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 Cp ratio and the process capability index Cpk.
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?)