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McWilliams

satisfy ^3 = r/0 = T] + T2. In addition to examining the effect of imposing increasing restrictive constraints, we also examine in Case 1 the impact of

increasing the shape parameter r. Since = r/0^, increasing r while maintaining r/0 = Ti + T2 serves to reduce the variability of the distribution assigned to Ti + T2. Guidelines for estimating r and 0 in practice can be found in Appendix C.

Tables 3A and 3B contain optimal control chart parameters and information regarding the distribution of T_out. For example, in Case 1 with no constraint imposed T₀ut has 95th percentile equal to 9.58 hours and standard deviation 2.96 hours. We examine the impact of successively reducing the 95th percentile to 6, 5, and 4 hours. This is the generaÅ‚ pattem followed in Cases 2 through 7. Values used for r and 0 can be found in Tables 4A and 4B. These tables also contain cost information and values of a, p, ECL, and the limiting percent of time, within a Ä…uality cycle, that the process is in control.

With respect to control chart parameters (n , L , and h ) the effect of constraining is not surprising. If an assignable cause must be discovered and eliminated in a reduced time period, then the process is morÄ™ closely monitored. Tables 4A and 4B show that sample sizes tend to increase, the time h* between samples decreases, and the n*, L* (or n*, R*) combination is chosen to increase p, the probability of detecting the out of control State with any sample. This pattem generally holds for all examples considered. Cases 8 and 9 are exceptions with regards to the observed increase in p. With no penalty for producing nonconforming items, there is less motivation to detect the out of control State. With respect to expected cycle lengths, the trend is to experience a decrease, with a corresponding increase in the percent of time the process is in control. Once again, Cases 8 and 9 are exceptions.

Cost behavior as illustrated in Tables 4A and 4B is also predictable. As constraints tighten, total cost increases. While the hourly cost due to producing nonconforming items invariably decreases, this savings is morÄ™ than offset by increases in both the costs of false alarms and of sampling. The naturÄ™ of the tradeoff between reduced variability and increased cost varies from example to example. In many cases, variability can be substantially reduced at relatively Iow cost. For example, in the p-chart model of Case 3 we see that by accepting a 10% increase in hourly cost, from $8.22 to $9.04, the 95th percentile of T_0U( can be reduced from 86.79 to 50.11 hours and the standard deviation reduced from 27.22 to 15.89 hours, a reduction of 42% in both cases. In Case 6, based on Duncan's X -chart model, the unconstrained