TY - JOUR AU - M. S Eliwa AU - Medhat EL-Damcese AU - A. H. El-Bassiouny AU - Abhishek Tyag AU - M. El-Morshedy PY - 2021/09/24 Y2 - 2024/03/28 TI - The Weibull Distribution: Reliability Characterization Based on Linear and Circular Consecutive Systems JF - Statistics, Optimization & Information Computing JA - Stat., optim. inf. comput. VL - 9 IS - 4 SE - Research Articles DO - 10.19139/soic-2310-5070-1132 UR - http://iapress.org/index.php/soic/article/view/1132 AB - 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. ER -