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?

Question

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?

Quizplus · Accepted Answer

The Answer of 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?

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