# Three ice-cream packing machines at the Creamy Treat Company are being evaluated for their...

## Question:

Three ice-cream packing machines at the Creamy Treat Company are being evaluated for their capability. The following data are recorded:

Packing Machine Standard Deviation
A 0.2
B 0.3
C 0.05

If specifications are set between 15.8 and 16.2 ounces, determine which of the machines are capable of producing within specifications.

Show work and provide explanation

## Machine operating capability

The process capability index is applied to the operating results of 3 machines to determine which, if any, are capable. An explanation of the index and illustration of the calculations is provided.

## Answer and Explanation:

The process capability index identifies the nearest result of a process to a specification limit. This translates identifying the output that is closest to becoming or currently being problematic.

The formula is the minimum of the difference between the mean and each of the specification limits divided by 3 standard deviations. An index at or exceeding 1 represents capability. Below 1 indicates a lack of capability.

Applying the data provided to the formula yields:

A. min (16-15.8) / (2*.2), (16.2-16) /(2*.2) = .50 so not capable

B. min (16-15.8) / (3*.2), (16.2-16) /(3*.2) = .33 so not capable

C. min (16-15.8) / (.05*.2), (16.2-16) /(.05*.2) = 2 so capable