The Weibull Distribution: Reliability Characterization Based on Linear and Circular Consecutive Systems
| Autor: | M. S. Eliwa, Abhishek Tyag, A. H. El-Bassiouny, M. A. El-Damcese, M. El-Morshedy |
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| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Physics Control and Optimization Artificial Intelligence Signal Processing Mathematical properties Thermodynamics Computer Vision and Pattern Recognition Function (mathematics) Statistics Probability and Uncertainty Characterization (mathematics) Information Systems Weibull distribution |
| Zdroj: | Statistics, Optimization & Information Computing. 9:974-983 |
| ISSN: | 2310-5070 2311-004X |
| DOI: | 10.19139/soic-2310-5070-1132 |
| Popis: | Linear and circular consecutive models play a vital role to study the mechanical systems emerging in various fields including survival analysis, reliability theory, biological disciplines, and other lifetime sciences. As a result, analysis of reliability properties of consecutive k − out − of − n : F systems has gained a lot of attention in recent years from a theoretical and practical point of view. In the present article, we have studied some important stochastic and aging properties of residual lifetime of consecutive k − out − of − n : F systems under the condition n − k + 1, k ≤ n and all components of the system are working at time t. The mean residual lifetime (MRL) and its hazard rate function are proposed for the linear consecutive k − out − of − n : F (lin/con/k/n:F) and circular consecutive k − out − of − n : F (cir/con/k/n:F) systems. Furthermore, several mathematical properties of the proposed MRL are examined. Finally, the Weibull distribution with two parameters is used as an example to explain the theoretical results. |
| Databáze: | OpenAIRE |
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