X barchart R chart UCL=626 UCL=18.795 Center line=620 Center line =8.236 LCL=614

Question

X barchart                        R chart

UCL=626                            UCL=18.795

Center line=620              Center line =8.236

LCL=614                               LCL=0

Both charts exhibit control.

a)     What is the estimated standard deviation of the process?

b)     Suppose an s chart were to be substituted for the R chart. Whatwould be the appropriate parameters of the s chart?

c)       If specifications on theproduct were 610 +/- 15, what would be your estimate of the processfraction nonconforming?

d)     What could be done to reduce this fraction nonconforming?

e)     What is the probability of detecting a shift in the process mean to610 on the first sample following the shift (sigma remainsconstant)?

f)       What is the probability ofdetecting a shift in part (e) by at least the third sample afterthe shift occurs?

Explanation / Answer

UCL = B4 * s(bar) = 2.266 * 3.682 = 8.75 CL = 3.682 LCL = 3.682 * B3 = 0

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