Use of exponential distribution in mathematical models of dependability

The exponential distribution of time to event or end of state is popular in the dependability theory. This distribution is characterized by the strength that is a convenient parameter used in mathematical models and calculations. The exponential distribution is used as part of dependability-related process simulation. Examples are given to illustrate the applicability of the exponential distribution.
Aim. The aim of the paper is to improve the dependability-related simulation methods when using the exponential distribution of periods of states or times to events.
Methods. The assumption of the exponential distribution of time between events can be justified or discarded using methods of the probability theory and/or mathematical statistics or on the basis of personal or engineering experience. It has been experimentally established that the failure flow in an established mode of operation is stationary, ordinary and produces no consequences. Such flow is Poisson and is distinct in the fact that the time between two consecutive failures is distributed exponentially with a constant rate. This exponential distribution is reasonably extended to the distribution of an item’s failure-free time. However, in other cases, the use of exponential distribution is often not duly substantiated. The methodological approach and the respective conclusions are case-based. A number of experience-based cases are given to show the non-applicability of exponential distribution.
Discussion. Cases are examined, in which the judgement on the applicability or non-applicability of exponential distribution can be made on the basis of personal experience or the probability theory. However, in case of such events as completion of recovery, duration of scheduled inspection, duration of maintenance, etc., a judgement regarding the applicability of exponential distribution cannot be made in the absence of personal experience associated with such events. The distribution of such durations is to be established using statistical methods. The paper refers to the author’s publications that compare the frequency of equipment inspections with regular and exponentially distributed periods. The calculated values of some indicators are retained, while for some others they are different. There is a two-fold difference between the unavailability values for the above ways of defining the inspection frequency.
Findings and conclusions. The proposed improvements to the application of exponential distribution as part of dependability simulation come down to the requirement of clear substantiation of the application of exponential distribution of time between events using methods of the probability theory and mathematical statistics. An unknown random distribution cannot be replaced with an exponential distribution without a valid substantiation. Replacing a random time in a subset of states with a random exponentially distributed time with a constant rate should be done with an error calculation.

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