Given are following information : Upper Specification Limit for Chicken Breast =

Question

Given are following information :

Upper Specification Limit for Chicken Breast = USL = 400 + 100 = 500 Calories

Lower Specification Limit for Chicken breast = LSL = 400 – 100 = 300 Calories

Process average distribution for chicken breast = m = 420 Calories

Standard deviation of population = Sd = 25 Calories

Thus,

Process capability Ratio, Cp

= ( USL – LSL) / 6 X Sd

= ( 500 – 300 ) / 6 x 25

= 200/150

= 1.333

Process Capability Index, Cpk

= Minimum ( ( USL – m)/3 x Sd , ( m – LSL)/3 x Sd)

= Minimum ( ( 500 - 420) / 3 x 25 , ( 420 -300) / 3x25)

= Minimum ( 80/75, 120/75)

= Minimum ( 1.066, 1.6)

= 1.06

For a process to be capable minimum requirement should be that Cp should be > 1 , which it is .

However target Cpk in the given case is 1.33 which does not get satisfied since Cpk is 1.06.

Therefore, it can be concluded that the process is not capable

Explanation / Answer

Process Capability Exercise Pioneer Chicken advertises "lite" chicken with 30 percent fewer calories. (The pieces are 33 percent smaller.) The process average distribution for "lite" chicken breasts is 420 calories, with a standard deviation of the population of 25 calories. Pioneer randomly takes samples of six chicken breasts to measure calorie content. The product design calls for the average chicken breast to contain 400-100 calories. Calculate the process capability index (target 1.33) and the process capability ratio. Interpret the results.

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