STATS two Problems 6.24 and 6.25

6.24. 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.

6.25. 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?