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Papers by Bharat Shah
IEEE Transactions on Reliability, 1971
This work demonstrates the feasibility of reliability Barlow and Proschan [2] used the semi-Marko... more This work demonstrates the feasibility of reliability Barlow and Proschan [2] used the semi-Markov process, a modeling of systems with repair capability using a semi-Markov process. generalization of Markov processes, to model a two-unit A two-unit system with exponential failure times but general repair system. Muth [12] analyzed multistate systems using a times is studied. Formulas for state-transition probabilities, waiting-Markov pro time distribution functions, and mean time in each state are developed. semicess by partitioning system states into two These quantities are expressed in terms of the Laplace transform of sets-up-states and down-states. repair time distribution functions. Once these quantities are known, Multiple-unit systems with exponential failure and general mean time to system failure and system availability, as well as other repair times have been studied using a semi-Markov model. system parameters, can be found using matrix manipulations. In Cinlar [4] found system availability under the assumption that addition, time-dependent results may be obtained. A numerical example varying the parameter in a repair-time law is presented. The faiuroo any one out of n units implies system failure. formulas developed can be extended to farger systems with repair Downton [5] obtained theLaplace transformofthedistribucapability for only one unit at a time and exponential failure times. tion of time to system failure by assuming that the system fails when k out of n units are inoperable. In addition, Osaki [14] Purpose Widen state of the art studied a variety of systems with different redundancy and Special math needed for explanations: Markov and semi-Markov preventive maintenance policies. In each example, his analysis processes, matrices yielded the distribution of time to system failure. Special math needed for results: Same This paper is also concerned with the reliability analysis of Results useful to: Reliability theorists systems composed of units with exponential failure times and general repair-tine probability laws. With the methods present-1. Introduction
IEEE Transactions on Reliability, 1971
This work demonstrates the feasibility of reliability Barlow and Proschan [2] used the semi-Marko... more This work demonstrates the feasibility of reliability Barlow and Proschan [2] used the semi-Markov process, a modeling of systems with repair capability using a semi-Markov process. generalization of Markov processes, to model a two-unit A two-unit system with exponential failure times but general repair system. Muth [12] analyzed multistate systems using a times is studied. Formulas for state-transition probabilities, waiting-Markov pro time distribution functions, and mean time in each state are developed. semicess by partitioning system states into two These quantities are expressed in terms of the Laplace transform of sets-up-states and down-states. repair time distribution functions. Once these quantities are known, Multiple-unit systems with exponential failure and general mean time to system failure and system availability, as well as other repair times have been studied using a semi-Markov model. system parameters, can be found using matrix manipulations. In Cinlar [4] found system availability under the assumption that addition, time-dependent results may be obtained. A numerical example varying the parameter in a repair-time law is presented. The faiuroo any one out of n units implies system failure. formulas developed can be extended to farger systems with repair Downton [5] obtained theLaplace transformofthedistribucapability for only one unit at a time and exponential failure times. tion of time to system failure by assuming that the system fails when k out of n units are inoperable. In addition, Osaki [14] Purpose Widen state of the art studied a variety of systems with different redundancy and Special math needed for explanations: Markov and semi-Markov preventive maintenance policies. In each example, his analysis processes, matrices yielded the distribution of time to system failure. Special math needed for results: Same This paper is also concerned with the reliability analysis of Results useful to: Reliability theorists systems composed of units with exponential failure times and general repair-tine probability laws. With the methods present-1. Introduction