Question

The temperature control unit on a commercial freezer in a 24-hour grocery store is set to maintain a mean temperature of 23 degrees Fahrenheit. The temperature varies because people are constantly opening the freezer door to remove items, but the thermostat is capable of maintaining a temperature with a standard deviation of 2 degrees Fahrenheit. The desired range is 18 to 30 degrees Fahrenheit. Find the Cpk capability indexes

Answer 1

The capability index of the freezer control unit is 0.83.

How to find capability index

The capability index is given by:

$C_{pk}=\frac{Z_{min}}{3} \\\\Z_{upper}=\frac{USL-Mean}{Standard\ deviation} \\\\Z_{lower}=\frac{Mean-LSL}{Standard\ deviation} \\\\From\ the\ question,mean=23,USL=30,LSL=18,deviation=2, hence:\\\\Z_{upper}=\frac{30-23}{2}=3.5 \\\\Z_{lower}=\frac{23-18}{2}=2.5 \\\\Z_{min}=2.5\\\\Hence:\\\\C_{pk}=\frac{2.5}{3} =0.83$

The capability index of the freezer control unit is 0.83.

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