The thickness of sheet metal (mm) used for making automobile bodies is a characteristic of interest. Random samples of size 4 are taken. The average and standard deviation are calculated for each sample and are shown in Table 7-19 for 20 samples. The specification limits are 9.95 ± 0.3 mm.
(a) Find the control limits for the - and s-charts. If there are out-of-control points, assume special causes and revise the limits.
(b) Estimate the process mean and the process standard deviation.
(c) If the thickness of sheet metal exceeds the upper specification limit, it can be reworked. However, if the thickness is less than the lower specification limit, it cannot be used for its intended purpose and must be scrapped for other uses. The cost of rework is $0.25 per linear foot, and the cost of scrap is $0.75 per linear foot. The rolling mills are 100 feet in length. The manufacturer has four such mills and runs 80 batches on each mill daily. What is the daily cost of rework? What is the daily cost of scrap?
(d) If the manufacturer has the flexibility to change the process mean, should it be moved to 10.00?
(e) What alternative courses of action should be considered if the product is nonconforming?