Assume in a cookie packaging machine, the process average (the average weight of the packages) is 10.0 ounces and the process standard deviation is .12 of an ounce. The customer is asking for a target value of 10.1 ounces with tolerances of plus or minus .5 ounce. Is the machine capable of meeting customer expectation? (Support your answer.)

the machine is capable of meeting customer expectation see the explanation below

Explanation:

For this question, to determine if the machine is capable of meeting customer expectation, we are going to calculate the process capability (Cpk) of cookie packaging machine.

Cpk = min (Cpl or CPU)

Where Cpl = (USL - Mean)/ 3 × standard deviation

Cpu= (mean - LSL)/3 × standard deviation

 Where

The process average (Mean) = 10.0 ounces

Tolerance = 0.5 ounces

Process Standard deviation (sd) = 0.12

Customer's Target value = 10.1 ounces ( plus or minus 0.5 ounce)

Therefore

Upper standard  limit (USL) = 10.1 + 0.5 = 10.6 ounces

Lower standard limit (LSL) = 10.1 - 0.5 = 9.6 ounces

So

Cpl = (USL - Mean)/ 3 × standard deviation

= (10.6 - 10.0)/3× 0.12

= 0.6/0.36

= 1.67

Cpu= (mean - LSL)/3 × standard deviation

= (10.0 - 9.6)/ 3 × 0.12

= 0.4/0.36

= 1.11

Since cpk = min(cpl,cpu)

Cpk is taken as 1.11

the machine is capable of meeting customer expectation

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