1. Quality Control McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

2. You should be able to: 1. List and briefly explain the elements in the control process 2. Explain how control charts are used to monitor a process, and the concepts that underlie their use 3. Use and interpret control charts 4. Perform run tests to check for nonrandomness in process output 5. Assess process capability Instructor Slides 10-2

3. Quality Control A process that evaluates output relative to a standard and takes corrective action when output doesn’t meet standards If results are acceptable no further action is required Unacceptable results call for correction action Instructor Slides 10-3

4. Instructor Slides 10-4

5. Inspection An appraisal activity that compares goods or services to a standard Inspection issues: 1. How much to inspect and how often 2. At what points in the process to inspect 3. Whether to inspect in a centralized or on-site location 4. Whether to inspect attributes or variables Instructor Slides 10-5

6. 10-6 How Much/How Often Where/When Centralized vs. On-site InputsTransformationOutputs Acceptance sampling Process control Acceptance sampling Figure 10.2

7. Instructor Slides 10-7

8. 10-8 University: Is each student achieving acceptable performance? Chemistry: Does each product contain the correct amount of chemical? Automobile: Does the automobile performs as intended? Bank: Are the transaction completed with precision?

9. 10-9 There are two general approaches to quality management. The inspection approach (inspects the quality of input and the finished product) The detection approach (focuses on the production process, and detects when it starts going out of control)

10. 10-10 There are two general approaches to quality management. The inspection approach (inspects the quality of input and the finished product) The detection approach (focuses on the production process, and detects when it starts going out of control)

11. Typical Inspection Points: Raw materials and purchased parts Finished products Before a costly operation Before an irreversible process Before a covering process Instructor Slides 10-11

12. Effects on cost and level of disruption are a major issue in selecting centralized vs. on-site inspection Centralized Specialized tests that may best be completed in a lab More specialized testing equipment More favorable testing environment On-Site Quicker decisions are rendered Avoid introduction of extraneous factors Quality at the source Instructor Slides 10-12

13. 10-13 Table 10.1

14. 10-14

15. Quality control seeks Quality of Conformance A product or service conforms to specifications A tool used to help in this process: SPC Statistical evaluation of the output of a process Helps us to decide if a process is “in control” or if corrective action is needed Statistical Process Control (SPC) is a form of hypothesis testing employed in industry. Its objective is to monitor the quality of a firm’s products and services Instructor Slides 10-15

16. Two basic questions: concerning variability: 1. Issue of Process Control Are the variations random? If nonrandom variation is present, the process is said to be unstable. 2. Issue of Process Capability Given a stable process, is the inherent variability of the process within a range that conforms to performance criteria? Instructor Slides 10-16

17. Variation Random (common cause) variation: Natural variation in the output of a process, created by countless minor factors Assignable (special cause) variation: A variation whose cause can be identified. A nonrandom variation Instructor Slides 10-17

18. SPC involves periodically taking samples of process output and computing sample statistics: Sample means The number of occurrences of some outcome Sample statistics are used to judge the randomness of process variation Instructor Slides 10-18

19. Sampling Distribution A theoretical distribution that describes the random variability of sample statistics The normal distribution is commonly used for this purpose Central Limit Theorem The distribution of sample averages tends to be normal regardless of the shape of the process distribution Instructor Slides 10-19

20. Instructor Slides 10-20

21. Sampling and corrective action are only a part of the control process Steps required for effective control: Define: What is to be controlled? Measure: How will measurement be accomplished? Compare: There must be a standard of comparison Evaluate: Establish a definition of out of control Correct: Uncover the cause of nonrandom variability and fix it Monitor: Verify that the problem has been eliminated Instructor Slides 10-21

22. Control Chart A time ordered plot of representative sample statistics obtained from an ongoing process (e.g. sample means), used to distinguish between random and nonrandom variability Control limits The dividing lines between random and nonrandom deviations from the mean of the distribution Upper and lower control limits define the range of acceptable variation Instructor Slides 10-22

23. Each point on the control chart represents a sample of n observations Instructor Slides 10-23

24. 10-24 The essence of statistical process control is to assure that the output of a process is random so that future output will be random.

25. 10-25

26. 10-26 Variations and Control Random variation: Natural variations in the output of a process, created by countless minor factors Assignable variation: A variation whose source can be identified

27. 10-27 All products exhibit some degree of variation. There are two sources of variation Random or chance variation: Natural variations in the output of process, created by countless minor factors that cannot be eliminated without changing the process Assignable variation: A variation whose source can be identified and eliminated

28. 10-28 Sampling distribution Process distribution Mean Figure 10.5 μ = E(X) s = σ/√n

29. 10-29 Mean  95.44% 99.74%  Standard deviation Figure 10.6

30. 10-30 Sampling distribution Process distribution Mean Lower control limit Upper control limit Figure 10.7

31. Type I error Concluding a process is not in control when it actually is. The probability of rejecting the null hypothesis when the null hypothesis is true. Manufacturer’s Risk Type II error Concluding a process is in control when it is not. The probability of failing to reject the null hypothesis when the null hypothesis is false. Consumer’s Risk Instructor Slides 10-31

32. 10-32 In controlOut of control In controlNo ErrorType I error (producers risk) Out of control Type II Error (consumers risk) No error Table 10.2

33. Instructor Slides 10-33

34. Instructor Slides 10-34

35. Variables generate data that are measured Mean control charts Used to monitor the central tendency of a process. “x- bar” charts Range control charts Used to monitor the process dispersion R charts Instructor Slides 10-35

36. 10-36

37. Instructor Slides 10-37

38. 10-38 Start with k samples when the process is under control. Average the k sample averages. Average the k sample ranges. The x chart This chart is employed to determine whether the distribution mean has changed. Upper control limit Lower control limit

39. 10-39    n zx 2 UCL = LCL =    n zx 2

40. 10-40 Given the following samples which have been collected from the length of time to process loan application:

41. 10-41 Q1: If the standard deviation of the process is σ =.02, find the three-sigma (z = 3) control limits. Grand Mean = (12.10 + 12.12 + 12.11 + 12.10 + 12.12)/5 = 12.11 UCL = 12.11 + (3)(.02 / 2) = 12.14 LCL = 12.11 - (3)(.02 /2) = 12.08

42. Used to monitor the central tendency of a process Instructor Slides 10-42

43. 10-43 Q2: Find the mean control limits assuming that the standard deviation is not known: R = (.03+.05+.06+.04+.05) / 5 =.046 UCL = 12.11 + (.73)(.046) = 12.14358 LCL = 12.11 – (.73)(.046) = 12.07642

44. Used to monitor process dispersion Instructor Slides 10-44

45. 10-45 Range chart UCL = (2.28)(.046) =.10488 LCL =(0)(.046) = 0

46. Instructor Slides 10-46

47. 10-47 x-Chart UCL Does not reveal increase UCL LCL R-chart Reveals increase Figure 10.10B (process variability is increasing) Sampling Distribution

48. To determine initial control limits: Obtain 20 to 25 samples Compute appropriate sample statistics Establish preliminary control limits Determine if any points fall outside of the control limits If you find no out-of-control signals, assume the process is in control If you find an out-of-control signal, search for and correct the assignable cause of variation Resume the process and collect another set of observations on which to base control limits Plot the data on the control chart and check for out-of-control signals Instructor Slides 10-48

49. Attributes generate data that are counted. p-Chart Control chart used to monitor the proportion of defectives in a process c-Chart Control chart used to monitor the number of defects per unit Instructor Slides 10-49

50. 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 Instructor Slides 10-50

51. Instructor Slides 10-51

52. 10-52 Using 4 samples of 100 credit card statements each, an auditor found the following: Sample ## with Error 14 23 35 48 Total20

53. 10-53 The fraction defective estimate is: = 20 / (4 x 100) =.05 Q: What is the probability distribution for this experiment? The standard deviation of fraction defective with sample size n = 100 is: σ p =

54. 10-54 σ p = σ p =.02179 Note that n = 100 is the sample size and not the number of samples

55. 10-55 Control limits are computed using the following formulas: UCL = P + Z σ p LCL = P - Z σ p For example Z =3 results in the following control limits: UCL =.05 + (3)(.02179) =.11537 LCL =.05 – (3)(.02179) =.01537

56. 10-56 Sample # # with Error Fraction Defective In control? 14.04Yes 23.03Yes 35.05Yes 48.08Yes

57. 10-57 For Z= 3, the type I error for example 2 is calculated from the Normal probability table: α = 1 –(.4987 x 2) =.0026

58. 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 Instructor Slides 10-58

59. 10-59 The following table displays the number of scratches in the exterior paint of 4 samples of ten automobiles each: Sample #Number 135 242 328 445 Total150

60. 10-60 The average number of defects is: = 150 / (4 x 10) = 3.75 Q: What is the probability distribution for this experiment? The standard deviation is: σ c = σ c = 1.9365

61. 10-61 Control limits are computed using the following formulas: UCL = + Z LCL = - Z For example Z =3 results in the following control limits: UCL = 3.75 + (3)(1.9365) = 9.5595 LCL = 3.75 – (3)(1.9365) = -2.0595 or 0

62. At what points in the process to use control charts What size samples to take What type of control chart to use Variables Attributes Instructor Slides 10-62

63. Even if a process appears to be in control, the data may still not reflect a random process Analysts often supplement control charts with a run test Run test A test for patterns in a sequence Run Sequence of observations with a certain characteristic Instructor Slides 10-63

64. Instructor Slides 10-64

65. 10-65 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

66. 10-66 Trend Cycles Bias Mean shift Too much dispersion

67. 10-67 Counting Above/Below Median Runs(7 runs) Counting Up/Down Runs(8 runs) U U D U D U D U U D B A A B A B B B A A B Figure 10.12 Figure 10.13 Counting Runs

68. 10-68 Statistical process control is based on repetitive sampling procedures and hypotheses tests. Therefore, we can run tests to detect an out of control state based on patterns developed by the repeated measurements. We may conclude that a process is out of control when certain patterns of the process behavior are detected, even if no observation falls outside the control limits.

69. 10-69 Above/Below Median runs: E(r) med = N/2 + 1 Up/Down runs: E(r) u/d = (2N – 1) /3

70. 10-70 Text example 6, pages 468-469

71. Once a process has been determined to be stable, it is necessary to determine if the process is capable of producing output that is within an acceptable range Tolerances or specifications Range of acceptable values established by engineering design or customer requirements Process variability Natural or inherent variability in a process Process capability The inherent variability of process output (process width) relative to the variation allowed by the design specification (specification width) Instructor Slides 10-71

72. Lower Specification Upper Specification Process variability (width) is less than the specification width Lower Specification Upper Specification Process variability (width) matches specifications width Lower Specification Upper Specification Process variability (width) exceeds specifications Instructor Slides 10-72

73. Instructor Slides 10-73

74. Used when a process is not centered at its target, or nominal, value Instructor Slides 10-74

75. 10-75 C C The control chart is divided into 6 horizontal zones. A A B B Upper control limit lower control limit – Several pattern-tests can be applied to these zones. Each one represents a rare event, which if it occurs indicates an out of control state. Example: Zones for the control chart. X

76. 10-76 2 out of 3 points in a row in zone A or beyond (same side of CL). AAAA CCCC BBBB One point beyond zone A. Nine points in a row in zone C or beyond (on same side of CL). Six increasing (decreasing) points in a row. Fourteen points in a row alternating up and down. 4 out of 5 points in a row in zone B or beyond. 15 points in a row in zone C (on both sides of CL). AAAA CCCC BBBB AAAA CCCC BBBB AAAA CCCC BBBB AAAA CCCC BBBB AAAA CCCC BBBB AAAA CCCC BBBB AAAA CCCC BBBB 8 points in a row beyond zone C (on both sides of CL). 1 2 3 4 5 6 7 8 9 One point beyond zone A. One point beyond zone A. One point beyond zone A. 12 3 4 5 6

77. 10-77 The proportion of defectives in a computer disks production line has to be monitored. The experiment Every hour a random sample of 200 disks is taken. Each disk is tested to determine if it is defective. Based on the first 40 samples, draw a p chart and determine whether the process was out of control.

78. 10-78 Solution Sample Defective Proportion 119.095 2 5.025 316.080..……………………………... Mean sample proportion = p = (.095+..25+.080+…)/40 =.05762 The zones

79. 10-79 Zone A.05762+3(.01648) =.1071.05762+2(.01648) =.09057.05762+(.01648) =.0741 Zone A Zone B Zone C There is no evidence to infer that the process was out of control

80. 10-80 Managers should have response plans to investigate cause May be false alarm (Type I error) May be assignable variation

81. Simplify Standardize Mistake-proof Upgrade equipment Automate Instructor Slides 10-81

82. Quality is a primary consideration for nearly all customers Achieving and maintaining quality standards is of strategic importance to all business organizations Product and service design Increase capability in order to move from extensive use of control charts and inspection to achieve desired quality outcomes Instructor Slides 10-82