Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Probability in the Engineering and Informational Sciences
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A generic equation is derived related to determining reliability that depends only on the relative configurations of random variables in a finite interval. It is demonstrated that the statistics of random failures in a finite time interval can be handled easily using the derived equation. The new equation forms the basis of a new methodology for analysis of the intervals between random failures in a finite time interval and setting reliability requirements based on the existence of such intervals. An upper bound of the hazard rate (a hazard rate envelope) is determined which guarantees that when the hazard rate is within the specified envelope a set of minimum failure-free operating intervals (MFFOP intervals) will exist with a specified probability before failure and replacement. Contrary to a common view, it is demonstrated that for a finite time interval the probability of existence of a set of minimum failure-free intervals is not a product of the probabilities of existence of the separate MFFOP intervals. A model for setting quantitative reliability requirements is also proposed based on specifying the hazard rate envelope which guarantees with a specified probability no clustering of failures over a specified critical distance.