13Examining Serially Dependent Processes

Many manufacturing and service processes are iterative—the units are produced or provided in a sequence one after another, although the throughput varies with the nature of the unit. It takes longer to produce an automobile than a printed circuit card and even longer to produce a ship. The output of such production systems can be said to be serial, and if the effort in each one is complete and independent of the next, so also the units should be complete and independent, one from the other.

Shewhart (1931) and others have shown that no process is perfect and that even a process in conformity to its design will suffer variation in the quality characteristics of its output because of a stable system of chance causes. However, if the process is stable, then this variation from one output to the next will be uncorrelated. Consider the variation of the quality characteristics of each produced unit as a random variable, Xj. In a stable process, there will be no correlation between, say, the value of Xj and the value of Xj+1. The set of these random variables is ...

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