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 sample standard deviation of $3.2 \mathrm{ppm}$ . Management uses $x$ - 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 $\bar{x}$ -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 $C_{p k}$ for this process using estimates of the process mean and standard deviation derived from the random sample.
c. Compute $C_{p k}$ for this process using estimates of the process mean and standard deviation derived from the control chart parameters.
d. What do the differences between the values of $C_{p}$ and $C_{p k}$ tell you?