1. 1 1 Slide Slides by JOHN LOUCKS & SPIROS VELIANITIS

2. 2 2 Slide n Philosophies and Frameworks n Statistical Process Control n Acceptance Sampling Chapter 20 Statistical Methods for Quality Control

3. 3 3 Slide Quality n Quality is “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 n They have increased the emphasis on methods for monitoring and maintaining quality.

4. 4 4 Slide Total QualityTotal Quality n Total Quality (TQ) is a people-focused management system that aims at continual increase in customer satisfaction at continually lower cost n TQ is a total system approach (not a separate work program) and an integral part of high-level strategy. n TQ works horizontally across functions, involves all employees, top to bottom, and extends backward and forward to include both the supply and customer chains. n TQ stresses learning and adaptation to continual change as keys to organization success. 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 organization participation and teamwork throughout the organization a focus on continuous improvement and learning a focus on continuous improvement and learning

5. 5 5 Slide Quality PhilosophiesQuality Philosophies n Dr. W. Edwards Deming One of Deming’s major contributions was to direct attention away from inspection of the final product or service towards monitoring the process that produces the final product or service with emphasis of statistical quality control techniques. In particular, Deming stressed that in order to improve a process one needs to reduce the variation in the process. One of Deming’s major contributions was to direct attention away from inspection of the final product or service towards monitoring the process that produces the final product or service with emphasis of statistical quality control techniques. In particular, Deming stressed that in order to improve a process one needs to reduce the variation in the process. n Joseph Juran Proposed a simple definition of quality: fitness for use Proposed a simple definition of quality: fitness for use His approach to quality focused on three quality processes: quality planning, quality control, and quality improvement His approach to quality focused on three quality processes: quality planning, quality control, and quality improvement

6. 6 6 Slide Quality FrameworksQuality Frameworks n Malcolm Baldrige National Quality Award: Established in 1987 and given by the U.S. president to organizations that apply and are judged to be outstanding in seven areas n ISO 9000: A series of five standards published in 1987 by the International Organization for Standardization in Geneva, Switzerland. n Six Sigma: Six sigma level of quality means that for every million opportunities no more than 3.4 defects will occur. The methodology created to reach this quality goal is referred to as Six Sigma. The methodology created to reach this quality goal is referred to as Six Sigma. Six Sigma is a major tool in helping organizations achieve Baldrige levels of business performance and process quality. Six Sigma is a major tool in helping organizations achieve Baldrige levels of business performance and process quality.

7. 7 7 Slide Quality Terminology n Quality Assurance: QA refers to the entire system of policies, procedures, and guidelines established by an organization to achieve and maintain quality. QA consists of two functions: Quality Engineering - Its objective is to include quality in the design of products and processes and to identify potential quality problems prior to production. Quality Engineering - Its objective is to include quality in the design of products and processes and to identify potential quality problems prior to production. Quality Control - QC consists of making a series of inspections and measurements to determine whether quality standards are being met. Quality Control - QC consists of making a series of inspections and measurements to determine whether quality standards are being met.

8. 8 8 Slide Statistical Process Control (SPC) n In order to reduce the variation of a process, one needs to recognize that the total variation is comprised of common causes and specific causes. At any time there are numerous factors which individually and in interaction with each other cause detectable variability in a process and its output. Those factors that are not readily identifiable and occur randomly are referred to as the common causes, while those that have large impact and can be associated with special circumstances or factors are referred to as specific causes. n When a process has variation made up of only common causes then the process is said to be a stable process, which means that the process is in statistical control and remains relatively the same over time. This implies that the process is predictable, but does not necessarily suggest that the process is producing outputs that are acceptable as the amount of common variation may exceed the amount of acceptable variation. If a process has variation that is comprised of both common causes and specific causes then it is said to be an unstable process, which means that the process is not in statistical control. An unstable process does not necessarily mean that the process is producing unacceptable products since the total variation (common variation + specific variation) may still be less than the acceptable level of variation.

9. 9 9 Slide Statistical Process Control (SPC) Example n Consider a manufacturing situation where a hole needs to be drilled into a piece of steel. We are concerned with the size of the hole, in particular the diameter, since the performance of the final product is a function of the precision of the hole. As we measure consecutively drilled holes, with very fine instruments, we will notice that there is variation from one hole to the next. Some of the possible common sources can be associated with the density of the steel, air temperature, and machine operator. As long as these sources do not produce significant swings in the variation they can be considered common sources. On the other hand, the changing of a drill bit could be a specific source provided it produces a significant change in the variation, especially if a wrong sized bit is used! n SPC Determination Steps: Sample and inspect the output of the production process. Sample and inspect the output of the production process. Using SPC methods, determined whether variations in output are due to common causes or assignable causes. Using SPC methods, determined whether variations in output are due to common causes or assignable causes. Decide whether the process can be continued or should be adjusted to achieve a desired quality level. Decide whether the process can be continued or should be adjusted to achieve a desired quality level.

10. 10 Slide 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.

11. 11 Slide Identification Tools n There are a number of tools used in practice to determine whether specific causes of variation exist within a process. In the remaining part of this chapter we will discuss how time series plots, the runs test, a test for normality and control charts are used to identify specific sources of variation. As will become evident there is a great deal of similarity between time series plots and control charts. In particular, the control charts are time series plots of statistics calculated from subgroups of observations, whereas when we speak of time series plots we are referring to plots of consecutive observations.

12. 12 Slide Time Series PlotsTime Series Plots n A time series plot is a graph where the horizontal axis represents time and the vertical axis represents the units in which the variable of concern is measured. For example, consider the following series where the variable of concern is the price of Anheuser Busch Co. stock on the last trading day for each month from June 1995 to June 2000 inclusive. Using the computer we are able to generate the following time series plot. Note that the horizontal axis represents time and the vertical axis represents the price of the stock, measured in dollars. n When using a time series plot to determine whether a process is stable, what one is seeking is the answer to the following questions: 1. Is the mean constant? 1. Is the mean constant? 2. Is the variance constant? 2. Is the variance constant? 3. Is the series random (i.e. no pattern)? 3. Is the series random (i.e. no pattern)? n Rather than initially showing the reader time series plots of stable processes, we show examples of non stable processes commonly experienced in practice.

13. 13 Slide Runs TestRuns Test n Frequently non-stable processes can be detected by visually examining their time series plots. However, there are times when patterns exist that are not easily detected. A tool that can be used to identify nonrandom data in these cases is the runs test. n To determine if the observed number significantly differs from the expected number, we encourage the reader to rely on statistical software (StatGraphics) and utilize the p-values that are generated.

14. 14 Slide Test for NormalityTest for Normality n Another attribute of a stable process, which you may recall lacks specific causes of variation, is that the series follows a normal distribution. To determine whether a variable follows a normal distribution one can examine the data via a graph, called a histogram, and/or utilize a test which incorporates a chi-square test statistic. n StatGraphics, will overlay the observed data with a theoretical distribution calculated from the sample mean and sample standard deviation in order to assist in the evaluation.

15. 15 Slide Example n Stationarity? From the visual inspection (top chart), one can tell the series is stationary. n Normality? From this, one can see that the distribution of the middle chart appears somewhat like a normal distribution. Not exactly, but in order to see how closely it does relate to theoretical normal distribution, we rely on the Chi-square test. As we can see from the table, the p-value (significance level) equals 0.1356. Since the p-value is greater than alpha (0.05), we retain the null hypothesis. n Random? Relying upon the nonparametric test for randomness. we can just look at the p-value, which in this case is 0.086 (rounded). So, since the p-value again is larger than our value of α = 0.05, we are able to conclude that we cannot reject the null hypothesis.

16. 16 Slide 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). n Two important lines on a control chart are the upper control limit (UCL) and lower control limit (LCL). 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.

17. 17 Slide Control Chart Types n Variables Control Charts X -bar Chart - This chart is used if the quality of the output is measured in terms of a variable such as length, weight, temperature, and so on. x represents the mean value found in a sample of the output. X -bar Chart - This chart is used if the quality of the output is measured in terms of a variable such as length, weight, temperature, and so on. x represents the mean value found in a sample of the output. R Chart - This chart is used to monitor the range of the measurements in the sample. R Chart - This chart is used to monitor the range of the measurements in the sample. The X-Bar and R Charts procedure creates control charts for a single numeric variable where the data have been collected in subgroups. The X-Bar and R Charts procedure creates control charts for a single numeric variable where the data have been collected in subgroups. n Attributes Control Charts p Chart - This chart is used to monitor the proportion defective in the sample. p Chart - This chart is used to monitor the proportion defective in the sample. np Chart - This chart is used to monitor the number of defective items in the sample. np Chart - This chart is used to monitor the number of defective items in the sample.

18. 18 Slide x Chart Structure UCL LCL Process Mean When in Control Center Line Time x Upper Control Limit Lower Control Limit

19. 19 Slide 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.

20. 20 Slide Control Limits for an R Chart: Process Mean and Standard Deviation Unknown n 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. 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. n 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.

21. 21 Slide 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

22. 22 Slide 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

23. 23 Slide 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

24. 24 Slide Control Limits For a p Chart Every check cashed or deposited at 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

25. 25 Slide Twenty samples, each consisting of 400 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

26. 26 Slide 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.

27. 27 Slide 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

28. 28 Slide NP Charts n The NP Chart procedure creates a control chart for data that describes the number of times an event occurs in m samples taken from a product or process. The data might represent the number of defective items in a manufacturing process, the number of customers that return a product, or any other attribute that can be classified as acceptable or unacceptable.

29. 29 Slide Interpretation of Control Charts n The location and pattern of points in a control chart enable us to determine, with a small probability of error, whether a process is in statistical control. n A primary indication that a process may be out of control is a data point outside the control limits. n Certain patterns of points within the control limits can be warning signals of quality problems: a large number of points on one side of center line OR six or seven points in a row that indicate either an increasing or decreasing trend.

30. 30 Slide Acceptance SamplingAcceptance Sampling n Acceptance sampling is a statistical method that enables us to base the accept-reject decision on the inspection of a sample of items from the lot. n The items of interest can be incoming shipments of raw materials or purchased parts as well as finished goods from final assembly. n Acceptance sampling has advantages over 100% inspection. n Acceptance sampling is based on hypothesis-testing methodology H 0 : Good-quality lot H 0 : Good-quality lot H a : Poor-quality lot H a : Poor-quality lot

31. 31 Slide Acceptance Sampling Procedure Lot received Sample selected Sampled items inspected for quality Results compared with specified quality characteristics Accept the lot Reject the lot Send to production or customer Decide on disposition of the lot Quality is not satisfactory satisfactory Quality is Quality issatisfactory