# The Weibull Distribution: Reliability Characterization Based on Linear and Circular Consecutive Systems

• M. S Eliwa Mansoura University
• Medhat EL-Damcese Tanta University
• A. H. El-Bassiouny Mansoura University
• Abhishek Tyag Chaudhary Charan Singh University
• M. El-Morshedy Prince Sattam bin Abdulaziz University
Keywords: Mean residual lifetime; Hazard rate function, Consecutive systems, Order statistics.

### Abstract

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.

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Published
2021-09-24
How to Cite
Eliwa, M. S., EL-Damcese, M., El-Bassiouny, A. H., Tyag, A., & El-Morshedy, M. (2021). The Weibull Distribution: Reliability Characterization Based on Linear and Circular Consecutive Systems. Statistics, Optimization & Information Computing, 9(4), 974-983. https://doi.org/10.19139/soic-2310-5070-1132
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Research Articles