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Statistical Quality Control

• Quality is when a product delivers what is stipulated for in its specifications

• Crosby: “quality is conformance to requirements”

• Feigenbaum: “quality is a customer determination”

• Garvin: five dimensions of quality

Quality

• Transcendent quality: “innate excellence” • Product quality: quality is measurable • User quality: quality is determined by the consumer • Manufacturing quality: quality is measured by the

manufacturer's ability to target the product specifications with little variability

• Value Quality: Has to do with the price and cost

Garvin’s Five Dimensions of Quality

Quality Control

• Quality control - the collection of strategies, techniques, and actions taken by an organization to assure themselves of a quality product.

• After-process quality control - involves inspecting the attributes of a finished product to determine whether the product is acceptable • reporting of the number of defects per time period • screening defective products from consumers

• In-process quality control - techniques measure product attributes at various intervals throughout the manufacturing process in an effort to pinpoint problem areas.

Total Quality Management

• W. Edwards Deming - the “father of the quality movement” said that the achievement of quality begins with top managers’ commitment and extends all the way to suppliers and consumers. • He believed that quality control is a long-term total company

effort that he entitled “total quality management (TQM)”. • Deming presented a cause-and-effect explanation of the

impact of TQM on a company, known as the Deming chain reaction. • The chain reaction begins with improving quality, which

decreases costs and improves productivity: • Productivity =

Deming's 14 Points to Improved TQM

1. Create constancy of purpose for improvement of product and service.

2. Adopt the new philosophy. 3. Cease dependence on mass inspection. 4. End the practice of awarding business on price tag

alone. 5. Improve constantly and forever the system of

production and service. 6. Institute training. 7. Institute leadership.

Deming's 14 Points to Improved TQM

8. Drive out fear. 9. Break down barriers between staff areas.

10. Eliminate slogans. 11. Eliminate numerical quotas. 12. Remove barriers to pride of workmanship. 13. Institute a vigorous program of education and

retraining. 14. Take action to accomplish the transformation.

Six Sigma

• Six sigma - total quality approach that measures the capacity of a process to perform defect free work.

• Requires that there be no more than 3.4 incorrectly filled prescriptions of 3.4 unsatisfactory landings per million, with a goal of approaching zero.

• Forces companies that adopt it to work much harder and more quickly to discover and reduce sources of variation in processes.

• May be required to attain world-class status and be a top competitor in the international market.

Six Sigma

• Contains a formalized problem-solving approach called the DMAIC process (Define, Measure, Analyze, Improve, and Control).

• Strong focus on the customer, both internal and external, that is often referred to as Critical to Quality (CTQ).

• Most members of an organization are trained in the methodology.

• Companies using Six Sigma discovered that so many problems existed that required a complete redesign.

• History shows that most companies can only achieve about a 5.0 sigma status.

Lean Manufacturing • A quality-management philosophy that focuses on

the reduction of wastes and the elimination of unnecessary steps in an operation or process.

• The Toyota Production System is generally credited with developing the notion of lean manufacturing.

• Focuses on 7 wastes: 1. Overproduction 2. Waiting time 3. Transportation 4. Processing 5. Inventory 6. Motion 7. Scrap

Important Quality Concepts

• Benchmarking - examine and emulate the best practices and techniques used in the industry. • a positive, proactive process to make changes that will

effect superior performance.

• Just-In-Time Inventory Systems - necessary parts for production arrive “just in time”. • reduced holding costs, personnel, and space needed for

inventory. • no extra raw materials or inventory of parts for production

are stored.

• Reengineering - complete redesign of the core business process in a company.

Other Quality Control Concepts

• Failure Mode and Effects Analysis: • A systematic way for identifying the effects of a potential

product or process failure and includes methodology for eliminating or reducing the chance of a failure occurring.

• Used for analyzing potential reliability problems early in the development cycle.

• Poka-Yoke: • “mistake proofing” • Uses devices, methods, or inspections in order to avoid

machine error or human error. • Two main types:

• Prevention-based • Detection-based

Other Quality Control Concepts

• Team Building: • Occurs when a group of employees are organized to

undertake management tasks and perform other functions such as organizing, developing, and overseeing projects.

• More workers take over managerial responsibilities. • A quality circle is a small group of workers and their

supervisor who meet regularly to consider quality issues.

Process Analysis

A process is a series of actions, changes or functions that bring about a result – examined through flow charts and diagrams.

The seven basic tools are as follows: 1. Flowchart or process map 2. Pareto chart 3. Cause-and-effect diagram (Ishikawa or fishbone chart) 4. Control chart 5. Check sheet or checklist 6. Histogram 7. Scatter chart or scatter diagram

Flowcharts A flowchart is a schematic representation of all the activities and interactions that occur in a process.

Flow Charts - schematic representation of all the activities and interactions that occur in a process.

Pareto Analysis • Pareto Analysis - quantitative tallying of the number and

types of defects that occur with a product. • Pareto Chart - ranked vertical bar chart with most frequently occurring

on the left.

Fishbone

Fishbone Diagram - display of potential cause-and-effect relationships.

Check Sheets

Check Sheets or Checklists – Display the frequency of outcomes for some quality-related event or activity under study.

Other Process Analysis

• Histograms – Depicts a frequency distribution of quantitative data.

• Scatter Chart or Scatter Diagram – for examining the relationship between two variables.

• Control chart – graphical method for evaluating whether a process is or is not in a “state of statistical control .

• Types of control charts: • Control charts for measurement: x-bar and R charts • Control charts for attribute compliance: p and c charts

• Elements of a control chart: • Centerline • Upper control limit (UCL) • Lower control limit (LCL)

Control Charts

• Chart of sample means computed for a series of small random samples over a period of time.

• The centerline is the average of the sample means,

• The upper control limit (UCL) is 3 standard deviations of means above the centerline.

• The lower control limit (LCL) is 3 standard deviations below the center line.

Control Chart

Steps to Creating an Control Chart

Monitor process location (center):

1. Decide on the quality to be measured. 2. Determine a sample size. 3. Gather 20 to 30 samples. 4. Compute the sample average for each sample. 5. Compute the sample range for each sample. 6. Determine the average sample mean for all

samples. 7. Determine the average sample range (or sample

standard deviation) for all samples. 8. Using the size of the samples, determine the value

of A2 or A3. 9. Compute the UCL and the LCL

R Control Chart

Monitor process variation:

1. Decide on the quality to be measured.

2. Determine a sample size.

3. Gather 20 to 30 samples.

4. Compute the sample range for each sample.

5. Determine the average sample mean for all samples.

6. Using the size of the samples, determine the values of D

3 and D

4 .

7. Compute the UCL and the LCL

R Chart Formulas

Control Chart: Formulas

A manufacturing facility produces bearings. The

diameter specified for the bearings is 5 millimeters.

Every 10 minutes, six bearings are sampled and their

diameters are measured and recorded. Twenty of

these samples of six bearings are gathered. Use the

resulting data and construct an chart.

Data for Demonstration Problem 18.1: Samples 1 - 10

1 2 3 4 5 6 7 8 9 10 5.13 4.96 5.21 5.02 5.12 4.98 4.99 4.96 4.96 5.03 4.92 4.98 4.87 5.09 5.08 5.02 5.00 5.01 5.00 4.99 5.01 4.95 5.02 4.99 5.09 4.97 5.00 5.02 4.91 4.96 4.88 4.96 5.08 5.02 5.13 4.99 5.02 5.05 4.87 5.14 5.05 5.01 5.12 5.03 5.06 4.98 5.01 5.04 4.96 5.11 4.97 4.89 5.04 5.01 5.13 4.99 5.01 5.02 5.01 5.04

4.9933 4.9583 5.0567 5.0267 5.1017 4.9883 5.0050 5.0167 4.9517 5.0450 0.25 0.12 0.34 0.10 0.07 0.05 0.03 0.09 0.14 0.18

X R

Data for Demonstration Problem 18.1: Samples 1 - 10

Data for Demonstration Problem 18.1: Samples 11 - 20

11 12 13 14 15 16 17 18 19 20 4.91 4.97 5.09 4.96 4.99 5.01 5.05 4.96 4.90 5.04 4.93 4.91 4.96 4.99 4.97 5.04 4.97 4.93 4.85 5.03 5.04 5.02 5.05 4.82 5.01 5.09 5.04 4.97 5.02 4.97 5.00 4.93 5.12 5.03 4.98 5.07 5.03 5.01 5.01 4.99 4.90 4.95 5.06 5.00 4.96 5.12 5.09 4.98 4.88 5.05 4.82 4.96 5.01 4.96 5.02 5.13 5.01 4.92 4.86 5.06

4.9333 4.9567 5.0483 4.9600 4.9883 5.0767 5.0317 4.9617 4.9200 5.0233 0.22 0.11 0.16 0.21 0.06 0.12 0.12 0.09 0.17 0.09

X R

Demonstration Problem 18.1: Control Chart Computations

Sigma level: 3

20 19

18 17

16 15

14 13

12 11

10 9

8 7

6 5

4 3

2 1

Bearing Diameter

UCL = 5.0679

Average = 5.0022

LCL = 4.9364

Control Chart: Bearing Diameter

Mean

5.10963

5.05590

5.00217

4.94844

4.89471

X Demonstration Problem 18.1:

Control Chart

Output for R Control Chart

Construct an R chart for the 20 samples of data in Demonstration Problem 18.1 on bearings.

Demonstration Problem 18.2: R Control Chart

Control Chart: Bearing Diameter

Sigma level: 3

20 19

18 17

16 15

14 13

12 11

10 9

8 7

6 5

4 3

2 1

Range

0.0

Bearing Diameter

UCL = .2725

Average = .1360

LCL = .0000

Demonstration Problem 18.2: R Control Chart

Monitor proportion in noncompliance: 1. Decide on the quality to be measured. 2. Determine a sample size. 3. Gather 20 to 30 samples. 4. Compute the sample proportion for each

sample. 5. Determine the average sample proportion

for all samples. 6. Compute the UCL and the LCL

P Charts

P Chart Formulas

A company produces bond paper and, at regular

intervals, samples of 50 sheets of paper are

inspected. Suppose 20 random samples of 50 sheets

of paper each are taken during a certain period of

time, with the following numbers of sheets in

noncompliance per sample.

Construct a p chart from these data.

Demonstration Problem 18.3: Twenty Samples of Bond Paper

Sample n

Number Out of

Compliance Sample n

Number Out of

Compliance 1 50 4 11 50 2 2 50 3 12 50 6 3 50 1 13 50 0 4 50 0 14 50 2 5 50 5 15 50 1 6 50 2 16 50 6 7 50 3 17 50 2 8 50 1 18 50 3 9 50 4 19 50 1

10 50 2 20 50 5

Demonstration Problem 18.3: Twenty Samples of Bond Paper

Sample n n non

1 50 4 0.08 11 50 2 0.04 2 50 3 0.06 12 50 6 0.12 3 50 1 0.02 13 50 0 0.00 4 50 0 0.00 14 50 2 0.04 5 50 5 0.10 15 50 1 0.02 6 50 2 0.04 16 50 6 0.12 7 50 3 0.06 17 50 2 0.04 8 50 1 0.02 18 50 3 0.06 9 50 4 0.08 19 50 1 0.02

10 50 2 0.04 20 50 5 0.10

Demonstration Problem 18.3: Preliminary Calculations

Demonstration Problem 18.3: Centerline, UCL, and LCL Computations

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

0 5 10 15 20

Sample Number

P = .053

UCL = .148

LCL = 0

Demonstration Problem 18.3: P Control Chart

Demonstration Problem 18.3: MINITAB P Control Chart

Monitor number of nonconformances per item: 1. Decide on nonconformances to be evaluated. 2. Determine the number of items to be studied

(at least 25). 3. Gather items. 4. Determine the value of c for each item by summing

the number of nonconformances in the item. 5. Determine the average number of

nonconformances per item. 6. Determine the UCL and the LCL.

c Charts

c Chart Formulas

A manufacturer produces gauges to measure oil pressure. As part of the company’s statistical process control, 25 gauges are randomly selected and tested for non-conformances. The results are shown here. Use these data to construct a c chart that displays the non-conformances per item.

Demonstration Problem 18.4: Number of Nonconformities in Oil Gauges

Item Number

Number of Nonconformities

Item Number

Number of Nonconformities

1 2 14 2 2 0 15 1 3 3 16 4 4 1 17 0 5 2 18 2 6 5 19 3 7 3 20 2 8 2 21 1 9 0 22 3

10 0 23 2 11 4 24 0 12 3 25 3 13 2

Demonstration Problem 18.4: Number of Nonconformities in Oil Gauges

Demonstration Problem 18.4: c Chart Calculations

0 1 2 3 4 5 6 7

0 5 10 15 20 25 Item Number

UCL = 6.2

LCL = 0

c = 2.0

Demonstration Problem 18.4: c Chart

Demonstration Problem 18.4: MINITAB c Chart

Interpreting Control Charts

• Points are above UCL and/or below LCL • Eight or more consecutive points fall above or below the

centerline. Ten out of 11 points fall above or below the centerline. Twelve out of 14 points fall above or below the centerline.

• A trend of 6 or more consecutive points (increasing or decreasing) is present

• Two out of 3 consecutive values are in the outer one-third.

• Four out 5 consecutive values are in the outer two-thirds.

• The centerline shifts from chart to chart.