Question

A process that produces computer chips has a mean of .04 defective chips and a standard deviation of .003 chips. The allowable variation is from .032 to .048 defective. a.Compute the capability index (Cp) for the process.

Answer 1

The capability index for the process is 0.889

Explanation:

Here, we want to compute the capability index for the process

To get this, we need some important parameters which we already have stated in the question

USL ( upper standard limit) = 0.048

LSL (lower standard limit) = 0.032

mean = 0.04

standard deviation = 0.003

We apply the formula as seen in the attachment below

Kindly understand that we are to calculate the Z upper and Z lower

The smallest value between the two will be our Z minimum

This is what we shall apply in the capability index formula which mathematically is;

Z minimum/3

From calculation:

Z lower = Z upper = 2.67

So therefore;

capability index = 2.67/3 = 0.889