Question:

A manufacturer of outdoor sportswear must control the water resistance and breathability of its jackets. Water resistance is measured by the amount of water (depth in millimeters) that can be suspended above the fabric before water seeps through. For its jackets, this test is done along the seams and Zipper, Where the resistance is likely the weakest. Each fourhour shift, an operator measures the resistance on a sample of four jackets. The accompanying table (and data le) gives the last 20 groups of samples. Group X1 X2 X3 X4 sample r sample 5 mean 1 2345 2723 2345 2723 2534.0 378 218.2 2 3111 3058 2385 2862 2854.0 726 330.5 3 2471 2053 2526 3161 2552.8 1108 457.2 4 2154 2968 2742 2568 2608.0 814 344.1 5 3279 2472 2833 2326 2727.5 953 425.0 6 3043 2363 2018 2385 2452.3 1025 428.2 7 2689 2762 2756 2402 2652.3 360 170.1 8 2821 2477 2598 2728 2656.0 344 150.3 9 2608 2599 2479 3453 2784.8 974 449.4 10 3293 2318 3072 2734 2854.3 975 425.0 11 2664 2497 2315 2652 2532.0 349 163.4 12 1688 3309 3336 3183 2879.0 1648 796.8 13 3499 3342 2923 3015 3194.8 576 271.1 14 2352 2831 2459 2631 2568.3 479 209.5 15 2573 2184 2962 2752 2617.8 778 330.0 16 2351 2527 3006 2976 2715.0 655 326.9 17 2863 2938 2362 2753 2729.0 576 256.2 18 3281 2726 3297 2601 2976.3 696 364.8 19 3164 2874 3730 2860 3157.0 870 406.9 20 2968 3505 2806 2598 2969.3 907 387.9 3:32: 2750.7 759.6 345.6 TASKS a) Determine trial control limits for the sample mean and range. b) Determine trial control limits for the sample mean and s. 0) Create appropriate charts and discuss whether the process is out of control