Answer :
A CpK value greater than 1 indicates that the process is capable of meeting the customer specifications. In this case, the CpK value of 0.605 suggests that the process may not be meeting the customer requirements consistently.
The CpK (Process Capability Index) is a statistical measure that helps determine how well a process is meeting customer requirements. It takes into account the overall average, variation, and customer specifications of a process. To calculate the CpK, we need to know the process variation and the distance between the process average and the customer specification limits.
In this case, the overall average temperature maintained by the refrigeration units is 46 degrees Fahrenheit. The average range, based on an X-bar chart, is 3 degrees Fahrenheit. The customer requires the units to operate between 43 and 48 degrees Fahrenheit.
First, let's calculate the process variation, which is the average range divided by a constant value called the d2 factor. The d2 factor depends on the subgroup size used in the data collection. Since we don't have that information, we'll assume a subgroup size of 2, which gives us a d2 factor of 2.704.
Process variation = Average range / d2 factor = 3 / 2.704 = 1.11 degrees Fahrenheit
Next, let's calculate the distance between the process average and the customer specification limits.
Upper specification limit (USL) = 48 degrees Fahrenheit
Lower specification limit (LSL) = 43 degrees Fahrenheit
Process capability index (Cp) = (USL - LSL) / (6 * process variation)
Cp = (48 - 43) / (6 * 1.11) = 0.901
The CpK is a more accurate measure that takes into account the process average and the worst-case deviation from the customer specifications.
CpK = min((USL - process average) / (3 * process variation), (process average - LSL) / (3 * process variation))
CpK = min((48 - 46) / (3 * 1.11), (46 - 43) / (3 * 1.11))
= min(0.605, 0.903)
= 0.605
Therefore, the CpK of the process is 0.605.
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