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

question 74

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?

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Definitions:

External Causes

Factors or circumstances outside of one's control that influence events or outcomes.

Perceivers

Individuals who interpret, process, and assign meaning to information and stimuli they receive from the environment.

Behavior

The behavior or responses of a person in reaction to outside or inside triggers.

Unconscious Attributions

The process of assigning causes to behaviors without conscious awareness, often based on implicit biases or heuristics.