Fuzzy semi-Markovian stochastic model for single-unit system with repairman arrival delay under Lindley lifetime distribution using bell-shaped membership function

Authors

  • Monika Saini
    Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur-303007, India
  • Ashish Kumar
    Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur-303007, India

Keywords:

Fuzzy Availability, Lindley Distribution, Single-unit system, Bell-shaped membership function, Regenerative point technique

Abstract

The key objective of the present analysis is to analyze the impact of fuzziness and repairman arrival delay on the mean time to system failure (MTSF) and availability of single-unit systems. Using a semi-Markovian approach, two stochastic models were developed, and recursive relations were obtained for the reliability measures. The lifetime, failure time, and repairman arrival time are considered Lindley-distributed random variables, with a parameter represented as a fuzzy number defined by a bell-shaped membership function. The switching devices and repairs are assumed to be as good as new. The numerical results show that increasing the \alpha-cut reduces fuzziness and improves the estimates, while immediate arrival of the repairman increases system availability. The importance of the results is highlighted using a numerical example generated from a Lindley-distributed random sample of size 1000 by considering \varepsilon = 0.1 and dynamic \delta in RStudio.

Dimensions

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Published

2026-06-29

How to Cite

Fuzzy semi-Markovian stochastic model for single-unit system with repairman arrival delay under Lindley lifetime distribution using bell-shaped membership function. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3438. https://doi.org/10.46481/jnsps.2026.3438

Issue

Volume 8, Issue 3, August 2026

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2026 Monika Saini, Ashish Kumar (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Fuzzy semi-Markovian stochastic model for single-unit system with repairman arrival delay under Lindley lifetime distribution using bell-shaped membership function. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3438. https://doi.org/10.46481/jnsps.2026.3438

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