Systems with non-exponential distributions
The derivations in many of the preceding chapters have been made assuming that the underlying distributions for the component state resident times are exponential. This is particularly the case in Chapter 8 onwards. It has been stressed in these preceding chapters that, although the assumption of exponential distributions may have been made, the results and equations are equally applicable to all distributions if only the limiting state or long term average values are being evaluated for systems containing statistically independent components. This is not true if the time dependent values are being evaluated. The effect of typical distributions on limiting state values is demonstrated in Section 12.6. If the underlying distribution is non-exponential, then the process becomes non-Markovian. The techniques proposed in Chapter 8 onwards are no longer applicable and the problem has to be treated differently. Before discussing these additional techniques, it is worth examining the assumption of exponential distributions a little more deeply.
KeywordsProbability Density Function Exponential Distribution Repair Time Series Stage Single Component System
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