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