The lower and upper specification limits for a mustard filling machine are 10.50 and 12.00 ounces, respectively. The standard deviation is 0.05. The process capability index of the machine will be:
A) less than or equal to 3.
B) more than 3 but less than or equal to 5.
C) more than 4 but less than or equal to 5.
D) more than 5.

Question

Quizplus · Accepted Answer

The process capability index (Cpk) can be calculated as:
Cpk = min[(USL - μ)/(3σ), (μ - LSL)/(3σ)]
where USL is the upper specification limit, LSL is the lower specification limit, μ is the mean of the process and σ is the standard deviation.

In this case, the mean of the process is not given. Therefore, we assume that the process is centered between the upper and lower specification limits, which gives us:
μ = (USL + LSL)/2 = (12.00 + 10.50)/2 = 11.25

Substituting the given values, we get:
Cpk = min[(12.00 - 11.25)/(3*0.05), (11.25 - 10.50)/(3*0.05)]
Cpk = min[5, 5]
Cpk = 5

Since the Cpk is greater than 4 but less than or equal to 5, the best choice is C. This indicates that the machine is very capable of producing mustard fillings within the specified range.

The Lower and Upper Specification Limits for a Mustard Filling