Question

A process is in control with mean 50 and standard deviation of 2. The upper specification limit for the product being produced is 60 and the lower specification limit is 42. What is the value of Cpk?

Answer 1

Cpk = 1.33

Step-by-step explanation:

Given:

Mean = 50

Sd = 2

USL = 60

LSL = 42

The Cpk means process capability index. it helps decide the specification limit when the nominal value is not the central value of upoer specification limint (USL) and lower specification limit (LSL).

The Cpk can be derived using the formula:

`Cpk = min [((usl - mean))/(3 * \sigma), ((mean - lsl))/(3*\sigma)]`

`Cpk = min [((60 - 50))/(3*2) , ((50 - 42))/(3*2)]`

Solving further,

`Cpk = min [(10)/(6) , (8)/(6)]`

Cpk = min ( 1.67 , 1.33)

Cpk = 1.33

Cpk = 1.33