Question

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.)

Answer 1

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

Step-by-step 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