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Simplified Approach to Analyse the Fuzzy Reliability of a Repairable System

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Advances in Reliability, Failure and Risk Analysis

Part of the book series: Industrial and Applied Mathematics ((INAMA))

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Abstract

This chapter presents a simplified approach to analysing the fuzzy reliability of a reparable system by utilising uncertain data collected from different sources. This technique uses fault tree to model the system, triangular fuzzy numbers to quantify uncertain information, and the Lambda-Tau (LT) method to discover functional equations for six distinct system reliability indices, whilst simplified arithmetic operations are using for calculation. The proposed strategy is utilised to estimate the efficiency of a paper producing plant’s washing system by determining its fuzzy reliability for various levels of uncertainty. Results are compared with two existing techniques, namely conventional LT and fuzzy Lambda-Tau (FLT). To determine how different operating conditions affect system performance, sensitivity analysis and long-term reliability evaluation are conducted. The significant system components are ranked using the V-index. The results indicate that, in comparison with the current FLT technique, the proposed approach is straightforward to implement for assessing the fuzzy reliability of any substantial and intricate repairable industrial system. The presented approach might be very useful to maintenance professionals in designing an effective maintenance strategy for enhancing system performance in a very easy manner.

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Abbreviations

\(\tilde{A}\) :

Fuzzy set \(\tilde{A}\)

\(\mu _{\tilde{A}}(x)\) :

Membership degree of x in \(\tilde{A}\)

\(a_1\), \(a_2\) and \(a_3\):

Left, modal, and right end values of TFN \(\tilde{A}=(a_1,a_2,a_3)\)

\(\lambda _i\) :

System’s ith component’s crisp failure rate

\(\lambda _s\) :

System’s crisp failure rate

\(\mu _s\) :

System’s crisp repair rate

\(\tilde{\tau }_i\) :

System’s ith component’s fuzzy repair time

\(\tilde{\tau }_s\) :

System’s fuzzy repair time

\(\overline{A}\) :

Defuzzified value of fuzzy set \(\tilde{A}\)

\(\tilde{q}_T\) :

System’s fuzzy failure rate

\(V(\tilde{q}_T,\tilde{q}_{T_i})\) :

V-index measures the difference between \(\tilde{q}_T\) and \(\tilde{q}_{T_i}\)

\(\text {MTTR}_s\) :

Mean time to repair

\(\text {ENOF}_s(0,t)\) :

Expected number of failures

\(R_s(t)\) :

System reliability at time t

x :

Element of fuzzy set \(\tilde{A}\)

X :

Universal set

\(+, -,\otimes ,/\) :

Sum, difference, product, and division between two TFNs

\(\tau _i\) :

System’s ith component’s crisp repair time

\(\tau _s\) :

System’s crisp repair time

\(\tilde{\lambda }_i\) :

System’s ith component’s fuzzy failure rate

\(\tilde{\lambda }_s\) :

System’s fuzzy failure rate

t :

Time t

\(\overline{R}\) :

Defuzzified value of any fuzzy reliability index \(\tilde{R}=(r_1,r_2,r_3)\) in TFN form

\(\tilde{q}_{T_i}\) :

System’s fuzzy failure rate by taking its ith component \(\tilde{\lambda }_{i}=\tilde{0}\)

\(\text {MTTF}_s\) :

Mean time to failure

\(\text {MTBF}_s\) :

Mean time between failures

\(A_s(t)\) :

System availability at time t.

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Acknowledgements

The author would like to thank the anonymous referees for their valuable suggestions for improving the readability of the chapter.

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Authors and Affiliations

  1. Department of Mathematics, School of Physical Sciences, Doon University, Dehradun, Uttarakhand, 248001, India

    Komal

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Correspondence to Komal .

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  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, India

    Harish Garg

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Komal (2023). Simplified Approach to Analyse the Fuzzy Reliability of a Repairable System. In: Garg, H. (eds) Advances in Reliability, Failure and Risk Analysis. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-9909-3_2

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