Question

Question 4: K-Log produces cereals that are sold in boxes labeled to contain 390 grams. If the cereal content is below 390 grams, K-Log may invite auditor’s scrutiny. Filling much more than 390 grams costs the company since it essentially means giving away more of the product. Accordingly, K-Log has set specification limits at 400 10 grams for the weight of cereal boxes. Currently a filling machine fills the boxes. The boxes weigh on average 380 grams with a standard deviation of 20 grams.

A) Determine the process capability C_p ratio and the process capability index C_pk.

B) Briefly comment on the implication of your finding in part a).

C) Calculate the probability that a randomly selected cereal box will not conform to specifications.

D) For a process capability index of 2, determine what process targets (in terms of mean and standard deviation of the filling process) are needed. (Hint: What are the required process characteristics to achieve 6-sigma?)

Answer 1

A.

		LSL	USL
		Min	Max
	Range	390	410
	Mean	380
S	Std Dev	20
	Ppl	(Mean-LSL)/(3*S)	-0.16667
	Ppu	(USL-Mean)/(3*S)	0.5
	CPk	(Min (CPl,Cpu)	-0.16667	Ans A
			-0.17
	Cp	USL-LSL/(6 *S)	0.166667	Ans A

B.

As the Cp is very low and far from 1, the system is far from perfect.

And as CPk is negative, means the process is very poor.

C.

	X1	390
P1	P value	0.691462
	X1	410
P2	P value	0.933193
P=(P2-P1)	So conforming	0.24173
1-P	So not conforming	0.75827	Ans C