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Reliability Analysis of a One-Unit System

Author

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  • Richard E. Barlow

    (Sylvania Electronic Defense Laboratories, Mountain View, California)

  • Larry C. Hunter

    (Sylvania Electronic Defense Laboratories, Mountain View, California)

Abstract

This paper considers an electronic system that upon failure is repaired Only two states---the “on” state and the “off” state---are distinguished. The time-to-failure and the time-to-repair are random variables with general distribution functions. The purpose of the paper is to make available, in single unified treatment, mathematical information that is relevant for a reliability analysis of a one-unit system. The following questions are answered ( a ) What is the probability that the system will be on at any given time t ? ( b ) What is the probability that it will be on t hours or more during a given time interval (0, T )? ( c ) What is the expected fractional amount of time that it will be on during (0, T )? ( d ) What is the probability distribution of the number of failures during a given time interval? ( e ) What is the expected number of failures during a given time interval?. In particular, it is noted that “down” time is approximately normally distributed for large time intervals. The special cases of exponential failure with exponential and constant repair are given as examples.

Suggested Citation

  • Richard E. Barlow & Larry C. Hunter, 1961. "Reliability Analysis of a One-Unit System," Operations Research, INFORMS, vol. 9(2), pages 200-208, April.
    • Handle: RePEc:inm:oropre:v:9:y:1961:i:2:p:200-208
    DOI: 10.1287/opre.9.2.200
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    Cited by:

    1. Wu, Xiaoyue & Hillston, Jane, 2015. "Mission reliability of semi-Markov systems under generalized operational time requirements," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 122-129.
    2. Harishchandra Kodialbail & Manjunatha Kammasandra M., 2010. "Statistical Inference on Software Reliability Assuming Exponential Fault Correction Time," Stochastics and Quality Control, De Gruyter, vol. 25(2), pages 269-279, January.
    3. Wu, Shaomin & Wu, Di & Peng, Rui, 2023. "Considering greenhouse gas emissions in maintenance optimisation," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1135-1145.
    4. Xu, Ren-Hong & Lai, Yung-Cheng & Huang, Kwei-Long, 2021. "Decision support models for annual catenary maintenance task identification and assignment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).

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