Anormally 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?