The baking time of painted corrugated sheet metal is of interest. Too much time will cause the paint to flake, and too little time will result in an unacceptable finish. The specifications on baking time are 10± 0.2 minutes. Random samples of size 6 are selected and their baking times noted. The sample means and standard deviations are calculated for 20 samples with the following results:

Σ_i=1 ²⁰ X_i^‾ = 199.8,

Σ_i=1 ²⁰ s_i^‾ = 1.40

(a) Calculate the centerline and control limits for the X‾- and s-charts.

(b) Estimate the process mean and standard deviation, assuming the process to be in control.

(c) Is the process capable? What proportion of the output is nonconforming?

(d) If the mean of the process can be shifted to 10 minutes, would you recommend such a change?

(e) If the process mean changes to 10.2 minutes, what is the probability of detecting this change on the first sample taken after the shift? Assume that the process variability has not changed.