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# Capability Index

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1) C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 4 ± .003 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 4.001 inches with a standard deviation of .002 inch.
A. Calculate the (capability index) for this machine.
B. Should C-Spec use this machine to produce this part? Why?

#### Solution Summary

This solution determines the capability index for a machine to see if it can meet certain specifications.

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## Process Capability Index

1. Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are:

Sample 1 | 2 | 3 | 4
1 | 0.594 | 0.622 | 0.598 | 0.590
2 | 0.587 | 0.611 | 0.597 | 0.613
3 | 0.571 | 0.580 | 0.595 | 0.602
4 | 0.610 | 0.615 | 0.585 | 0.578
5 | 0.580 | 0.624 | 0.618 | 0.614
6 | 0.585 | 0.593 | 0.607 | 0.569

a. Assume that only these six samples are sufficient, and use the data to determine control limits for an R- and an x-bar chart.

b. Suppose that the specification for the bottle neck diameter is 0.600 in ± 0.050 and the population standard deviation is 0.013 in. What is the Process Capability Index? The Process Capability Ratio?

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