Consider the small factory of Example 9.25 where the probability of a bad part was 0.10. S...

Consider the small factory of Example 9.25 where the probability of a bad part was 0.10. Suppose that the company is considering a new manufacturing process that will lower the probability of a bad part to 0.05. The company wants to compare the two manufacturing processes on the basis of the steady-state mean time in system, and it decides to make 10 independent replications of each process of length 12,400 minutes with a warmup period of 2400 minutes (40 hours). Let X_ij be the average time in system for process i (i = 1, 2 for the original and proposed processes, respectively) over the last 10,000 minutes on replication j (j = 1, 2, …, 10), and let Z_j = X_1j – X_2j.

Compute the sample variance of the Z_j’s for each of the following cases of synchronization:

(a) The two manufacturing processes are simulated completely independently (no synchronization).

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(b) Only interarrival times of new parts are synchronized.

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(c) Only times to failure and repair times for the machine are synchronized.

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(d) Only processing times and inspection times of a part on its first pass through the system (if more than one pass is required) are synchronized.

Compute the variance reductions corresponding to cases (b), (c), and (d), using case (a) as the base case. What random variates are the most important to synchronize?

Example 9.25

FIGURE 9.9 Small factory consisting of a machining center and an inspection station.