The main aim of this article is the presentation of the way of making calculation with the application of the semi-Markov processes, with the continuous time t, where nonexponential distribution function is going to be applied. These type of calculations were published but the time there was approaching infinity. Engineering practice proves that the lack of solutions of this issue leads to obtainment of solutions that are encumbered with errors. This article is the first attempt of the error analysis.SEMI-MARKOV METHOD FOR DETERMINING SELECTED CHARACTERISTICS IN SIMPLE TRANSPORTATION SYSTEMS
The aim of the article is to present a method for determining basic characteristics related to the operation and reliability of transportation systems using semi-Markov processes. Usually, in technical articles, simplifications are made assuming that phenomena “always” have an exponential character. Meanwhile, reality can be described by other, more complex probability density distributions of various phenomena. In such cases, typical programmed calculation methods do not work, and one must reach for advanced mathematical tools, such as semi-Markov processes. The article is a kind of discussion on the dilemmas that arise when determining reliability and operational characteristics with non-exponential probability distribution functions of transitions between states.
1. INTRODUCTION
Dependability sub-functions like reliability and related measures, as availability, maintainability, failure rate, mean times, etc., are very important in design, development and life of real technical systems. While calculation dependability contributors for technical objects usually is assumed, that probabilities of transition between states or sojourn times’ probabilities are exponential. Lack of information, too little number of samples or inaccurate assessment of data may cause that such assumption is abused. In some cases, (…)
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Source: Logistyka Magazine