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

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