4.3: The Problem of Correlated Observations

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Most statistical analysis procedures require independent (and identically distributed) observations of performance measure values. However, the observations in a simulation experiment are typically dependent (correlated). This section illustrates why a simulation experiment generates correlated observations. Approaches to dealing with this issue are presented later in this chapter.

Consider the time the nth part arriving to workstation A in the two stations in a series model would spend at the workstation:

Time at workstation A_n = Time in buffer_n + Operation time_n

The time in the buffer for the nth part is composed of the operation times for the parts that preceded it in processing while the nth part was in the buffer. For example, suppose the fourth part to arrive does so while the second part to arrive is being processed. So the time the fourth part spends in the buffer is equal to a portion of the operation time for the second part and the entire operation time for the third part:

Time at workstation₄ = f(operation time₂, operation time₃) + Operation time₄

Thus, the time spent at the workstation by the fourth part is correlated with the time spent by the second and the third parts.

Rather than using correlated performance measure observations directly in statistical analysis computations, independent observations are constructed. How to do this is discussed later in this chapter.

The statistical analysis of simulation results is greatly aided by the construction of independent observations of the performance measures.