K-Log Produces Cereals That Are Sold in Boxes Labeled to Contain

Essay

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 FDA 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 between 390 and 410 grams for the weight of cereal boxes. Currently the boxes are filled automatically by a filling machine and they have an average weight of 405 g with a standard deviation of 4 g. What process targets (in terms of mean and standard deviation of the filling process) are needed for the filling machine to have a six-σ capability?