Question: Sample Size, n Lower Range, D3 2 3 4 5 6 Mean Factor, A2 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.266 Upper

Sample Size, n Lower Range, D3 2 3 4 5 6 Mean

Sample Size, n Lower Range, D3 2 3 4 5 6 Mean Factor, A2 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.266 Upper Range, D4 3.268 2.574 2.282 2.115 2.004 1.924 1.864 1.816 1.777 1.716 7 8 9 10 12 0.076 0.136 0.184 0.223 0.284 Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day 1 2 3 4 5 Mean x (mm) 158.9 151.2 155.6 153.5 156.6 Range R (mm) 4.4 4.6 4.3 4.8 4.3 a) What is the value of ? x = 154.54 mm (round your response to two decimal places). b) What is the value of ? R = 4.48 mm (round your response to two decimal places). c) What are the UCL; and LCL; using 3-sigma? Upper Control Limit (UCL;) = 155.92 mm (round your response to two decimal places). Lower Control Limit (LCL;) = 153.16 mm (round your response to two decimal places)

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