Question

The manager of an organic yogurt processing plant desires with a mean of 16 ounces +/- 0.5 ounces. The process has a mean of 15.9 ounces and a standard deviation of 1 ounce. 1) Determine the Cp and Cpk of the process. Is the process capable of meeting specifications? Now the management has redesigned the system and so the standard deviation of the process is reduced to 0.1 ounces. 2) What is the Cp and Cpk of the new process? Is the new process capable of meeting specifications? 3) What happens to Cp as the process slides to the right? (the mean of the system increases?) 4) What happens to Cpk as the process slides to the right? (the mean of the system increases?) 5) What is the maximum value of Cpk?

Answer 1

Given: Upper Specification limit, USL= 16.5

Lower Specification limit, LSL = 15.5

Actual Mean, M = 15.9, Standard deviation: sd= 1

Answer 1: Process capability ratio: Cp= (upper specification-lower specification)/6sd

Process capability index: Cpk= Min [(M-LSL)/3sd; (USL-M)/3sd]

Process	Mean	Std	LSL	USL	Cpk= MIN[(Mean-LSL)/(3*std),(USL-Mean)/(3*std)]	CP= (USL-LSL)/6sd
A	15.9	1.0	15.5	16.5	0.1333	0.1667

the process is not capable as the value of Cpk is less than 1.33.

Answer 2: Now, sd= 0.1

Process	Mean	Std	LSL	USL	Cpk= MIN[(Mean-LSL)/(3*std),(USL-Mean)/(3*std)]	CP= (USL-LSL)/6sd
A	15.9	0.1	15.5	16.5	1.3333	1.6667

the process is capable as the value of Cpk is 1.33.

Answer 3: Now, if process slides to the right: This means that process mean has shifted to right

it won't affect Cp, as Cp does not take process mean in account for its calculation.

Answer 4: Now, if process slides to the right: This means that process mean has shifted to right

It will increase the Cpk value until it becomes 16 and will decrease after that , as Cpk takes process mean in account for its calculation. Cpk= MIN[(Mean-LSL)/(3*std),(USL-Mean)/(3*std)]

(Mean-LSL) value will increase and hence the value of Cpk

after 16 ounces mean

(USL-Mean) value will decrease and hence the value of Cpk

Answer 5: the Cpk will be max when the mean is between the USL and LSL that is 16

Process	Mean	Std	LSL	USL	Cpk= MIN[(Mean-LSL)/(3*std),(USL-Mean)/(3*std)]
A	16.0	0.1	15.5	16.5	1.6667

max of Cpk is 1.667