TABLE 18-4
a Factory Supervisor Is Concerned That

question 4

Short Answer

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.
$\begin{array} { l l l }\text { Hour } &\bar{X} & \text { R }\\ \hline1 & 18.4 & 25 \\ 2 & 16.9 & 27 \\ 3 & 23.0 & 30 \\ 4 & 21.2 & 23 \\ 5 & 21.0 & 24 \\ 6 & 24.0 & 25 \\ 7 & 19.3 & 12 \\ 8 & 15.8 & 14 \\ 9 & 20.0 & 13 \\ 10 & 23.0 & 11 \end{array}$
She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.
-Referring to Table 18-4, what is the value of the C_pk index?

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Definitions:

Confidence Interval

A spectrum of values obtained from sample data, which has a high probability of encompassing an unknown characteristic of the entire population.

Mean

The mean, often referred to as the average, is a statistic that represents the central or typical value in a set of data, calculated by dividing the sum of all values by the number of values.

Population Standard Error

A measure that estimates the variability of sample means around the population mean if multiple samples were taken from the population.

Confidence Interval

A band of values, yielded by analyzing sample data, which has a good chance of capturing the value of an unknown population variable.