six sigma case study?
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lecture2020320-20statistical20process20control20-20spc.pptLecture 3
Statistical Process
Control (SPC)
Data collection for Six Sigma
- Data are simply facts and figures without context or interpretation.
- Information refers to useful or meaningful patterns found in the data.
- Knowledge represents information of sufficient quality and/or quantity that actions can be taken based on the information.
- If data are not collected and used wisely, their vary existence can lead to activities that are ineffective and possibly even counterproductive.
- An organization collects data & reacts whenever an out-of-specification condition occurs.
“Common cause” & “ special cause” variation
There are two causes of process variations:
1) Common cause variation: This variation is due to the process only. It may not tell you whether the process meets the needs of the customer unless it is compared with the specification. This can be improved by focusing on the process.
2) Special cause variation: This variation is due the individual employee, if the point is beyond specification limits. In this case the focus should be about what happened relative to the individual employee as though it were a “special” condition.
Attribute versus Variable Data
Attribute data: It is a data with yes or no decision such as:
- whether an iten passed or failed a test
- pass/fail, go/no go gaging, true/false, accept/reject. There are no quantifiable values
Variable data: are related to measurements with quantifiable values such as:
- Diameter of a part which has been machined
- length or thickness of the machined part
The success of Six Sigma
- The success of Six Sigma depends upon knowing the difference between special & common cause variations and how the organization reacts to the data.
- If the management focuses on wrong cause of variation, it can lead to waste of time (firefighting).
- It can also effect employee motivation & morale.
- Reacting to one data point that do not meet the specification limit can be counterproductive and very expensive.
- Do not use “firefighting” actions just because the data point is out of specification limits. It must first be determined whether the condition is common or special cause.
Example of variability due to common cause
- Control limits are calculated from the sample data.
- There are no data points outside the control limits therefore there are no special causes within the data.
- The source of variation in this case is “common cause” due to process.
Type of firefighting done by management before evaluating the cause of variability
- Production supervisors might constantly review production output by employee, machine, product line, work shift etc.
- An administrative assistant’s daily output & memo’s may be monitored.
- The average time per call may be monitored in a call center.
- The efficiency of computer programmers may be monitored by tracking “lines of code produced per day”.
All of these actions would be a waste of time if the cause of variability is “common cause” and due to the process rather than individual employees who have no control over it.
Goals for Six Sigma projects
- The success of Six Sigma depends upon how goals are set & any boundaries that are set relative to meeting those objectives.
- Arbitrary goals that are set for employees can be counterproductive and costly, when the outcome is beyond the employee’s control.
- If management extends the scope of what can be done by employees to fix problems, real productivity improvement can result.
- Organization sometimes can be trapped into “declaring victory” with one metric at the expense of another metric.
Strategy for Six Sigma success
- It should deal with numbers, information & knowledge.
- It should quantify & track measurements that are vital to the success of the organization.
- A wisely applied Six Sigma strategy can facilitate productive utilization of information.
- It can be used in manufacturing, service, product design, and transactional applications.
- Visual observations, pictures, data analysis and statistical assessments are the key to the success of a Six Sigma projects.
CONTROL CHARTS
What is a Control Chart ?
A control chart is simply a run chart with confidence intervals calculated and drawn in. These “Statistical control limits” form the trip wires which enable us to determine when a process characteristic is operating under the influence of a “Special cause”.
+/- 3s =
99% Confidence Interval
Control charts are useful to:
- determine the occurrence of “special cause” situations.
- Utilize the opportunities presented by “special cause” situations” to identify and correct the occurrence of the “special causes” .
IMPROVEMENT ROADMAP
Uses of Control Charts
Breakthrough
Strategy
Phase 4:
Control
Characterization
Phase 1:
Measurement
Phase 2:
Analysis
Optimization
Phase 3:
Improvement
- Control charts can be effectively used to determine “special cause” situations in the Measurement and Analysis phases
Common Uses
KEYS TO SUCCESS
Use control charts on only a few critical output characteristics
Ensure that you have the means to investigate any “special cause”
What is a “Special Cause”?
Remember our earlier work with confidence intervals? Any occurrence which falls outside the confidence interval has a low probability of occurring by random chance and therefore is “significantly different”. If we can identify and correct the cause, we have an opportunity to significantly improve the stability of the process. Due to the amount of data involved, control charts have historically used 99% confidence for determining the occurrence of these “special causes”
Special cause occurrence.
X
Point Value
+/- 3s = 99% Confidence Band
So how do I construct a control chart?
First things first:
- Select the metric to be evaluated
- Select the right control chart for the metric
- Gather enough data to calculate the control limits
- Plot the data on the chart
- Draw the control limits (UCL & LCL) onto the chart.
- Continue the run, investigating and correcting the cause of any “out of control” occurrence.
How do I select the correct chart ?
Note: A defective unit can have more than one defect.
What type of data do I have?
Variable
Attribute
Counting defects or defectives?
X-s Chart
IMR Chart
X-R Chart
n > 10
1 < n < 10
n = 1
Defectives
Defects
What subgroup size is available?
Constant Sample Size?
Constant Opportunity?
yes
yes
no
no
np Chart
u Chart
p Chart
c Chart
SPC Charts
Steps for SPC implementation
Processes ideally suited for SPC
- Are repetitive (produce simmilar items)
- Have a high inspection content
- Have higher than desired reject rate
- Items (parts) with dimensions that are easy to measure
SPC charts
The most frequently SPC charts are:
1) Xbar:r charts
2) p-charts
Xbar:r charts are used for controlling processes which have “variable” data.
p-charts are used for controlling processes which have “attribute” data
Example of Xbar:r chart for a machined part
Example of a process which is in control
Example of a process which is heading out of control
Example of out of control process
(If 7 or more sequential data points are above or below Xbar line)
Steps to develop Xbar chart
Step 1: Collect 100 different data points as follows:
(20 different subgroups with 5 data points in each subgroup)
Step 2: Calculate the value of the grand average as follows:
- Calculate the average value of each of the 20 subgroups.
- Calculate the average of all 20 subgroups called Xbar.
- This is the center-line of the Xbar chart.
Step 3: Calculate the standard deviation (s) of the average values of 20 subgroups
Step 4: Multiply the standard deviation value by 3
Upper control limit = Xbar + 3s
Lower control limit = Xbar - 3s
Steps to develop r-chart
Step 1: Determine the ranges for each of the 20 subgroups
Step 2: Calculate the value of the grand average as follows:
- Calculate the grand average by summing all 20 values and then dividing the sum by 20. This is called rbar
- This is the center-line of the rbar chart.
Step 3: Calculate the standard deviation (s) of the average
r-values values of 20 subgroups
Step 4: Multiply the standard deviation value by 3
Upper control limit = rbar + 3s
Lower control limit = rbar - 3s
Example of out of control process
(If a pattern is repeated in the Xbar chart)
Steps to develop p-chart
Step 1: determine the number of samples “n” to develop the chart.
Step 2: Inspect each sample and identify the number of defects in each sample.
Step 3 Calculate the percentage defects “p” for each sample.
Step 4: Calculate the paverage as follows:
paverage = (n1p1+n2p2+ ….. nkpk) / (n1+ n2 +…….nk)
Step 5: Calculate the upper and lower control limits as follows:
Components of a control chart
Cases when the process is “out of control”
and should be stopped for investigation
What do I do when the process is “out of control”?
Time to Find and Fix the cause
- Look for patterns in the data
- Analyze the “out of control” occurrence
- Fishbone diagrams and Hypothesis tests are valuable “discovery” tools.
Stages of continuous improvement
UCL =
Paverage
+ 3
(
Paverage
)
(
1
-
Paverage
)
n
LCL =
Paverage
-
3
(
Paverage
)
(
1
-
Paverage
)
n
