Regression Modelling on Reliability Variation of a Parallel Series System of (m, ni) Order with Addition and Removal of Parallel Paths

Abstract

A regression model is fitted on variation of reliability of parallel series system of (m, ni) order (called initial system) by adding (or removing) the arbitrary number of parallel paths. The initial system is transformed by adding (or removing) the ‘p’ (or ‘k’) parallel paths. A reliability variation method is devised to obtain directly the reliability of the transformed system in terms of reliability of the initial system and reliability of the added (or removed) system. The variation in reliability is evaluated in both cases to see the effect of parallel paths on initial system reliability. Also, the variation in reliability of a particular parallel series system of order (4, 1) is obtained by assuming constant failure rate of the components. The effect of parallel paths and failure rate of the components on variation of reliability of the system is examined by fitting the linear regression model. The values of R2 and adjusted R2 are calculated to see the best fit of the model in order reduce the computing efforts to obtain the reliability of the transformed system. The results are shown numerically and graphically. The application of the study is discussed with justification.

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Acknowledgements

The 1st author of the paper is very thankful to the Department of Science and Technology (DST), New Delhi for providing financial assistance under INSPIRE Fellowship Scheme. The authors are grateful to the reviewers for suggesting effective and technical valuable comments which enable us to make the work given in this manuscript more meaningful and worthy.

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Correspondence to Nitika Ahlawat.

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Ahlawat, N., Malik, S.C. Regression Modelling on Reliability Variation of a Parallel Series System of (m, ni) Order with Addition and Removal of Parallel Paths. J Stat Theory Pract 15, 28 (2021). https://doi.org/10.1007/s42519-020-00155-y

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Keywords

  • Reliability variation
  • Parallel-series system
  • Regression modelling
  • Parallel paths and exponential distribution