Write a discussion paper on the production of vitamin capsules, the proportion of calcium in each capsule has a specification of 48 ± 18 parts per million (ppm). An initial random sample of 100 capsules revealed a sample average calcium content of 44.5 ppm and a sample standard deviation of 3.2 ppm. Management uses x-bar- and R-charts to monitor the calcium amount using samples of size 4 for each.
The charts depict an in-control process. The center line of the R-chart is 6.7 and the center line of the x-bar-chart is 44.8.
a. Compute Cp for this process using estimates of the process mean and standard deviation derived from the random sample.
b. Compute Cp for this process using estimates of the process mean and standard deviation derived from the control chart parameters.
c. Compute Cpk for this process using estimates of the process mean and standard deviation derived from the random sample.
d. Compute Cpk for this process using estimates of the process mean and standard deviation derived from the control chart parameters.
e. What do the differences between the values of Cp and Cpk tell you?
