In the Production of Vitamin Capsules,the Proportion of Calcium in Each

Essay

In 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
- and R-charts to monitor the calcium amount using samples each of size 4.
The charts depict an in-control process.The center line of the R-chart is 6.7 and the center line of the
-chart is 44.8.
a.Compute C_p for this process using estimates of the process mean and standard deviation derived from the random sample.
b.Compute C_p for this process using estimates of the process mean and standard deviation derived from the control chart parameters.
c.Compute C_pk for this process using estimates of the process mean and standard deviation derived from the control chart parameters.
c.Compute C_pk for this process using estimates of the process mean and standard deviation derived from the random sample.
d.What do the differences between the values of C_p and C_pk tell you?