Matrix stochastic analysis of the maintainability of a machine under shocks

• Published in: Reliability engineering & system safety 2014-01, Vol.121, p.11-17
• Main Authors: Montoro-Cazorla, Delia, Pérez-Ocón, Rafael
• Format: Article
• Language: English
• Subjects: Applied sciences; Availability; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Markovian arrival process; Matrix-analytic methods; Operational research and scientific management; Operational research. Management science; Phase-type distribution; Physics; Reliability theory. Replacement problems; Repair; Replacement; Solid mechanics; Structural and continuum mechanics
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2013.07.002

We study the maintenance of a machine operating under environmental conditions producing shocks affecting the lifetime of the machine. The shocks cause different types of damage depending on their strength and eventually the total failure. The maintenance of the machine is performed by repairs and replacement. The interarrival times of shocks are dependent. We introduce a multidimensional stochastic model for simulating the evolution of the lifetime of the machine. This model implies the application of the matrix-analytic methods, that are being used in stochastic modelling with interesting results. Under this methodology, the availability, the reliability, and the rates of occurrence of the different types of failures and of the replacements are calculated, obtaining mathematically tractable expressions. The results are applied to a numerical example. •A machine under random environmental conditions producing shocks and wear is studied under matrix-analytic methods.•There is dependence in the interarrival times of shocks.•Different types of failure producing damage in the internal and external structure of the machine are considered.•Maintenance is performed by repair and replacement.•Explicit expressions for the main reliability performance measures are given.