Homework: HW5 Score: 15.2 of 32 pts (%) Save 20f515 complete) Hw Score: 62.9%, 6

Question

Homework: HW5 Score: 15.2 of 32 pts (%) Save 20f515 complete) Hw Score: 62.9%, 62.9 of 100 pts Problem 657 Question Help * 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 Mean xRange R Day (mm) 154.9 151.2 151.6 155.5 158.6 4.6 4.1 4.5 a) What is the value ofx? x154.36 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 UCLi and LCL using 3-sigma? Upper Control Limit (UCL)-155.74 mm (round your response to two decimal places). Lower Control Limit (LCL? = 152.98 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)mm (round your response to two decimal places)

Explanation / Answer

Value of X bar = (154.9+151.2+151.6+155.5+158.6)/5 = 154.36 mm

Value of R bar = (4.4+4.6+4.1+4.8+4.5)/5 = 4.48 mm

X chart

For sample size of 10 (pistons produced) , value of A2 = 0.308

UCL = x bar + A2 * R bar = 154.36 +(0.308 * 4.48) = 155.74 mm

LCL = x bar - A2 * R bar = 154.36 +(0.308 * 4.48) = 152.98 mm

R chart

For sample size of 10 (pistons produced) , value of D3 = 0.223 and D4 = 1.777

UCL = D4 * R bar = 1.777 * 4.48 = 7.96 mm

LCL = D3 * R bar = .223 * 4.48 = 1 mm

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