Chapter 10

1. Chapter 10 Quality Control

2. Acceptance sampling Process control Continuous improvement Phases of Quality Assurance Inspection and corrective action during production Inspection of lots before/after production Quality built into the process The least progressive The most progressive Figure 10.1

3. How Much/How Often Where/When Centralized vs. On-site Inputs Transformation Outputs Inspection Acceptance sampling Acceptance sampling Process control Figure 10.2

4. Cost Optimal Amount of Inspection Inspection Costs Total Cost Cost of inspection Cost of passing defectives Figure 10.3

5. Raw materials and purchased parts Finished products Before a costly operation Before an irreversible process Before a covering process Where to Inspect in the Process

6. Examples of Inspection Points Table 10.1

7. Statistical Process Control: Statistical evaluation of the output of a process during production The essence of statistical process control is to assure that the output of a process is random so that future output will be random. Quality of Conformance :A product or service conforms to specifications Statistical Control

8. Abnormal variationdue to assignable sources Out ofcontrol UCL Mean Normal variationdue to chance LCL Abnormal variationdue to assignable sources 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample number Control Chart Figure 10.4

9. Control Chart Purpose: to monitor process output to see if it is random A time ordered plot representative sample statistics obtained from an on going process (e.g. sample means) Upper and lower control limits define the range of acceptable variation Control Chart

10. Standard deviation     Mean 95.44% 99.74% Normal Distribution Figure 10.6

11. Samplingdistribution Processdistribution Mean Lowercontrollimit Uppercontrollimit Control Limits: Sampling Distribution & Process Distribution Figure 10.7

12. Type I error Concluding a process is not in control when it actually is. Type II error Concluding a process is in control when it is not. SPC Errors

13. /2 /2 Mean LCL UCL Probabilityof Type I error Type I Error Figure 10.8

14. UCL LCL 1 2 3 4 Sample number Observations from Sample Distribution Figure 10.9

15. Control Charts for Variables Variables generate data that are measured. Image: http://www.asprova.jp/mrp/glossary/en/cat254/x-r-1.html

16. x-Chart Mean and Range Charts (process mean is shifting upward) Sampling Distribution UCL Detects shift LCL UCL Does notdetect shift R-chart LCL Figure 10.10A

17. x-Chart Mean and Range Charts Sampling Distribution (process variability is increasing) UCL Does notreveal increase LCL UCL R-chart Reveals increase LCL Figure 10.10B

18. Used to monitor the proportion of defectives in a process When observations can be placed into two categories. Good or bad Pass or fail Operate or don’t operate When the data consists of multiple samples of several observations each p chart Control Chart for Attributes Attributes generate data that are counted

19. Used to monitor the number of defects per unit Advantages Use only when the number of occurrences per unit of measure can be counted; non-occurrences cannot be counted. Scratches, chips, dents, or errors per item Cracks or faults per unit of distance Breaks or Tears per unit of area Bacteria or pollutants per unit of volume Calls, complaints, failures per unit of time c Chart

20. At what point in the process to use control charts What size samples to take What type of control chart to use Variables Attributes Use of Control Charts

21. Run test – a test for randomness Any sort of pattern in the data would suggest a non-random process All points are within the control limits - the process may not be random Run Tests

22. Trend Cycles Bias Mean shift Too much dispersion Nonrandom Patterns in Control charts

23. Counting Above/Below Median Runs (7 runs) B A A B A B B B A A B Counting Up/Down Runs (8 runs) U U D U D U D U U D Counting Runs

24. Managers should have response plans to investigate cause May be false alarm (Type I error) May be assignable variation NonRandom Variation

25. Process Capability • Tolerances or specifications • Range of acceptable values established by engineering design or customer requirements • Process variability • Natural variability in a process • Process capability • Process variability relative to specification

26. LowerSpecification UpperSpecification Process Capability Figure 10.15 A. Process variability matches specifications LowerSpecification UpperSpecification B. Process variability well within specifications LowerSpecification UpperSpecification C. Process variability exceeds specifications

27. specification width process width Process capability ratio, Cp = Upper specification – lower specification 6 Cp = Process Capability Ratio If the process is centered use Cp If the process is not centered use Cpk

28. Process may not be stable Process output may not be normally distributed Process not centered but Cp is used Limitations of Capability Indexes

29. Example 8 Cp > 1.33 is desirable Cp = 1.00 process is barely capable Cp < 1.00 process is not capable

30. Upperspecification Lowerspecification 1350 ppm 1350 ppm 1.7 ppm 1.7 ppm Processmean +/- 3 Sigma +/- 6 Sigma 3 Sigma and 6 Sigma Quality

31. Simplify Standardize Mistake-proof Upgrade equipment Automate Improving Process Capability

32. Traditionalcost function Cost Taguchicost function Lowerspec Target Upperspec Taguchi Loss Function Figure 10.17

33. List and briefly explain the elements of the control process. Explain how control charts are used to monitor a process, and the concepts that underlie their use. Use and interpret control charts. Use run tests to check for nonrandomness in process output. Assess process capability. Learning Objectives