A Normally distributed quality characteristic is monitored throughuse of an x bar and R chart. These charts have the followingparameters n=4
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?