Question & Answer: Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging…..

S6.7Auto pistons at Wemming Chungs 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 MEAN (MM) 156.9 153.2 153.6 155.5 156.6 RANGE (MM) 4.2 4.6 4 5.0 4.5 a) What is the value of x? b) What is the value of R? c) What are the UCLT and LCL, using 3a? Plot the data d) What are the UCLR and LCLR, using 3o? Plot the data e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCLr and LCL? PX

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: a) What is the value of x? b) What is the value of R bar? c) What are the UCL_x bar and LCL_x bar, using 3 sigma? Plot the data. d) What are the UCL_R and LCL_R, using 3 sigma? Plot the data. e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL_x bar and LCL_x bar?

Expert Answer

Answer

x double bar = mean of means = mean or average of (day 1 to day 5 means in MM ) = average of (156.9, 153.2, etc, 156.6)

x
156.9
153.2
153.6
155.5
156.6
Mean = Average = 155.16

a) x double bar = 155.16 mm

Similarly, add up all the range values and divide by 5 to find the arithmetic mean or average:

Excel Function: Average(values)

Range
4.2
4.6
4.1
5
4.5
(4.2+4.6+4.1+5+4.5)/5 = 4.48

b) R bar = 4.4799999999 mm

c)

X:

The control chart built in value A 2 = 0.307999999 for 10 piston samples

Upper Control Limit UCL x bar = average + A 2 R = 155.16 + (0.30799999999 * 4.479999999999) = 156.54 mm = 157 mm (approximately(approx))

Lower Control Limit LCL x bar = average – A 2 R = 155.16 – (0.30799999999 * 4.479999999999) = 153.779999999mm = 154 mm (Approx)

d)

R:

R is already found to be R = 4.479999999999999999

The standard tables give D4 = 1.777 and D3 = 0.223

UCL R = D 4 * R = 1.777 * 4.479999999999999999 = 7.961 mm

LCL R = D 3 * R = 0.223 * 4.479999999999999999 = 0.999 = 1 mm

e)

new mean = 155

new UCL x = 155 + (0.30799999999 * 4.479999999999) = 156.37999999 mm

new LCL x = 155 – (0.30799999999 * 4.479999999999) = 153.6202 mm

Charts:

X:

Question & Answer: Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging..... 1

R:

Question & Answer: Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging..... 2

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