7. Statistical Process Control Steps Produce Good Provide Service Stop Process Yes No Assign. Variation? Take Sample Inspect Sample Find Out Why Create Control Chart Start

9. Control Chart Types Control Charts R Chart Variables Charts Attributes Charts X Chart P Chart C Chart Continuous Numerical Data Categorical or Discrete Numerical Data

10. Natural and Assignable Variations

11. Monitoring Variations by Using Control Charts

14. Theoretical Basis of Sampling As sample size gets large enough, sampling distribution becomes almost normal regardless of population distribution. Central Limit Theorem

15. Central Limit Theorem Mean Standard deviation (STD)

16. Normalization of Sample Distributions Uniform Normal Beta (mean) Three population distributions

17. Relationship of Confidence and Number of STD (  ) Properties of normal distribution

20.  X Chart and Control Limits (Formula 1)  If the process mean and standard deviation are known: where: _ X = average mean of samples Z = number of standard deviations  x = standard deviation of sample means  x = process standard deviation, n = number of observations in a sample

21. Sample Range at Time i # Samples Sample Mean at Time i From Table S6.1  X Chart and Control Limits (Formula 2)

22. Factors for Computing Control Chart Limits (3 sigma, p.227)

25. R Chart Control Limits Sample Range at Time i # Samples From Table S6.1

28. X-bar and R Charts Complement Each Other

29. Three Types of Output for Variable Frequency Lower control limit Size Weight, length, speed, etc. Upper control limit (b) In statistical control, but not capable of producing within control limits. A process in control (only natural causes of variation are present) but not capable of producing within the specified control limits; and (c) Out of control. A process out of control having assignable causes of variation. (a) In statistical control and capable of producing within control limits. A process with only natural causes of variation and capable of producing within the specified control limits.

31. Control limit of p Charts # Defective Items in Sample i Size of sample i z = 2 for 95.5% limits; z = 3 for 99.7% limits

34. Control Limits of c-Charts # Defects in Unit i # Units Sampled Use 3 for 99.7% limits

37. Process Capability C pk Measure difference between actual and desire output quality Application of Process Capacity : Technology selection Performance evaluation

38. Meanings of C pk Measures C pk = negative number C pk = zero C pk = between 0 and 1 C pk = 1 C pk > 1

41. OC Curve 100% Inspection % Defective in Lot P(Accept Whole Shipment) 100% 0% Cut-Off Return whole shipment Keep whole shipment 1 2 3 4 5 6 7 8 9 10 0

42. OC Curve with Less than 100% Sampling P(Accept Whole Shipment) 100% 0% % Defective in Lot Cut-Off Return whole shipment Keep whole shipment Probability is not 100%: Risk of keeping bad shipment or returning good one. 1 2 3 4 5 6 7 8 9 10 0

45. An Operating Characteristic (OC) Curve Showing Risks  = 0.10 Consumer’s risk for LTPD Probability of Acceptance Percent Defective 0 1 2 3 4 5 6 7 8 100 95 75 50 25 10 0  = 0.05 producer’s risk for AQL Bad lots Indifference zone Good lots LTPD AQL