1. CHAPTER 11 Quality and Assurance McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Definition of Quality Conformance to specifications uThis definition is good because conformance is something that can be measured, and therefore can be improved. uThis definition is bad because it does not capture all of the things we mean by quality, especially when talking about the perception of the customer. Quality includes many things that are hard to measure. 11-2

3. Statistical Quality Control uRelies on properties of the normal distribution. The Central Limit Theorem justifies the assumption that the average of measurements within a subgroup follows a normal distribution. uControl charts are based on the following property of the normal distribution: the likelihood that an observation falls within two standard deviations of the mean(that is,  2  ) is about 0.95 and within three standard deviations of the mean (  3  ) is larger than 0.99. 11-3

4. The X Bar Chart uGoal: To test if the mean of a process is stable. Appropriate when measuring a variable such as length, width, weight, etc. uThe method relies on the fact that averages of observations tend towards the normal distribution by the Central Limit Theorem. 11-4

5. Summary of Steps for Constructing X Bar Charts 1.Form Subgroups of data of size 4 or 5 typically. 2.Average observations within a subgroup. 3.Maintain a running graph on the subgroup averages. 4.Define UCL and LCL as the upper and lower control limits. They are of the form: 5.One chooses k to be either 2 or 3 typically. An observation that falls outside the control limits is more likely to be due to a shift in the process mean than due to chance. This event signals an out-of- control situation for which an assignable cause is sought. (A typical X bar chart appears on the next slide.) 11-5

6. Chart for Tracking Arm Data Chart for Tracking Arm Data 11-6

7. R Charts Goal: To determine if the process variation appears to changed significantly. In most cases, one is concerned only if variation increases significantly, so that the lower control limit is often taken to be 0. 11-7

8. Summary of Steps for Constructing R Charts uForm subgroups typically of size 4 or 5 as one does for an X bar chart. uCompute the range of each subgroup. The range is the difference between the largest and smallest observations within a subgroup. uThe upper and lower control limits are given by: 11-8

9. R Chart for Tracking Arm Data 11-9

10. Control Charts for Attributes. The p chart. uThe X bar and R charts are appropriate when considering a measurable quantity such as length or width. uHowever, one is often concerned if the item has a specific attribute. Examples: does the item function or not? Does it have the right color? Does it possess the right scent or taste? uAssign a 1 to an item that possesses the desirable attribute and a 0 to an item that doesn’t (or vice versa). 11-10

11. Constructing p charts uSubgroups for p charts are typically larger than for X bar and R charts. For most applications n>30 should suffice. uThe upper and lower control limits are given by: Where p bar is the average of the observed values of the 1’s and 0’s observed in the subgroup. (See the next slide for an example.) 11-11

12. Revised p chart for Xezet floppy disk data (Refer to Example 11.2) 11-12

13. The c Chart uThe c chart is appropriate when counting the number of defects per unit. For example, five dings on an automobile might be considered acceptable for shipping, but any more would require re-work. It is based on the property that if defects occur completely at random, the number of defects per unit follows the Poisson distribution. One uses the normal approximation of the Poisson, again justified by the Central Limit Theorem. 11-13

14. Constructing the c chart uThe upper and lower control limits for the c chart (assuming 3  limits) are: which is based on the fact that both the mean and variance of Poisson random variable with parameter c is equal to c. 11-14

15. Acceptance Sampling Acceptance sampling utilizes statistical principles to determine the acceptability of a lot of items based on the number of defects observed in a sample. The purpose is to avoid 100% inspection, which is too costly in most applications (or impossible if inspection results in destruction of the item). 11-15

16. Types of Sampling Plans uSingle Sampling. Sample n items. If the number of defectives exceeds a number c, reject the lot. Otherwise accept the lot. uDoubling Sampling. First select a sample of size n 1. If the number of defects in the sample is less than c 1, accept the lot. If it is greater than c 2, reject the lot, and if it is between the two, take another sample of size n 2. Accept the lot if the cumulative number of defects in the two samples is less than c 3. uSequential Sampling. After each item is sampled on decides to a) accept the lot, b) reject the lot, or c) continue sampling. 11-16

17. Notation N = number of items in a lot n = number of items in a sample M = number of defectives in a lot  = Consumer’s risk. The probability of accepting bad lots.  = Producer’s risk. The probability of rejecting good lots. c = rejection level X = number of defectives in the sample p = Proportion of defectives in the lot p 0 = Acceptable Quality Level (AQL) p 1 = Lot Tolerance Percent Defective (LTPD) 11-17

18. Single Sampling Plans for Attributes These plans are based on the properties of the binomial distribution, since the number of defectives in a sample of size n when the true proportion of defectives in the lot is p, has the binomial distribution with parameters n and p. 11-18

19. The OC (Operating Characteristic) Curve OC(p) = P{Accepting the lot |proportion of defectives in lot = p} = P{X  c | proportion of defectives in the lot = p} 11-19

20. Revised OC Curve for Spire Records (n = 25) 11-20

21. Double Sampling Plans for Attributes uA double sampling plan depends on five numbers: n 1, n 2, c 1, c 2, and c 3. One initially draws a sample of size n 1 and counts the number of defectives. If it is less than or equal to c 1 the lot is accepted. If it is more than c 2, the lot is rejected. If it is larger than c 1, but less than or equal to c 2, another sample of size n 2 is drawn. If the total number of defectives in both samples is less than or equal to c 3, the lot is accepted, otherwise it is rejected. uTables are available for optimizing double sampling plans to achieve desired values of  and . 11-21

22. Sequential Sampling Plans After each item is sampled, the lot is either accepted, rejected, or sampling is continued. The three regions are separated by two straight lines of the form: L 1 = - h 1 + sn L 2 = h 2 + sn (Refer to Figure 11-16 on the next slide for a typical sequential sampling plan. Formulas for the constants h 1, h 2, and s can be found in the text.) 11-22

23. Two Realizations of a Sequential Sampling Plan 11-23

24. Average Outgoing Quality 11-24

25. AOQ Curves for Spire Records (Refer to Example 11.9) 11-25

26. Total Quality Management According to Feigenbaum “ Total quality control is an effective system for integrating the quality development, quality- maintenance, and quality improvement efforts of the various groups in an organization so as to enable marketing, engineering, production, and service at the most economical levels which allow for full customer satisfaction.” 11-26

27. Listening to the Customer An important part of TQM is determining what the customer wants. This is done via uFocus groups uCustomer interviews uCustomer surveys Downsides: customers are not in a position to think of new possibilities, or customers desires are technically impossible to achieve. Also, surveys can lead to bias depending on the manner in which questions are worded. 11-27

28. Organizing for Quality uThe quality function should not be relegated to a single department, but should permeate the entire organization uThe quality function must have an ongoing contact with customers. uMust transcend functional organizational boundaries uMust be overseen from a high level of the firm. 11-28

29. Recognizing Quality uDeming Prize. Established in Japan in 1951 by quality guru W. Edwards Deming. The prestigious prize has been awarded to Japanese companies almost every year since inception in several categories. uMalcolm Baldrige National Quality Award established by the U.S. Dept of Commerce in 1987 recognizes excellence in a) manufacturing companies b) service companies and subsidiaries, and c) small businesses. uISO 9000. A certification program established by the International Organization for Standards based in Switzerland. Certification can cost upwards of $1 million for large companies. 11-29

30. Designing for Quality While much of quality control deals with monitoring a process or inspecting items after production, there is a substantial literature on means of designing quality into the product directly. Taguchi methods focus on: uSystem Design uParameter Design uTolerance Design. 11-30

31. Design for Manufacturability DFM Definition: Designing a product so that it is easy to manufacture. Better designs promote better quality. uBoothroyd and Dewhurst developed effective scoring techniques for designs in terms of ease of manufacturability. uUlrich and Eppinger recommend develop a scorecard for measuring manufacturing complexity. 11-31

32. DFM (concluded) Reasons why firms resist DFM efforts: uNo time. uNot invented here. uAssembly cost already low. uVolume low. uClassical accounting systems do not recognize cost savings of DFM. 11-32