1. 1 1 Slide Statistical Process Control (Quality Control) Professor Ahmadi

2. 2 2 Slide What is Quality? “ The quality of a product or service is a customer’s perception of the degree to which the product or service meets his or her expectations.” Dimensions of QualityDimensions of Quality Determinants of QualityDeterminants of Quality Costs of QualityCosts of Quality

3. 3 3 Slide Introduction n Quality control (QC) includes the activities from the suppliers, through production, and to the customers. n Incoming materials are examined to make sure they meet the appropriate specifications. n The quality of partially completed products are analyzed to determine if production processes are functioning properly. n Finished goods and services are studied to determine if they meet customer expectations.

4. 4 4 Slide QC Throughout Production Systems Raw Materials, Parts, and SuppliesProductionProcesses Products and Services Inputs ConversionOutputs Control Charts and Acceptance Tests Control Charts and Acceptance Tests Control Charts Quality of Inputs Outputs Partially Completed Products n

5. 5 5 Slide Quality Gurus n W. Edwards Deming Assisted Japan in improving productivity and quality after World War IIAssisted Japan in improving productivity and quality after World War II In 1951 Japan established Deming PrizeIn 1951 Japan established Deming Prize US was slow in recognizing his contributionsUS was slow in recognizing his contributions Introduced Japanese companies to the Plan-Do- Check-Act (PDCA) cycle (developed by Shewart)Introduced Japanese companies to the Plan-Do- Check-Act (PDCA) cycle (developed by Shewart) Developed 14 Points for managersDeveloped 14 Points for managers n Joseph M. Juran Played early role in teaching Japan about qualityPlayed early role in teaching Japan about quality Wrote Quality Control HandbookWrote Quality Control Handbook

6. 6 6 Slide Quality Gurus (Continued) n Philip B. Crosby Wrote Quality Is Free in 1979Wrote Quality Is Free in 1979 Company should have the goal of zero defectsCompany should have the goal of zero defects Cost of poor quality is greatly underestimatedCost of poor quality is greatly underestimated n Armand V. Feigenbaum Developed concept of total quality control (TQC)Developed concept of total quality control (TQC) Responsibility for quality must rest with the persons who do the work (quality at the source)Responsibility for quality must rest with the persons who do the work (quality at the source)

7. 7 7 Slide ISO 9000 Standards n Quality management guidelines developed by the International Organization for Standardization n Companies become certified by applying to third-party providers who assess the level of conformity to the standards n More than 300,000 companies worldwide are ISO 9000- certified n The US big three automakers have adopted a similar set of standards called QS-9000

8. 8 8 Slide Elements of TQM n Top management commitment and involvement n Customer involvement n Design products for quality n Design production processes for quality n Control production processes for quality n Developing supplier partnerships n Customer service, distribution, and installation n Building teams of empowered employees n Benchmarking and continuous improvement

9. 9 9 Slide Statistical Process Control (SPC) n The goal of SPC is to determine whether the process can be continued or whether it should be adjusted to achieve a desired quality level. n If the variation in the quality of the production output is due to assignable causes (operator error, worn-out tooling, bad raw material,... ) the process should be adjusted or corrected as soon as possible. n If the variation in output is due to common (natural) causes (variation in materials, humidity, temperature,.) which the manager cannot control, the process does not need to be adjusted.

10. 10 Slide Decisions and State of the Process n Type I and Type II Errors State of Production Process State of Production Process Decision Decision CorrectDecision Type II Error Allow out-of-control process to continue CorrectDecision Type I Error Adjust in-control process AdjustProcess ContinueProcess H 0 True In Control H a True Out of Control

11. 11 Slide Definitions n Type I error - Based on sample information, a good (quality) population is rejected n Type II error - Based on sample information, a bad (quality) population is accepted Producer’s risk (  ) - For a particular sampling plan, the probability that a Type I error will be committed Producer’s risk (  ) - For a particular sampling plan, the probability that a Type I error will be committed Consumer’s risk (  ) - For a particular sampling plan, the probability that a Type II error will be committed Consumer’s risk (  ) - For a particular sampling plan, the probability that a Type II error will be committed

12. 12 Slide Control Charts n SPC uses graphical displays known as control charts to monitor a production process. n Control charts provide a basis for deciding whether the variation in the output is due to common causes (in control) or assignable causes (out of control) n Two important lines on a control chart are the upper control limit (UCL) and lower control limit (LCL) n These lines are chosen so that when the process is in control, there will be a high probability that the sample finding will be between the two lines n Values outside of the control limits provide strong evidence that the process is out of control.

13. 13 Slide Types of Control Charts n An x chart is used if the quality of the output is measured in terms of a variable such as length, weight, temperature, and so on. n x represents the mean value found in a sample of the output. n An R chart is used to monitor the range of the measurements in the sample. n A p chart is used to monitor the proportion defective in the sample. n An C chart is used to monitor the number of defective items in the sample.

14. 14 Slide Control Charts n Primary purpose of control charts is to indicate at a glance when production processes might have changed sufficiently to affect product quality. n If the indication is that product quality has deteriorated, or is likely to, then corrective is taken. n If the indication is that product quality is better than expected, then it is important to find out why so that it can be maintained. n Use of control charts is often referred to as statistical process control (SPC).

15. 15 Slide Constructing Control Charts n Vertical axis provides the scale for the sample information that is plotted on the chart. n Horizontal axis is the time scale. n Horizontal center line is ideally determined from observing the capability of the process. n Two additional horizontal lines, the lower and upper control limits, typically are 3 standard deviations below and above, respectively, the center line.

16. 16 Slide Central Limit Theorem n The central limit theorem is: Sampling distributions can be assumed to be normally distributed even though the population (lot) distributions are not normal. n The theorem allows use of the normal distribution to easily set limits for control charts and acceptance plans for both attributes and variables.

17. 17 Slide Sampling Distributions n The sampling distribution can be assumed to be normally distributed unless sample size (n) is extremely small. The mean of the sampling distribution ( x ) is equal to the population mean (  ). The mean of the sampling distribution ( x ) is equal to the population mean (  ). The standard error of the sampling distribution (  x ) is smaller than the population standard deviation (  ) by a factor of 1/ The standard error of the sampling distribution (  x ) is smaller than the population standard deviation (  ) by a factor of 1/ = -

18. 18 Slide 3  Control Chart Factors for Variables (Source: American Society of Testing Materials) Control Limit Factor Control Limit Factor Samplefor Sample Mean for Sample Range Size n A 2 D 3 D 4 21.88003.267 31.02302.575 40.72902.282 50.57702.116 100.3080.2231.777 150.2230.3481.652 200.1800.4141.586 250.1530.4591.541 Over 25[0.75(1/SQRT(n)]0.45+.001n1.55-.0015n

19. 19 Slide Definitions n Acceptance plan - Sample size (n) and maximum number of defectives (c) that can be found in a sample to accept a lot n Acceptable quality level (AQL) - If a lot has no more than AQL percent defectives, it is considered a good lot n Lot tolerance percent defective (LTPD) - If a lot has greater than LTPD, it is considered a bad lot