Two models for a repairable two-system with phase-type sojourn time distributions

Abstract This paper investigates a general repairable two-system. The operational and repair times are general, but for applicability, are approached by phase-time distributions, given that this class is dense in the set of distribution functions on the positive real line. Two models are studied, depending on the remembering of the failure phase when the unit is repaired. The versatility of this class of functions is shown. For these models, the availability and the rate of occurrence of failures are calculated. These performance measures are presented in a well-structured form, and are computationally implemented. The method and results are illustrated by a numerical example. The present work generalizes others in the specialized literature, and completes the study of two-systems under the Markov system.

[1]  Yuan Lin Zhang.  An optimal geometric process model for a cold standby repairable system , 1999 .

[2]  Rommert Dekker,et al.  Applications of maintenance optimization models : a review and analysis , 1996 .

[3]  M. Vangel.  System Reliability Theory: Models and Statistical Methods , 1996 .

[4]  S. Chakravarthy.  Reliability analysis of a parallel system with exponential life times and phase type repairs , 1983 .

[5]  B. Sericola,et al.  Interval-availability distribution of 2-state systems with exponential failures and phase-type repairs , 1994 .

[6]  Lam Yeh.  The rate of occurrence of failures , 1997 .

[7]  Odd O. Aalen,et al.  Phase type distributions in survival analysis , 2005 .

[8]  Lam Yeh,et al.  Calculating the Rate of Occurrence of Failures for Continuous-time Markov Chains with Application to a Two-component Parallel System , 1995 .

[9]  M. Neuts,et al.  On the use of phase type distributions in reliability modelling of systems with two components , 1981 .

[10]  Igor Ushakov,et al.  Reliability: Past, Present, Future , 2000 .

[11]  Necip Doganaksoy,et al.  Handbook of Reliability Engineering , 1994 .

[12]  M. Marseguerra,et al.  Simulation modelling of repairable multi-component deteriorating systems for 'on condition' maintenance optimisation , 2002, Reliab. Eng. Syst. Saf..

[13]  M. Neuts,et al.  Repairable models with operating and repair times governed by phase type distributions , 2000, Advances in Applied Probability.

[14]  Ruey Huei Yeh.  State-age-dependent maintenance policies for deteriorating systems with Erlang sojourn time distributions , 1997 .

[15]  David J. Sherwin,et al.  System Reliability Theory—Models and Statistical Methods , 1995 .

[16]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .

[17]  Marcel F. Neuts,et al.  Matrix-Geometric Solutions in Stochastic Models , 1981 .

[18]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[19]  Bo Henry Lindqvist,et al.  Markov Models for Periodically Tested Components 1 , 1998 .

[20]  Michael Tortorella,et al.  Reliability Theory: With Applications to Preventive Maintenance , 2001, Technometrics.

[21]  Frank A. Van der Duyn Schouten,et al.  Transient analysis of a two-unit standby system with Markovian degrading units , 1994 .