- Five samples of ten auto parts were chosen from a process for quality inspecti

Question

- Five samples of ten auto parts were chosen from a process for quality inspection, and their diameters were measured. The sample averages and sample ranges are shown in the following table SampleMean (mm) Range (mm) 2 3 4 5 10.1 10.2 9.6 9.7 9.4 0.8 0.7 0.6 0.8 1. What are the 3-sigma control limits for the mean chart and range chart? Is the process in control? 2. If the true diameter mean should be 10mm, and you set this as your center line, what are the new controls limits of the mean chart? Is the process in control?

Explanation / Answer

X-bar-bar = Average of Mean = (10.1+10.2+9.6+9.7+9.4)/5 = 9.8

R-bar = Average of Range = (1.1+0.8+0.7+0.6+0.8)/5 = 0.8

1) Mean chart:

m=10, A2 = 0.308

UCL = X-bar-bar + A2*R-bar = 9.8 + 0.308*0.8 = 10.05

LCL = X-bar-bar - A2*R-bar = 9.8 - 0.308*0.8 = 9.55

Range chart:

D3 = 0.223

D4 = 1.777

UCL = D4*R-bar = 1.777*0.8 = 1.42

LCL = D3*R-bar = 0.223*0.8 = 0.18

Process is not in control as values are beyond Mean UCL

2) If X-bar-bar = 10

UCL = 10 + 0.308*0.8 = 10.25

LCL =  10 - 0.308*0.8 = 9.75

So, this is in control

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