Food Storage Technologies produces refrigeration units for food producers and retail food establishments. The overall average temperature that these units maintain is 46 degrees Fahrenheit. The average range of the process based on an x-bar chart is a total of 3 degrees Fahrenheit. The customer requires the units to operate between 43 and 49 degrees Fahrenheit.

The Cpk of the process is:

a. 1.33
b. 2
c. 3
d. 6
e. None of the above

The Cpk can be calculated using the formula: Cpk = min((USL - μ)/3σ, (μ - LSL)/3σ). In this case, the Cpk of the process is not one of the options provided.

Explanation:

The Cpk of the process is calculated using the formula: Cpk = min((USL - μ)/3σ, (μ - LSL)/3σ), where USL is the upper specification limit, LSL is the lower specification limit, μ is the process mean, and σ is the process standard deviation. In this case, the USL is 49, the LSL is 43, and the process average (μ) is 46. The average range of the process based on an x-bar chart is 3. The process standard deviation (σ) can be calculated using the formula: σ = range/2.66, where range is the average range. After calculating the standard deviation, we can substitute the values into the Cpk formula to find the Cpk of the process.

Using the given values, we have:

σ = 3/2.66 = 1.13

Cpk = min((49 - 46)/3(1.13), (46 - 43)/3(1.13)) = min(0.84, 0.84) = 0.84

Therefore, the Cpk of the process is 0.84, which is not one of the options provided. So, the correct answer is e. None of the above.

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