Standard deviation | English homework help

A normally distributed quality characteristic is monitored through use of an  and an chart. These charts have the following parameters (=4):

 Chart R Chart UCL = 626.0 UCL = 18.795 Center line = 620.0 Center line = 8.236 LCL = 614.0 LCL = 0

Both charts exhibit control.

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

(b) Suppose an chart were to be substituted for the chart. What would be the appropriate parameters of the chart?

(c) If specifications on the product were 610 ??15, what would be your estimate of the process fraction nonconforming?

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

(e) What is the probability of detecting a shift in the process mean to 610 on the first sample following the shift (σ remains constant)?

(f) What is the probability of detecting the shift in part (e) by at least the third sample after the shift occurs?

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