A soft drink bottling company is interested in controlling its filling operation. Random samples of size 4 are selected and the fill weight is recorded. Table 7-19 shows the data for 24 samples. The specifications on fill weight are 350±5 grams (g). Daily production rate is 20,000 bottles.
(a) Find the trial control limits for the X - and R-charts.
(b) Assuming special causes for out-of-control points, find the revised control limits.
(c) Assuming the distribution of fill weights to be normal, how many bottles are nonconforming daily?
(d) If the cost of rectifying an under filled bottle is $0.08 and the lost revenue of an overfilled bottle is $0.03, what is monthly revenue lost on average?
(e) If the process average shifts to 342 g, what is the probability of detecting it on the next sample drawn after the shift?
(f) What proportion of the output is nonconforming at the level of process average indicated in part (e)?
