1.A process is to be monitored with standard values m = 10 and s = 2.5. The sample size is n = 2.

(a) Find the center line and control limits for the chart.

(b) Find the center line and control limits for the R chart.

(c) Find the center line and control limits for the s chart.

2. Samples of n=5 units are taken from a process every hour. The and R values for a particular quality char- acteristic are determined. After 25 samples have been collected, we calculate = 20 and - R = 4.56.

(a) What are the three-sigma control limits for and R?

(b) Both charts exhibit control. Estimate the process standard deviation.

(c) Assume that the process output is normally dis- tributed. If the specifications are 19 ± 5, what are your conclusions regarding the process capability?

(d) If the process mean shifts to 24, what is the prob- ability of not detecting this shift on the first sub- sequent sample?