Two parts are assembled as shown in Figure 6.28. Assume that the dimensions x and y are normally distributed with means x and y and standard deviations x and y, respectively. The parts are produced on different machines and are assembled at random. Control charts are maintained on each dimension for the range of each sample (n = 5). Both range charts are in control.
(a) Given that for 20 samples on the range chart controlling x and 10 samples on the range chart controlling y, we have
(b) If it is desired that the probability of a smaller clearance (i.e., x – y) than 0.09 should be 0.006, what distance between the average dimensions (i.e., x − y) should be specified?

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