Journal of Applied Probability

Availability analysis of periodically inspected systems with random walk model

Lirong Cui and M. Xie

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In this paper, the instantaneous availability of a system maintained under periodic inspection is investigated using random walk models. Two cases are considered. In the first model, the system is repaired or modified and it is assumed to be as good as new upon periodic inspection and maintenance. In the second model, the system is not modified after the inspection if the system is still working, and the condition of the system is assumed to be the same as that before the inspection. For both models the failures only can be found through the inspection. Perfect repair or replacement of a failed system is assumed to be carried out, but the time it takes can be constant or of a random length. The relationship between this problem and the random walk model in a two-dimensional plane is described. Several new results are also shown.

Article information

J. Appl. Probab. Volume 38, Number 4 (2001), 860-871.

First available in Project Euclid: 25 January 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05]
Secondary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

Random walk periodic inspection instantaneous availability repair or replacement stochastic process


Cui, Lirong; Xie, M. Availability analysis of periodically inspected systems with random walk model. J. Appl. Probab. 38 (2001), no. 4, 860--871. doi:10.1239/jap/1011994177.

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