Activity Control Charts & Measurement System Analysis Solve the problem using MlNlTAB Software. Show the results of the control chart and interpret the results 1. A TiW layer is deposited on a substrate using a sputtering tool. Table 6E.1 3 contains layer thickness measurements (in Angstroms) on 20 subgroups of four substrates. (a) Set up X and Rcontrol charts on this process. Is the process in control? Revise the control limits as necessary. (b) Estimate the mean and standard deviation of the process. (C) Is the layer thickness normally distributed? (d) If the specifications are at 450 i 30, estimate the process capability l TAB L E B E _ 1 3 Layer Thickness Data for Fixer-rise: 6.26 Subgroup 1'1 :1 x3 :4 l 459 449 43-5 450 2 443 440 442 442 3 457 444 449 444 4 469 463 453 433 5 443 457 4-45 454 IS 444 456 456 45'?I 3' 445 449 450 445 3 446 455 449 452 9 444 452 45'? 440 ID 432 463- 463 4-43 1 l 445 452 453 433- 12 456 457 436 45'? 13 459 445 44] 447' 14 441 465 438 450 15 4-60- 453 45? 433 I IS 45 3 444 45 l 435 l? 45 1 460' 450 45? 18 422 43 l 43'}r 429 19 444 446 448 46'? 20 456 450 454 45-4 2. The number of nonconforming switches in samples of size 150 are shown in Table below Construct a fraction nonconforming control chart for these data. Does the process appear to be in control? If not, assume that assignable causes can be found for all points outside the control limits and calculate the revised control limits Number of Number of Sample Noncenforming Sample Nonconferming Number Assemblies Number Assemblies 1 T l I IS 2 4 12 15 3 1 l3 {1 4 3 M- 9 5 6 15 5 6 3 16 l 7 10 l T 4 3 5 18 5 9 2 19 T 10 7 ED 1?. 3. Based on the data in Table below if an np chart is to be established, what would you recommend as the center line and control limits? Assume that n = 500. Number of Day Nance-\"fuming Units 3 2 4 3 3 4 2 5 l5 6 12 7 5 S 1 9 2 ll] 2 4. A quality control engineer collected a set of 15 samples of size n = 5. The data are shown in the following table. Based on these data, determine control limits for the X and S control charts. Plot the data on the control charts, and examine whether the process is in statistical control. Sample II x1 x2 x3 x4 x5 1 10.51 9.30 9.73 9.72 1027 2 10.83 9.79 9.27 9.84 9.48 3 9.91 10.52 9.41 9.75 1023 4 10.34 10.20 9.66 9.72 10.57 5 9.68 10.35 9.31 9.91 10.47 6 10.57 11.36 9.65 9.48 10.1 1 7 10.77 9.93 9.17 9.88 9.47 8 9.81 10.00 9.62 9.06 8.99 9 10.86 10.05 8.76 10.24 10.19 10 9.38 9.61 10.37 9.45 8.46 11 10.01 10.05 10.86 8.62 9.80 12 10.29 9.82 9.65 9.64 10.54 13 10.51 10.38 8.89 9.77 9.85 14 9.21 9.60 9.60 11.08 10.1 2 15 10.86 9.87 9.84 10.88 9.30 5. The following data show the number of nonconformities per 100 square yards (one unit) of woolen cloth. Select and set up an appropriate control chart that you would use to determine whether the process is in statistical control. Give your conclusion. Sample # Nonconfonnities Sample all Nonconformities Sample # Nonconformities 1 3 17 3 2 7 18 5 3 5 19 11 4 10 20 13 5 2 21 16 6 1 22 9 7 B 23 10 8 7 24 8 6. A measurement systems experiment involving 20 parts, three operators, and two measurements per part is shown in the Table below (a) Estimate the repeatability and reproduciblety of the gauge. (b) What is the estimate of total gauge variability? (c) If the product specifications are at LSL = 6 and USL = 60, what can you say about gauge capability? Operator 2 Operator 3 Operator 1 Measurements Measurements Measurements Part 2 1 2 1 2 1 Number 20 20 19 21 21 20 24 24 23 24 24 23 20 22 20 21 19 21 27 28 27 27 28 26 19 18 19 18 18 21 24 21 23 22 23 21 22 20 22 22 24 18 19 18 20 24 25 23 24 GUA W N E ODD JAVA WN 25 26 25 20 20 18 17 19 23 25 25 24 24 23 25 29 30 30 28 26 26 25 26 17 20 20 19 20 18 19 21 19 19 19 25 26 25 19 19 18 20