1. Chapter 36 Quality Engineering Part 2 (Review) EIN 3390 Manufacturing Processes Summer A, 2012

2. 36.3 Inspection to Control Quality Inspection is the function that controls the quality manually, or automatically. How much should be inspected: 1. Inspect every item being made 2. Sample 3. None. Assume that everything is acceptable or the product is inspected by customer, who will exchange it in case it is defective.

3. 36.3.1 Statistical Process Control (SPC) Sampling requires statistical techniques for decisions about the acceptability of the whole based on sample’s quality. This is known as statistical process control (SPC). The most widely used basic SPC technique is the control charts.

4. Control charts for variables are used to monitor the output of a process by 1) sampling, 2) measuring selected quality characteristics, and 3) plotting the sample data on the chart, then making decisions about the performance of the process.

5. Figure 36 – 13 shows the basic structure of two charts commonly used for variable types of measurements. 1. X chart tracks the aim (accuracy) of the process. 2. R chart (or  chart) tracks the precision or variability of the process. Usually, only X chart and R chart are used unless the sample size is large (n > 12), and then  chart are used in place of R chart.

6. 36.3 Inspection to Control Quality

7. Quality Calculations FIGURE 36-13 Quality control chart calculations. On the charts, X plot and R values over time. The constants for calculating UCL and LCL values for the X and R charts are based on 3 standard deviations. R = Xhigh – X low  = R/d 2 A2 = 3/[d 2 SQRT(n)] Where, n – sample size  x/n + -

8. Samples are drawn over time. Because some sample statistics tend to be normally distributed about their own mean, x value are normally distributed about x, and R values are normally distributed about R, and  values are normally distributed . Quality control charts are widely used as aids in maintaining quality and detecting trends in quality variation before defective parts are actually produced.

9. When sampling inspection is used, the typical sample sizes are from 3 to about 12. Fig 16 – 4 shows one example of X and R charts for measuring a dimension of a gap on a part with 25 samples of size 5 over 6 days.

10. FIGURE 36-14 Example of X and R charts and the data set of 25 samples [k 25 of size 5 (n = 5)]. (Source : Continuing Process Critical and Process Capability Improvement, Statistical Methods Office, Ford Motor Co., 1985.) 0.178

11. Corrections in textbook

12. After control charts have been established, the charts act as a control indicator for the process. If the process is operating under chance cause conditions, the data will appear random (no trends or pattern). If X, R or  values fall outside the control limits or if nonrandom trends occur, like a.) 7 points on one side of the central line or b.) 6 successive increasing or decreasing points appear, an assignable cause or change may have occurred, and action should be taken to correct the problem.

13. 36.4 Process Capability Determination from Control Chart Data

14. 36.4 Process Capability Determination from Control Chart Data After the process is determined to be “under control”, the data can be used to estimate the process capability parameters. A sample size 5 was used in the example, so n = 5 (Fig 36 – 14). 25 groups of samples were drawn from the process, so K = 25. For each sample, the sample mean x and sample range R are computed. For large samples, N > 12, the standard deviation of each sample should be computed rather than the range.

15. 36.4 Process Capability Determination from Control Chart Data X, sometimes called grand average is used to estimate the mean of the process, . For the standard deviation of the process  ’, we can use either R, the average of the sample ranges, or the average of the sample standard deviations  to estimate  ’.  ’ = R/d 2 or  ’ c  

16. 36.5 Determining Causes For Problems in Quality Fishbone diagram developed by Kaorw Ishikowa in 1943 is used in conjunction with control chart to root out the causes of problems. Fishbone diagram is also known as Cause-and- effect. Fishbone lines are drawn from the main line. These lines organize the main factors. Branching from each of these factors are even more detailed factors.

17. 36.5 Determining Causes For Problems in Quality Four “M” are often used in fishbone diagram: Men, Machines, Materials, and Methods. CEDAC – Cause-and-Effect Diagram with the Additional of Cards. The effect is often tracked with a control chart. The possible causes of defects or problems are written on cards and inserted in slots in the cards.

18. Fishbone Diagram FIGURE 36-15 Example of a fishbone diagram using a control chart to show effects.

19. Fishbone Diagram FIGURE 36-15 Example of a fishbone diagram using a control chart to show effects.

20. 36.5.1 Sampling Errors Two kinds of decision errors: Type I Error ( error): process is running perfectly, but sample data indicate that something is wrong. Type II error ( error): process is not running perfectly and was making defective products, but sample data didn’t indicate that anything was wrong.

21. Errors FIGURE 36-16 When you look at some of the output from a process and decide about the whole (i.e., the quality of the process), you can make two kinds of errors.

22. Errors FIGURE 36-16 When you look at some of the output from a process and decide about the whole (i.e., the quality of the process), you can make two kinds of errors.

23. 36.5.3 Design of Experiments (DOE) and Taguchi Methods SPC looks at processes and control, Taguchi methods loosely implies “improvement”. DOE and Taguchi methods span a much wider scope of functions and include the design aspects of products and processes, areas that were seldom treated from quality standpoint view. Consumer is the focus on quality, and the methods of quality design and controls have been incorporated into all phases of production.

24. Taguchi Method FIGURE 36-18 The use of Taguchi methods can reduce the inherent process variability, as shown in the upper figure. Factors A, B, C, and D versus process variable V are shown in the lower figure.

25. 36.5.4 Six Sigma FIGURE 36-19 To move to six sigma capability from four sigma capability requires that the process capability (variability) be greatly improved (  reduced). The curves in these figures represent histograms or curves fitted to histograms.

26. 36.5.5 Total Quality Control (TQC) Total Quality Control (TQC) was first used by A. V. Feigenbaum in may 1957. TQC means that all departments of a company must participate in quality control (Table 36 – 1).

28. HW for Chapter 36 HW for Chapter 36 Review Questions: 13, 17, 24, 27, 28 (page 997) Problems: 6 (page 999) Final Exam: Date: June 18, 2012 (Monday) Time: 3:30 pm– 5:00pm