Efficient algorithm for reliability and importance measures of linear weighted-(n, f, k) and 〈n, f, k〉 systems

Reliability & importance measures for weighted-(n,f,k) & n,f,k system are studied.The basis of the study is joint probability distribution of weighted run statistic.Algorithm is more efficient in terms of cpu time than one of the existing methods. A weighted-(n,f,k):F/G(n,f,k:F/G) system consists of n components ordered in a line or circle and the system fails/works if and only if the total weight of failed/working components is at least f or (and) total weight of consecutive failed/working components is at least k. In this paper, we study the reliability and probability based reliability importance measures for linear weighted-(n,f,k):F and n,f,k:F system through a joint distribution of weighted failure-run-statistics in the sequence of Weighted Markov Binary Trials. Through the joint distributions studied, the reliability and reliability importance measures of f-out-of-n:F, consecutive-k-out-of-n:F, (n,f,k):F and n,f,k:F systems and their weighted versions (in all eight systems) can also be obtained. We also bring out the inter-relationships between reliabilities and Birnbaum importance of the weighted-f-out-of-n:F, weighted-consecutive-k-out-of-n:F, weighted-(n,f,k):F and n,f,k:F systems.Further, we demonstrate the results developed numerically. Our formula for reliability of weighted-(n,f,k):F system is more efficient in terms of cpu time than the existing method.

[1]  Marvin Rausand,et al.  System Reliability Theory , 2020, Wiley Series in Probability and Statistics.

[2]  Serkan Eryilmaz,et al.  Reliability of linear (n, f, k) systems with weighted components , 2010 .

[3]  Wei Li,et al.  Optimal design of multi-state weighted k-out-of-n systems based on component design , 2008, Reliab. Eng. Syst. Saf..

[4]  Kirtee K. Kamalja,et al.  Computational Methods for Reliability and Importance Measures of Weighted-Consecutive-System , 2014, IEEE Transactions on Reliability.

[5]  Rong-Jaye Chen,et al.  An algorithm for computing the reliability of weighted-k-out-of-n systems , 1994 .

[6]  Serkan Eryilmaz,et al.  Computing Barlow-Proschan Importance in Combined Systems , 2016, IEEE Transactions on Reliability.

[7]  Lirong Cui,et al.  Reliability and Birnbaum Importance for Sparsely Connected Circular Consecutive-$k $ Systems , 2015, IEEE Transactions on Reliability.

[8]  Ioannis S. Triantafyllou Reliability Study of Military Operations: Methods and Applications , 2015 .

[9]  Ming Jian Zuo,et al.  Computing and Applying the Signature of a System With Two Common Failure Criteria , 2010, IEEE Transactions on Reliability.

[10]  S. Erylmaz,et al.  Lifetime of Combined k-out-of-n and Consecutive kc-out-of-n Systems , 2008, IEEE Trans. Reliab..

[11]  Sevcan Demir Atalay,et al.  Reliability of Circular Systems With Markov Dependencies , 2014, IEEE Transactions on Reliability.

[12]  Serkan Eryilmaz Reliability of Combined m-Consecutive- k-out-of- n: F and Consecutive kc-out-of-n: F Systems , 2012, IEEE Trans. Reliab..

[13]  Baha-Eldin Khaledi,et al.  Importance of components in k-out-of-n system with components having random weights , 2016, J. Comput. Appl. Math..

[14]  Z W Birnbaum,et al.  ON THE IMPORTANCE OF DIFFERENT COMPONENTS IN A MULTICOMPONENT SYSTEM , 1968 .

[15]  K. K. Kamalja Birnbaum Reliability Importance for (n,f,k) and ⟨n,k,f⟩ System , 2014 .

[16]  Baha-Eldin Khaledi,et al.  Stochastic comparisons of total capacity of weighted-k-out-of-n systems , 2016 .

[17]  Lirong Cui,et al.  On the dual reliability systems of (n,f,k) and , 2006 .

[18]  Lirong Cui,et al.  Reliabilities for (n,f,k) systems , 1999 .

[19]  Serkan Eryilmaz,et al.  An algorithmic approach for the dynamic reliability analysis of non-repairable multi-state weighted k-out-of-n: G system , 2014, Reliab. Eng. Syst. Saf..

[20]  S. Demir Reliability of Combined $k{\hbox{-out-of-}}n$ and Consecutive $k_{c}{\hbox{-out-of-}}n$ Systems of Markov Dependent Components , 2009, IEEE Transactions on Reliability.

[21]  Ceki Franko,et al.  Signature Based Reliability Analysis of Repairable Weighted k-Out-of-n:G Systems , 2016, IEEE Transactions on Reliability.

[22]  Moshe Shaked,et al.  Systems with weighted components , 2008 .

[23]  K. K. Kamalja,et al.  On the Reliability of (n, f, k) and 〈n, f, k〉 Systems , 2014 .

[24]  Way Kuo,et al.  Importance Measures in Reliability, Risk, and Optimization: Principles and Applications , 2012 .

[25]  Rong-Jaye Chen,et al.  Efficient algorithms for k-out-of-n and consecutive-weighted-k-out-of-n:F system , 1994 .

[26]  Ioannis S. Triantafyllou Consecutive-Type Reliability Systems: An Overview and Some Applications , 2015 .

[27]  Yoichi Higashiyama,et al.  New algorithm to reduce the number of computing steps in reliability formula of weighted-k-out-of-n system , 2007 .

[28]  Serkan Eryilmaz Capacity loss and residual capacity in weighted k-out-of-n: G systems , 2015, Reliab. Eng. Syst. Saf..

[29]  Lirong Cui,et al.  Reliability Modeling on Consecutive-$k_r $ -out-of-$n_r $:F Linear Zigzag Structure and Circular Polygon Structure , 2016, IEEE Transactions on Reliability.

[30]  Serkan Eryilmaz,et al.  Computing marginal and joint Birnbaum, and Barlow-Proschan importances in weighted-k-out-of-n: G systems , 2014, Comput. Ind. Eng..

[31]  Markos V. Koutras,et al.  Measures of component importance for markov chain imbeddable reliability structures , 1999 .

[32]  Wei Li,et al.  Reliability evaluation of multi-state weighted k-out-of-n systems , 2008, Reliab. Eng. Syst. Saf..

[33]  Serkan Eryilmaz On reliability analysis of a k-out-of-n system with components having random weights , 2013, Reliab. Eng. Syst. Saf..

[34]  S. Eryilmaz,et al.  Modeling and analysis of weighted-k-out-of-n: G system consisting of two different types of components , 2014 .

[35]  Serkan Eryilmaz,et al.  Reliability Evaluation of Linear Consecutive-Weighted-k-Out-of-n: F System , 2009, Asia Pac. J. Oper. Res..

[36]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[37]  Narayanaswamy Balakrishnan,et al.  Start‐up demonstration tests: models, methods and applications, with some unifications , 2014 .

[38]  Ming Jian Zuo,et al.  Reliability evaluation of combined k-out-of-n: F, consecutive-k-out-of-n: F and linear connected-(r, s)-out-of-(m, n): F system structures , 2000, IEEE Trans. Reliab..

[39]  Markos V. Koutras,et al.  Reliability Properties of $(n,f,k)$ Systems , 2014, IEEE Transactions on Reliability.

[40]  Kirtee K. Kamalja,et al.  RELIABILITY AND IMPORTANCE MEASURES OF WEIGHTED-k-OUT-OF-n SYSTEM , 2014 .

[41]  Xiaoyan Zhu,et al.  Joint Reliability Importance in a Consecutive-k-out-of-n : F System and an m-Consecutive-k-out-of-n: F System for Markov-Dependent Components , 2015, IEEE Trans. Reliab..

[42]  Amos E. Gera Different weights of tests within a start-up demonstration procedure: A. E. GERA , 2016 .

[43]  Frank K. Hwang,et al.  A fast reliability-algorithm for the circular consecutive-weighted-k-out-of-n:F system , 1998 .

[44]  Manju Agarwal,et al.  Combined m -Consecutive- k -Out-of- n: F & Consecutive kc -Out-of- n: F Systems , 2009, IEEE Trans. Reliab..

[45]  Kirtee K. Kamalja,et al.  BIRNBAUM IMPORTANCE FOR CONSECUTIVE-k SYSTEMS , 2012 .

[46]  Shudong Sun,et al.  Optimization of linear consecutive-k-out-of-n system with a Birnbaum importance-based genetic algorithm , 2016, Reliab. Eng. Syst. Saf..

[47]  Amos E. Gera,et al.  Combined k-out-of-n:G, and consecutive k/sub c/-out-of-n:G systems , 2004, IEEE Transactions on Reliability.

[48]  David W. Coit,et al.  Dynamic k-out-of-n system reliability with component partnership , 2015, Reliab. Eng. Syst. Saf..