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2 Safety and Reliability of Systems and Processes

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Modeling reliability of systems with repair by stochastic processes with long memory

Filus Jerzy K., Filus Lidia Z.

Safety and Reliability of Systems and Processes

2023

Summer Safety and Reliability Seminar 2023

69--78

In modelling reliability of systems with repair by stochastic processes of times between consecutive failures the usual Markovianity assumption was significantly relaxed. Instead of the Markovian stochastic processes, processes with long memory were constructed for the reliability and maintenance applications. The Markovianity restriction on the process’s memory could be omitted as two (relatively) new methods of the processes construction were employed. In this work, one of the two available methods, the ‘method of triangular transformations’, is presented. Other, the ‘method of parameter dependence’, is shortly described in Section 5. Since using an arbitrarily long memory has serious drawbacks in modelling process we, on the other hand, limited it by introducing the notion of k-Markovianity (k = 1,2,…), where the memory is reduced to the last k previous (discrete) time epochs. The discussion of this kind of problems together with construction of some new classes of stochastic processes with discrete time and their reliability application is provided.

General stochastic models for series multicomponent system reliability (short communication)

Filus Jerzy K., Filus Lidia Z.

Safety and Reliability of Systems and Processes

2022

Summer Safety and Reliability Seminar 2022

225--226

Multicomponent systems with known reliabilities (survival functions of the life-times) of their components are considered. Based on known either baseline or marginal survival functions of the component life-times we construct joint survival functions of random vectors of the life-times. These multivariate survival functions (here considered as system reliability models) are to be given in their general (universal) forms by means of joiners or system functions (instead of copula methodology) as a stochastic dependences determination.