Question

Need Instructions on how to complete with EXCEL.... Handwritten answer not adequate, need to know how EXCEL can be used to solve this problem....

A process is in control and centered at nominal. Output from the process is normally distributed and the process capability index, Cp, equals 1.02. Determine the expected number of nonconforming units that will result from a production run of 20,000 units. Assume that all previously stated conditions regarding the process remain as described during the production run of 20,000 units.

Answer 1

It is given that the process is in control and centered at nominal. Also, from the process is normally distributed and the process capability index, Cp = 1.02.

So first we need to find P( -3*Cp < Z < 3*Cp ) where Z is the standard normal variate

P( -3*Cp < Z < 3*Cp ) = P( -3*1.02 < Z < 3*1.02 ) = P( -3.06 < Z < 3.06 ) = P( Z < 3.06 ) - P( Z < -3.06 ) .....( 1 )

Let's use excel:

P( Z < 3.06 ) = "=NORMSDIST(3.06)" = 0.998893

P( Z < -3.06 ) = "=NORMSDIST(-3.06)" = 0.001107

Plug this in equation 1), we get

P( -3*Cp < Z < 3*Cp ) = 0.998893 - 0.001107 = 0.997787

So probability of nonconforming units = 1 - P( -3*Cp < Z < 3*Cp ) = 1 - 0.997787 = 0.002213

So the expected number of nonconforming units that will result from a production run of 20,000 units are as

0.002213 * 20000 = 44.2674 = 44 units ( approximate after rounding to the nearest integer).