1 /2
0 1
0 4
/2 0
/2 0
1 0
5 /1
0 /2
0 1
0 6
/2 /2
0 1
0 6
/2 2
/2 0
1 0
7 /1
4 /2
0 1
0 8
/9 /2
0 1
0 9
/1 6
/2 0
1 0
1 0
/1 8
/2 0
1 0
1 1
/4 /2
0 1
0 1
1 /2
9 /2
0 1
0 1
2 /1
6 /2
0 1
0 1
/1 0
/2 0
1 1
2 /1
/2 0
1 1
2 /2
2 /2
0 1
1 3
/1 4
/2 0
1 1
Moving Range Chart
Jan 1, 2010-April 4, 2011
Began testing new material
June 7,2010
100806040200
40
30
20
10
0
% Vendor A
% R
e je
c t s
Scatterplot of % Rejects vs % Vendor A
The r2 shows that the amount of raw material used from
Vendor A explains 46.6 % of the change in reject rate.
0.00% 5.00% 10.00%
Frequency
Pattern
Contaminates
Quartz
Marks/Scratc
hes
Low Activity
Pareto Chart of Defects
Oct 4,2010 -April 4, 2011
8) Probable Cause 2 – Evaporation Fixture Geometry
7) Probable Cause 1 - Raw Material Supply
The sensors are held in a fixture positioned over a
evaporation source that coats them with metal. I
performed a test run to measure baseline
performance. The data revealed that the metallic
coating has too much variation in thickness w/ a
mean of 2235 Å, but the range should be 500 Å.
This could be caused by the position of the source,
size of mask or angle of the holding fixture.
2) Work on largest category of
defect for MAXIUM IMPACT
Before
After
4) Out-of-Control:
Process is highly variable to begin
w/ but much worse after change.
5) Change of Focus
The change did cause an increase in
variability, but the process is not
very good to start w/ a DPMO of
19,263! Finding the root cause of
the inherent process variability
should solve the new issue.
6) Identify Primary Inputs (Y)
A second run was done to test if a centered evaporation
source would decrease thickness variability (Ha). A
one-tail test was performed & the P value was high,
thus it did not significantly improve the process. This
points to the mask size & fixture as the root cause of
the variation.
Z=
Z = -1.19 P = 1-Z = 1-1.19 =0.86 =86%
=
Ho: Test 1 thickness variability ≤ Test 2
-Receipt of material from Vendor A
was halted. A comparison of their
measurements vs. ours found a 7.6 KHz
difference!
6058500605700060555006054000605250060510006049500
30
25
20
15
10
5
0
Frequency
F r e
q u
e n
c y
Mean 6053366
StDev 1569
N 200
Histogram of Frequency Normal
They recalibrated their instruments &
next shipment was markedly improved
with a mean very close to the center of
our specification range of 6.055 as
shown on this histogram.
9) Solution to Probable Cause 1
10) Solution to Probable Cause 2 I’m working with engineering to
develop a new fixture that will
improve the geometry.
Scatter plot reveals that using raw materials
from Vendor A has a strong positive
correlation of 0.7 with the reject rate.
0.00
5000.00
10000.00
1 2
2 4
3 6
4 8
5 1
0 6
1 2
7 1
4 8
1 6
9 1
9 0
2 1
1 2
3 2
2 5
3 2
7 4
2 9
5 3
1 6
3 3
7 3
5 8
3 7
9 4
0 0
4 2
1 4
4 2
4 6
3 4
8 4
Range Chart - Vendor A
Constructing a control chart of measurements taken by QC
of frequency illustrates that the vendors process is out of
control.
10) Changes to be Made:
QC technician does acceptance
testing of raw materials w/ zero
tolerance.
Vendor supplies Certificate of
Analysis w/ test statistics.
Control chart created for raw
materials.
New fixture for more uniform
thickness to prevent any frequency
rejects.
Control – 8/8/11
Rick, Steve & Production Staff
project_ideas_withxy_examples_pdf.pdf
**Example** **Example**
Process Improvement Projects Output (y) Potential inputs (x) but there could be many more/others
Increase product sales Sales dollars
Types of product, number of sales people, time spent on calls, dollars
spent on ads, dollars of inventory on hand
Reduce cost of rework Rework dollars
Defect types, different production lines, different operators, shifts, time
spent on rework per defect type, operator training-level
Increase time with family (Reducing non-value added activities) Time for NVA in minutes
Time at work, time to bed, hours slept, meals purchased, meals made,
time per activities, homework time, dollars spent
Decrease your landfill waste Waste in pounds (or ounces)
Categories of waste, days /time waste is disposed, who generates the
waste, hours at work, hours at home, activity types
Improve sleep time/quality Sleep time in hours (or minutes)
Time to bed, hours worked, calories after 8pm, time to wake, minutes
of exercise, total oz. beverages consumed, caffeine consumed
More Project Ideas
Improve the quality of a baked good while decreasing cost
Reduce the number of defects
Increase beer production efficiency
Reduce produce (fruits and vegetable) waste
Decrease home or facility energy use
Decrease your carbon footprint
Improve Twitter utilization
Reduce headache frequency/severity
Increase billable hours
Reduce document registration errors
Decrease time on cellphone
Improve Instagram utilization
Increase furniture sales
Reduce time to assign nursing care
Decrease blood sugar levels
Increase number of loans processed
Increase revenue
Increase customer satisfaction
Reduce cycle time
Decrease the amount of time it takes to place/process an order
Decrease the time to repair
Reduce process variation between production plants
Reduce rejected material
Reduce wait time per patient
Improve revenue generated per client
Improve the effectiveness of marketing communication
Reduce the number of cosmetic defects per product
Increase net profit per product
Reduce fraudulent loss
Improve cycle time of payments
Increase revenue generated per loan application
Increase number of contacts
Increase number of website hits
Increase number of leads
Decrease time late to work
Reduce the amount of time it takes to certify a supplier
Reduce the number of customer complaints
Improve the performance rating of a piece of equipment
Reduce variation between equipment
Increase the number of customer calls
Reduce time to order advertising space
Increase customer contact time
Increase investment dollars
Decrease inspection time
Decrease grocery bill
Reduce overall food expense
Reduce commute time to/from school or work
Reduce personal expenses
Decrease time associated with dealing with "behavior issues"
Maximize quality study time
Increase attendance to a particular event
Reduce time spent managing the budget
Improve indoor air temperature
Decrease cost of living expenses
Reduce the time it takes to produce a status report
Reduce test variability between labs
Reduce the number of steps in the quoting process
Improve the ratio of dollars spent per prescription written
Reduce the time it takes to close a real estate deal
Generate incremental revenue from existing customers
Reduce backlog of claims
Increase server utilization
Reduce raw material inventory
Reduce time to mitigate/process a raw material discrepancy
Reduce the number of delays and cancellations
Optimize a truck delivery
Reduce gallons of fuel consumed
Reduce overall processing time of RFQs
Reduce process time to ship parts
Reduce overtime
Increase the number of deliveries
Increase customer service calls processed
Increase customer (client) visits
Reduce start-up costs
Reduce time to solve customer problem
Increase school enrollment and revenue
Improve advertising agency workflow
Increase reliability test performance
Reduce travel time
Increase online sales profit
Reduce average number of golf putts per round
Reduce errors found by auditors
Improve utilization of trailer space
Reduce cost overruns in IT
Reduce gap between actual billed hours vs. estimate
Improve meeting efficiency
Increase throughput providing a service
Reduce errors made per invoice
Increase number of transactions that occur online
Reduce cycle time to process grants
Increase time available in a day to exercise
Decrease clean-up costs
Reduce parking expense
Reduce food/grocery expenses
Improve consistency of each batch produced
Improve email response time
Reduce discretionary spending
Reduce multiple shipments per client
Reduce morning time (out the door) process
Reduce travel expenses
Increasing number of clients
Reduce repair time
Reduce number of open purchase orders
Reduce fuel consumption
Increase sales payouts
Improve staffing utilization
Reduce cycle time for trash removal process
Reduce room temperature variation
Increase quality leads
Increase adoption rate of sales tool
Generate more internet traffic
Reduce the gap between estimated and actual asset value
Reduce raw material costs
Reduce scrap rate
Data Measurement Plan Template.pptx
Data Measurement Plan
| Performance Measure | Data Source and Location | How Will Data Be Collected | Who will Collect Data | When will Data be Collected | Target Sample Size |
1
Data Stratification Tree Template.pptx
Data Stratification Tree
| Questions About the Process | Stratification Factors | Measurements | |
| X Variables | |||
| (Output Y) | |||