Algorithm for a general discrete k-out-of- n: G system subject to several types of failure with an indefinite number of repairpersons

• Published in: European journal of operational research Vol. 211; no. 1; pp. 97 - 111
• Main Authors: Ruiz-Castro, Juan Eloy, Li, Quan-Lin
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.05.2011; Elsevier
• Series: European Journal of Operational Research
• Subjects: Algorithms; Applied sciences; Blocking; Discrete phase-type distribution; Exact sciences and technology; Failure; k-out-of- n: G system; Maintenance; Mathematical analysis; Mathematical models; Matlab; Operational research; Operational research and scientific management; Operational research. Management science; Optimization; Reliability; Reliability Maintenance k-out-of-n: G system Discrete phase-type distribution; Reliability theory. Replacement problems; Discrete phase-type distribution; Maintenance; Reliability; k-out-of- n: G system; Performance evaluation; Phase type distribution; Rupture; Algorithmics; Durability; State space; Conditional probability; k-out-of-n: G system; Failures; Modeling; Optimization; Stationary condition; Transients; Markov chain; K out of n system; Lifetime; Discrete distribution; Matrix method; Reward; Repair
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2010.10.024

A discrete k-out-of- n: G system with multi-state components is modelled by means of block-structured Markov chains. An indefinite number of repairpersons are assumed and PH distributions for the lifetime of the units and for the repair time are considered. The units can undergo two types of failures, repairable or non-repairable. The repairability of the failure can depend on the time elapsed up to failure. The system is modelled and the stationary distribution is built by using matrix analytic methods. Several performance measures of interest, such as the conditional probability of failure for the units and for the system, are built into the transient and stationary regimes. Rewards are included in the model. All results are shown in a matrix algorithmic form and are implemented computationally with Matlab. A numerical example of an optimization problem shows the versatility of the model.