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The Availability and Hazard of a System Under a Cumulative Damage Process With Replacements

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  • S. Zacks

    (Binghamton University)

Abstract

Zacks (Failure distribution associated with general renewal damage processes. In: Nikulin M, Commenges D, Haber C (eds) Probability statistics and modelling in public health. Springer, Berlin, pp 465–475, 2006) studied the reliability function, the hazard function and the distribution of the failure time when a system is subject to a cumulative, compound renewal damage process. The failure occurs when the damage process crosses a threshold β. In the present paper these results are generalized to the model where the system is replaced after failures. Two cases are considered: instant replacement and random positive replacement time. The distribution of the age of the current renewal cycle, as well as its excess life, and the availability function are studied. We derive also the distribution of total time in (0, t) at which the system has been operational.

Suggested Citation

  • S. Zacks, 2010. "The Availability and Hazard of a System Under a Cumulative Damage Process With Replacements," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 555-565, December.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:4:d:10.1007_s11009-008-9098-y
    DOI: 10.1007/s11009-008-9098-y
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    Cited by:

    1. R. Jiang, 2022. "Two approximations of renewal function for any arbitrary lifetime distribution," Annals of Operations Research, Springer, vol. 311(1), pages 151-165, April.
    2. Parsa, Hossein & Jin, Mingzhou, 2013. "An improved approximation for the renewal function and its integral with an application in two-echelon inventory management," International Journal of Production Economics, Elsevier, vol. 146(1), pages 142-152.
    3. Jiang, R., 2020. "A novel two-fold sectional approximation of renewal function and its applications," Reliability Engineering and System Safety, Elsevier, vol. 193(C).

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