1. 1 1 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. John Loucks St. Edward’s University...................... SLIDES. BY

2. 2 2 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 19 Statistical Methods for Quality Control n Acceptance Sampling | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | UCL CL LCL n Statistical Process Control n Philosophies and Frameworks

3. 3 3 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality n The American Society for Quality (ASQ) defines quality as: “ the totality of features and characteristics of a product or service that bears on its ability to satisfy given needs.” n Organizations recognize that they must strive for high levels of quality. high levels of quality. n They have increased the emphasis on methods for monitoring and maintaining quality.

4. 4 4 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. n Total Quality (TQ) is a people-focused management system that aims at continual increase in customer system that aims at continual increase in customer satisfaction at continually lower real cost. satisfaction at continually lower real cost. n TQ is a total system approach (not a separate work program) and an integral part of high-level strategy. program) and an integral part of high-level strategy. n TQ works horizontally across functions, involves all employees, top to bottom, and extends backward employees, top to bottom, and extends backward and forward to include both the supply and and forward to include both the supply and customer chains. customer chains. Total Quality n TQ stresses learning and adaptation to continual change as keys to organization success. continual change as keys to organization success.

5. 5 5 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Total Quality n Regardless of how it is implemented in different organizations, Total Quality is based on three fundamental principles: a focus on customers and stakeholders a focus on customers and stakeholders participation and teamwork throughout the participation and teamwork throughout the organization organization a focus on continuous improvement and a focus on continuous improvement and learning learning

6. 6 6 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Philosophies n Dr. Walter A. Shewhart Developed a set of principles that are the basis for Developed a set of principles that are the basis for what is known today as process control what is known today as process control Constructed a diagram that would now be Constructed a diagram that would now be recognized as a statistical control chart recognized as a statistical control chart Brought together the disciplines of statistics, Brought together the disciplines of statistics, engineering, and economics and changed the engineering, and economics and changed the course of industrial history course of industrial history Recognized as the father of statistical quality Recognized as the father of statistical quality control control First honorary member of ASQ First honorary member of ASQ

7. 7 7 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Philosophies n Dr. W. Edwards Deming Helped educate the Japanese on quality Helped educate the Japanese on quality management shortly after World War II management shortly after World War II Stressed that the focus on quality must be led Stressed that the focus on quality must be led by managers by managers Developed a list of 14 points he believed Developed a list of 14 points he believed represent the key responsibilities of managers represent the key responsibilities of managers Japan named its national quality award the Japan named its national quality award the Deming Prize in his honor Deming Prize in his honor

8. 8 8 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Philosophies n Joseph Juran Helped educate the Japanese on quality Helped educate the Japanese on quality management shortly after World War II management shortly after World War II Proposed a simple definition of quality: Proposed a simple definition of quality: fitness for use fitness for use His approach to quality focused on three His approach to quality focused on three quality processes: quality planning, quality quality processes: quality planning, quality control, and quality improvement control, and quality improvement

9. 9 9 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Philosophies n Other Significant Individuals Philip B. Crosby Philip B. Crosby A. V. Feigenbaum A. V. Feigenbaum Karou Ishikawa Karou Ishikawa Genichi Taguchi Genichi Taguchi

10. 10 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Frameworks 1. Leadership 1. Leadership 2. Strategic Planning 2. Strategic Planning 3. Customer and 3. Customer and Market Focus Market Focus In 2003, the “Baldrige Index” ( a hypothetical stock In 2003, the “Baldrige Index” ( a hypothetical stock index comprised of Baldrige Award winning index comprised of Baldrige Award winning companies) outperformed the S&P 500 by 4.4 to 1. companies) outperformed the S&P 500 by 4.4 to 1. Established in 1987 and given by the U.S. president Established in 1987 and given by the U.S. president to organizations that apply and are judged to be to organizations that apply and are judged to be outstanding in seven areas: outstanding in seven areas: 4. Measurement, Analysis 4. Measurement, Analysis and Knowledge Mgmt. and Knowledge Mgmt. 5. Human Resource Focus 5. Human Resource Focus 6. Process Management 6. Process Management 7. Business Results 7. Business Results n Malcolm Baldrige National Quality Award

11. 11 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Frameworks In 2003, the “Baldrige Index” ( a hypothetical stock In 2003, the “Baldrige Index” ( a hypothetical stock index comprised of Baldrige Award winning index comprised of Baldrige Award winning companies) outperformed the S&P 500 by 4.4 to 1. companies) outperformed the S&P 500 by 4.4 to 1. The first awards were presented in 1988. The first awards were presented in 1988. n Malcolm Baldrige National Quality Award (continued) The Award is named for Malcolm Baldrige, who The Award is named for Malcolm Baldrige, who served as U.S. Secretary of Commerce from 1981-87. served as U.S. Secretary of Commerce from 1981-87. The U.S. Commerce Department’s National Institute The U.S. Commerce Department’s National Institute of Standards and Technology (NIST) manages the of Standards and Technology (NIST) manages the Award. Award.

12. 12 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Frameworks The standards describe the need for: The standards describe the need for: an effective quality system, an effective quality system, ensuring that measuring and testing equipment ensuring that measuring and testing equipment is calibrated regularly, and is calibrated regularly, and maintaining an adequate record-keeping system. maintaining an adequate record-keeping system. A series of five standards published in 1987 by the A series of five standards published in 1987 by the International Organization for Standardization in International Organization for Standardization in Geneva, Switzerland. Geneva, Switzerland. n ISO 9000 ISO 9000 registration determines whether a ISO 9000 registration determines whether a company complies with its own quality system. company complies with its own quality system.

13. 13 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Frameworks n Six Sigma The methodology created to reach this quality goal The methodology created to reach this quality goal is referred to as Six Sigma. is referred to as Six Sigma. Six Sigma is a major tool in helping organizations Six Sigma is a major tool in helping organizations achieve Baldrige levels of business performance and achieve Baldrige levels of business performance and process quality. process quality. Six sigma level of quality means that for every Six sigma level of quality means that for every million opportunities no more than 3.4 defects will million opportunities no more than 3.4 defects will occur. occur.

14. 14 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Frameworks n Six Sigma (continued) Six Sigma is a major tool in helping organizations Six Sigma is a major tool in helping organizations achieve Baldrige levels of business performance. achieve Baldrige levels of business performance. Six Sigma places a heavy emphasis on statistical Six Sigma places a heavy emphasis on statistical analysis and careful measurement. analysis and careful measurement. Two kinds of Six Sigma projects can be undertaken: Two kinds of Six Sigma projects can be undertaken: DMAIC (Define, Measure, Analyze, Improve,DMAIC (Define, Measure, Analyze, Improve, and Control) and Control) DFSS (Design for Six Sigma)DFSS (Design for Six Sigma)

15. 15 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Frameworks n Six Sigma (continued) x -6  -2  -2  -4  +2  +4  +6  99.9999998% LowerQualityLimitUpperQualityLimit -5  -3  -1  +1  +3  +5  Roughly 2 defectives in 10 million

16. 16 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Frameworks n Six Sigma (continued) If the process mean shifts by 1.5 standard deviations, If the process mean shifts by 1.5 standard deviations, there will be approximately 3.4 defects per million there will be approximately 3.4 defects per million opportunities. Using Excel: opportunities. Using Excel: 1 – NORM.S.DIST(4.5,TRUE) = 0.0000034 1 – NORM.S.DIST(4.5,TRUE) = 0.0000034 NORM.S.DIST(6,TRUE) – NORM.S.DIST(-6,TRUE) NORM.S.DIST(6,TRUE) – NORM.S.DIST(-6,TRUE) = 0.999999998 NORM.S.DIST(6,TRUE) – NORM.S.DIST(-6,TRUE) NORM.S.DIST(6,TRUE) – NORM.S.DIST(-6,TRUE) = 0.999999998 99.9999998% of the process output will be within 99.9999998% of the process output will be within +/-3 standard deviations of the mean. Using Excel: +/-3 standard deviations of the mean. Using Excel:

17. 17 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Quality Frameworks n Quality in the Service Sector Quality efforts in the service sector focus on Quality efforts in the service sector focus on ensuring customer satisfaction and improving the ensuring customer satisfaction and improving the customer experience. customer experience. Services provided are often intangible, and thus Services provided are often intangible, and thus customer satisfaction is subjective. So, measuring customer satisfaction is subjective. So, measuring quality can be challenging. quality can be challenging. Quality control is also very important to businesses Quality control is also very important to businesses that focus primarily on providing services (e.g. – that focus primarily on providing services (e.g. – law firms, hotels, airlines, restaurants and banks). law firms, hotels, airlines, restaurants and banks).

18. 18 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. QC consists of making a series QC consists of making a series of inspections and measure- of inspections and measure- ments to determine whether quality standards are ments to determine whether quality standards are being met. being met. QA refers to the entire system of QA refers to the entire system of policies, procedures, and guide- policies, procedures, and guide- lines established by an organization to achieve and lines established by an organization to achieve and maintain quality. QA consists of two functions... maintain quality. QA consists of two functions... Its objective is to include quality Its objective is to include quality in the design of products and in the design of products and processes and to identify potential quality problems processes and to identify potential quality problems prior to production. prior to production. Quality Terminology Quality Assurance Quality Engineering Quality Control

19. 19 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Statistical Process Control (SPC) n Output of the production process is sampled and inspected. Using SPC methods, it can be determined whether Using SPC methods, it can be determined whether variations in output are due to common causes or variations in output are due to common causes or assignable causes. assignable causes. The goal is decide whether the process can be The goal is decide whether the process can be continued or should be adjusted to achieve a desired continued or should be adjusted to achieve a desired quality level. quality level.

20. 20 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Causes of Process Output Variation Common Causes randomly occurring variations in materials, randomly occurring variations in materials, humidity, temperature,... humidity, temperature,... variations the producer cannot control variations the producer cannot control process is in statistical control process is in statistical control process does not need to be adjusted process does not need to be adjusted randomly occurring variations in materials, randomly occurring variations in materials, humidity, temperature,... humidity, temperature,... variations the producer cannot control variations the producer cannot control process is in statistical control process is in statistical control process does not need to be adjusted process does not need to be adjusted

21. 21 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Causes of Process Output Variation Assignable Causes non-random variations in output due to tools non-random variations in output due to tools wearing out, operator error, incorrect machine wearing out, operator error, incorrect machine settings, poor quality raw material,... settings, poor quality raw material,... variations the producer can control variations the producer can control process is out of control process is out of control corrective action should be taken corrective action should be taken non-random variations in output due to tools non-random variations in output due to tools wearing out, operator error, incorrect machine wearing out, operator error, incorrect machine settings, poor quality raw material,... settings, poor quality raw material,... variations the producer can control variations the producer can control process is out of control process is out of control corrective action should be taken corrective action should be taken

22. 22 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. H a is formulated in terms of the production H a is formulated in terms of the production process being out of control. process being out of control. Null Hypothesis Null Hypothesis Alternative Hypothesis SPC Hypotheses SPC procedures are based on hypothesis-testing methodology. H 0 is formulated in terms of the production H 0 is formulated in terms of the production process being in control. process being in control.

23. 23 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Decisions and State of the Process CorrectDecisionCorrectDecision Type II Error Allow out-of-control process to continue Type II Error Allow out-of-control process to continue CorrectDecisionCorrectDecision Type I Error Adjust in-control process Type I Error Adjust in-control process Reject H 0 Adjust Process Reject H 0 Adjust Process Accept H 0 Continue Process Accept H 0 Continue Process H 0 True In-Control In-Control H 0 False Out-of-Control Out-of-Control DecisionDecision State of Production Process n Type I and Type II Errors

24. 24 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. 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).

25. 25 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. n Two important lines on a control chart are the upper control limit (UCL) and lower control limit (LCL). Control Charts 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.

26. 26 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. This chart is used to monitor the range of the This chart is used to monitor the range of the measurements in the sample. measurements in the sample. R Chart Variables Control Charts x Chart This chart is used if the quality of the output is This chart is used if the quality of the output is measured in terms of a variable such as length, measured in terms of a variable such as length, weight, temperature, and so on. weight, temperature, and so on. x represents the mean value found in a sample x represents the mean value found in a sample of the output. of the output.

27. 27 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Attributes Control Charts This chart is used to monitor the number of defective This chart is used to monitor the number of defective items in the sample. items in the sample. np Chart p Chart This chart is used to monitor the proportion defective This chart is used to monitor the proportion defective in the sample. in the sample.

28. 28 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. x Chart Structure UCL LCL Process Mean When in Control Center Line Time xUpperControlLimitUpperControlLimit LowerControlLimitLowerControlLimit

29. 29 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Control Limits for an x Chart Process Mean  and Standard Deviation  Known Process Mean  and Standard Deviation  Known where: n = sample size n = sample size

30. 30 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. n Example: Granite Rock Co. Control Limits for an x Chart: Process Mean and Standard Deviation Known When Granite Rock’s packaging process is in When Granite Rock’s packaging process is in control, the weight of bags of cement filled by the process is normally distributed with a mean of 50 pounds and a standard deviation of 1.5 pounds. What should be the control limits for samples of 9 bags?

31. 31 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part.  = 50,  = 1.5, n = 9 UCL = 50 + 3(.5) = 51.5 LCL = 50 - 3(.5) = 48.5 Control Limits for an x Chart: Process Mean and Standard Deviation Known CL = 50 CL = 50

32. 32 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. = n Process Mean and Standard Deviation Unknown Control Limits for an x Chart where: x = overall sample mean x = overall sample mean R = average range R = average range A 2 = constant that depends on n ; taken from A 2 = constant that depends on n ; taken from “Factors for Control Charts” table “Factors for Control Charts” table= _ =

33. 33 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Factors for x Control Chart n “Factors for Control Charts” Table (Partial)

34. 34 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Control Limits for an R Chart n Process Mean and Standard Deviation Unknown where: where: R = average range R = average range D 3, D 4 = constants that depend on n ; taken D 3, D 4 = constants that depend on n ; taken from “Factors for Control Charts” from “Factors for Control Charts” table table_

35. 35 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Factors for R Control Chart n “Factors for Control Charts” Table (Partial)

36. 36 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. R Chart n In practice, the R chart is usually constructed before the x chart. n If the R chart indicates that the process variability is in control, then the x chart is constructed. n Because the control limits for the x chart depend on the value of the average range, these limits will not have much meaning unless the process variability is in control.

37. 37 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Control Limits for an R Chart: Process Mean and Standard Deviation Unknown n Example: Granite Rock Co. The twenty samples, collected when the process was in control, resulted in an overall sample mean of 50.01 pounds and an average range of.322 pounds. Suppose Granite does not know the true mean and standard deviation for its bag filling process. It wants to develop x and R charts based on twenty samples of 5 bags each.

38. 38 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. UCL = RD 4 =.322(2.114) =.681 _ LCL = RD 3 =.322(0) = 0 _ x = 50.01, R =.322, n = 5 _= Control Limits for an R Chart: Process Mean and Standard Deviation Unknown CL = R =.322 CL = R =.322_

39. 39 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. R Chart for Granite Rock Co. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 05101520 Sample Number Sample Range R LCL UCL Control Limits for an R Chart: Process Mean and Standard Deviation Unknown

40. 40 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. x = 50.01, R =.322, n = 5 _= UCL = x + A 2 R = 50.01 +.577(.322) = 50.196 =_ LCL = x  A 2 R = 50.01 .577(.322) = 49.824 =_ Control Limits for an x Chart: Process Mean and Standard Deviation Unknown CL = x = 50.01 =

41. 41 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. 49.7 49.8 49.9 50.0 50.1 50.2 50.3 05101520 Sample Number Sample Mean UCL LCL x Chart for Granite Rock Co. Control Limits for an x Chart: Process Mean and Standard Deviation Unknown

42. 42 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Control Limits for a p Chart where: assuming: np > 5 n (1- p ) > 5 n (1- p ) > 5 Note: If computed LCL is negative, set LCL = 0

43. 43 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Control Limits for a p Chart Every check cashed or deposited at Norwest Bank Every check cashed or deposited at Norwest Bank must be encoded with the amount of the check before it can begin the Federal Reserve clearing process. The accuracy of the check encoding process is of utmost importance. If there is any discrepancy between the amount a check is made out for and the encoded amount, the check is defective. n Example: Norwest Bank

44. 44 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Twenty samples, each consisting of 400 checks, Twenty samples, each consisting of 400 checks, were selected and examined when the encoding process was known to be operating correctly. The number of defective checks found in the 20 samples are listed below. Control Limits for a p Chart n Example: Norwest Bank

45. 45 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. n Suppose Norwest does not know the proportion of defective checks, p, for the encoding process when it is in control. Control Limits for a p Chart n We will treat the data (20 samples) collected as one large sample and compute the average number of defective checks for all the data. That value can then be used to estimate p.

46. 46 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Note that the computed LCL is negative. Estimated p = 128/((20)(400)) = 128/8000 =.016 Control Limits for a p Chart np =400(.016) = 6.4 > 5; n (1- p ) = 400(.984) = 393.6 > 5

47. 47 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Control Limits for a p Chart Encoded Checks Proportion Defective 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 05101520 Sample Number Sample Proportion p UCL LCL

48. 48 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Control Limits for an np Chart Note: If computed LCL is negative, set LCL = 0 assuming: np > 5 n (1- p ) > 5

49. 49 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. The location and pattern of points in a control chart The location and pattern of points in a control chart enable us to determine, with a small probability of enable us to determine, with a small probability of error, whether a process is in statistical control. error, whether a process is in statistical control. The location and pattern of points in a control chart The location and pattern of points in a control chart enable us to determine, with a small probability of enable us to determine, with a small probability of error, whether a process is in statistical control. error, whether a process is in statistical control. A primary indication that a process may be out of A primary indication that a process may be out of control is a data point outside the control limits. control is a data point outside the control limits. A primary indication that a process may be out of A primary indication that a process may be out of control is a data point outside the control limits. control is a data point outside the control limits. Interpretation of Control Charts

50. 50 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Certain patterns of points within the control limits Certain patterns of points within the control limits can be warning signals of quality problems: can be warning signals of quality problems: Certain patterns of points within the control limits Certain patterns of points within the control limits can be warning signals of quality problems: can be warning signals of quality problems: a large number of points on one side of a large number of points on one side of center line center line a large number of points on one side of a large number of points on one side of center line center line six or seven points in a row that indicate six or seven points in a row that indicate either an increasing or decreasing trend either an increasing or decreasing trend six or seven points in a row that indicate six or seven points in a row that indicate either an increasing or decreasing trend either an increasing or decreasing trend Interpretation of Control Charts

51. 51 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Acceptance Sampling Acceptance sampling is a statistical method that Acceptance sampling is a statistical method that enables us to base the accept-reject decision on the enables us to base the accept-reject decision on the inspection of a sample of items from the lot. inspection of a sample of items from the lot. Acceptance sampling is a statistical method that Acceptance sampling is a statistical method that enables us to base the accept-reject decision on the enables us to base the accept-reject decision on the inspection of a sample of items from the lot. inspection of a sample of items from the lot. The items of interest can be incoming shipments of The items of interest can be incoming shipments of raw materials or purchased parts as well as raw materials or purchased parts as well as finished goods from final assembly. finished goods from final assembly. The items of interest can be incoming shipments of The items of interest can be incoming shipments of raw materials or purchased parts as well as raw materials or purchased parts as well as finished goods from final assembly. finished goods from final assembly.

52. 52 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Acceptance Sampling Acceptance sampling has advantages over 100% Acceptance sampling has advantages over 100% inspection including: inspection including: Acceptance sampling has advantages over 100% Acceptance sampling has advantages over 100% inspection including: inspection including: usually less expensive usually less expensive less product damage due to less handling less product damage due to less handling fewer inspectors required fewer inspectors required provides only approach possible if provides only approach possible if destructive testing must be used destructive testing must be used provides only approach possible if provides only approach possible if destructive testing must be used destructive testing must be used

53. 53 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Acceptance Sampling Procedure Lot received Sample selected Sampled items inspected for quality Sampled items inspected for quality Results compared with specified quality characteristics Results compared with specified quality characteristics Accept the lot Reject the lot Send to production or customer Send to production or customer Decide on disposition of the lot Decide on disposition of the lot Quality is not satisfactory satisfactory Quality is Quality issatisfactory

54. 54 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Acceptance Sampling The hypotheses are: The hypotheses are: H 0 : Good-quality lot H 0 : Good-quality lot Acceptance sampling is based on hypothesis-testing Acceptance sampling is based on hypothesis-testing methodology. methodology. Acceptance sampling is based on hypothesis-testing Acceptance sampling is based on hypothesis-testing methodology. methodology. H a : Poor-quality lot H a : Poor-quality lot

55. 55 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. The Outcomes of Acceptance Sampling n Type I and Type II Errors CorrectDecisionCorrectDecision Type II Error Accepting a Poor-quality lot Type II Error Accepting a Poor-quality lot CorrectDecisionCorrectDecision Type I Error Rejecting a Good-quality lot Type I Error Rejecting a Good-quality lot Reject H 0 Reject the Lot Reject H 0 Reject the Lot Accept H 0 Accept the Lot Accept H 0 Accept the Lot H 0 True Good-Quality Lot H 0 True Good-Quality Lot H 0 False Poor-Quality Lot H 0 False Poor-Quality Lot DecisionDecision State of the Lot

56. 56 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. n Binomial Probability Function for Acceptance Sampling Probability of Accepting a Lot where: n = sample size p = proportion of defective items in lot x = number of defective items in sample f ( x ) = probability of x defective items in sample f ( x ) = probability of x defective items in sample

57. 57 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Example: Acceptance Sampling An inspector takes a sample of 20 items from a lot. His policy is to accept a lot if no more than 2 defective items are found in the sample. Assuming that 5 percent of a lot is defective, what is the probability that he will accept a lot? Reject a lot?

58. 58 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Example: Acceptance Sampling Example: Acceptance Sampling P (Accept Lot) =.3585 +.3774 +.1887 =.9246 P (Accept Lot) = f (0) + f (1) + f (2) n = 20, c = 2, and p =.05

59. 59 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. n = 20, c = 2, and p =.05 n = 20, c = 2, and p =.05 Example: Acceptance Sampling Example: Acceptance Sampling P (Reject Lot) = 1 – P (Accept Lot) = 1 -.9246 = 1 -.9246 =.0754 =.0754

60. 60 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Selecting an Acceptance Sampling Plan In formulating a plan, managers must specify In formulating a plan, managers must specify two values for the fraction defective in the lot. two values for the fraction defective in the lot. In formulating a plan, managers must specify In formulating a plan, managers must specify two values for the fraction defective in the lot. two values for the fraction defective in the lot.  = the probability that a lot with p 0 defectives will be rejected p 0 defectives will be rejected  = the probability that a lot with p 0 defectives will be rejected p 0 defectives will be rejected  = the probability that a lot with p 1 defectives will be accepted p 1 defectives will be accepted  = the probability that a lot with p 1 defectives will be accepted p 1 defectives will be accepted

61. 61 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Then, the values of n and c are selected that Then, the values of n and c are selected that result in an acceptance sampling plan that result in an acceptance sampling plan that comes closest to meeting both the  and  comes closest to meeting both the  and  requirements specified. requirements specified. Then, the values of n and c are selected that Then, the values of n and c are selected that result in an acceptance sampling plan that result in an acceptance sampling plan that comes closest to meeting both the  and  comes closest to meeting both the  and  requirements specified. requirements specified. Selecting an Acceptance Sampling Plan

62. 62 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Probability of Accepting the Lot 0 5 10 15 20 25.10.20.30.40.50.60.70.80.90 1.00 Percent Defective in the Lot p0p0p0p0 p1p1p1p1  (1 -  )  n = 15, c = 0 p 0 =.03, p 1 =.15  =.3667,  =.0874 Operating Characteristic Curve

63. 63 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Multiple Sampling Plans n A multiple sampling plan uses two or more stages of sampling. n Multiple sampling plans often result in a smaller total sample size than single-sample plans with the same Type I error and Type II error probabilities. n At each stage the decision possibilities are: stop sampling and accept the lot, stop sampling and accept the lot, stop sampling and reject the lot, or stop sampling and reject the lot, or continue sampling. continue sampling.

64. 64 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. A Two-Stage Acceptance Sampling Plan Inspect n 1 items Find x 1 defective items in this sample x1 < c1 ?x1 < c1 ?x1 < c1 ?x1 < c1 ? x1 < c1 ?x1 < c1 ?x1 < c1 ?x1 < c1 ? x1 > c2 ?x1 > c2 ?x1 > c2 ?x1 > c2 ? x1 > c2 ?x1 > c2 ?x1 > c2 ?x1 > c2 ? Inspect n 2 additional items Accept the lot Accept Reject x 1 + x 2 < c 3 ? Find x 2 defective items in this sample Yes Yes No No No Yes FirstStage SecondStage

65. 65 Slide © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. End of Chapter 19