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.

44 nonconforming units

Explanation:

Calculate The expected number of nonconforming units

Given that :

Cp = 1.02

number of units ( N )  = 20,000

standard deviation  of defective units = 3 * 1.02 = 3.06

proportion of defective units = 1 - P ( -3.06 < Z < 3.06)

                                                = 1 - ( 0.9989 - 0.0011 ) = 1 - 0.9978 = 0.0022

Hence the number of nonconforming units

= N * proportion of defective units

= 20,000 * 0.0022 = 44

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