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Problem 1 Components used in a cellular telephone are manufactured with nominal dimension of 0.3 mm and lower and upper specification limits of 0.295 mm and 0.305 mm respectively. The x and R control charts for this process are based on subgroups of size 3 and they exhibit statistical control, with the center line on and the center line on the R chart at 0.00154 mm (a) Estimate the mean and standard deviation of this process. (b) Suppose that parts below the lower specification limits can be reworked, but parts above the upper specification limit must be scrapped. Estimate the proportion of scrap and rework produced by this process. (c) Suppose that the mean of this process can be reset by fairly simple adjustments. What value of the process mean would you recommend? Assume the cost of scrapped parts is double the cost of reworked ones. Problem 2 E The thickness of a printed circuit board is an important quality parameter. Data on board thickness (in inches) are given in Table 6.5 for 25 samples of three board each. TABLE 6E.S Printed Circuit Board Thickness for 610 2000 13 006 006310060 0065 006 006 0.06190060062 00006 16 001 002 006 0000060062 17 00:16 ot 1 000 000 00633 18 0 0 0 0 0 0 0.0631 1900 0 00 0.0619 0.06 0.06 0 00 00 00 0061100006 21 000 000 00616 0.0610 0.06 0.0675 0.06 07 02 OOO 900621 002 001 2400615 00 0615 10 0.06 0.06310063 5 000 000 110065 006 006 (a) Set up x and R control charts. Is the process in statistical control? If it was found to be out-of-control, assume there are assignable causes for signals and recalculate the limits. (b) Estimate the process standard deviation (c) What are the limits that you would expect to contain nearly all the process measurements? (d) If the specifications are at 0.0630 in 0.0015 in., what is the value of the PCR C