System reliability of the functions using Pareto-Rayleigh distribution

Shakila Bashir, Ahmad Mahmood Qureshi and Noor Waseem

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 23, 8130-8148

Abstract: Reliability is a basic requirement of household and industrial products. The engineers have to make sure that a particular product will perform effectively within the specific lifetime. In a way, the constituent components should be reliable so that the product as a whole perform effectively. Statistical tools to be used in order to model the life-length of the product as a whole based on the information of the performance of components for a particular product. These components may be assembled in series, parallel and series-parallel system. In this article, we develop distribution for each system using Pareto-Rayleigh distribution (PRD): distribution for series system, distribution for parallel system and distribution for series-parallel system from PRD. Various reliability measures as reliability function, hazard function, reversed hazard rata function, cumulative hazard rate function and mean residual functions have been derived for series system, parallel system and series-parallel system from PRD. The moments, mode, median, skewness, kurtosis, quantiles function, Shannon entropy and Renyi entropy have been developed for each system distribution from PRD. The graphical shapes have been shown for each system distribution from PRD and can be seen that distributions for each system are positively skewed which is applicable to measure lifetime of components. For specific values of parameter and life-length, the hazard rates have been discussed. Simulation study have carried out to check the performance of the proposed model.

Date: 2022
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DOI: 10.1080/03610926.2021.1888124

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