Question

A process on a machine has a standard deviation of 0.04 inches. If a product with specifications of /- 0.07 inches has to be processed on that machine, is the machine capable of performing that job

Answer 1

No, it can't perform because C_p < 1

Explanation:

We are told that a product with specifications of ± 0.07 inches has to be processed on that machine. This means that the product is centered on the machine.

Thus;

Specification Width = 2 × 0.07 = 0.14

Now, formula for capability index is;

C_p = specification width/(6 × standard deviation)

We are given standard deviation = 0.04. Thus;

C_p = 0.14/(6 × 0.04)

C_p = 0.5833

Now, for this process, C_p should not be less than 1. However in this case it is less than 1,thus it means that the machine will not be able to perform the job.