On the Mean Remaining Strength of the k-Out-of-n:F System with Exchangeable Components

In this article, we consider the mean remaining strength of a k-out-of-n:F system in the stress–strength setup for the exchangeable components. We provide some results for parallel and series systems under this setup, where X1, X2, …, Xn are the strengths of the components designed under the common stress. An illustrative example is given for the k-out-of- n:F system using the multivariate FGM distribution.

[1]  Richard A. Johnson,et al.  3 Stress-strength models for reliability , 1988 .

[2]  J. Navarro,et al.  Systems with Exchangeable Components and Gumbel Exponential Distribution , 2006 .

[3]  Richard A. Johnson,et al.  Estimation of Reliability in a Multicomponent Stress-Strength Model , 1974 .

[4]  M. Zuo,et al.  Optimal Reliability Modeling: Principles and Applications , 2002 .

[5]  Ismihan Bayramoglu,et al.  Order statistics from mixed exchangeable random variables , 2011, J. Comput. Appl. Math..

[6]  N. L. Johnson,et al.  Continuous Multivariate Distributions, Volume 1: Models and Applications , 2019 .

[7]  Serkan Eryilmaz.  Consecutive k-Out-of-n : G System in Stress-Strength Setup , 2008, Commun. Stat. Simul. Comput..

[8]  Serkan Eryilmaz,et al.  Reliability Evaluation for a Multi-State System Under Stress-Strength Setup , 2011 .

[9]  Majid Asadi,et al.  On the Mean Residual Life Function of Coherent Systems , 2008, IEEE Transactions on Reliability.

[10]  Nader Ebrahimi.  Estimation of Reliability For a Series Stress-Strength System , 1982, IEEE Transactions on Reliability.

[11]  David,et al.  [Wiley Series in Probability and Statistics] Order Statistics (David/Order Statistics) || Basic Distribution Theory , 2003 .

[12]  David D. Hanagal.  Estimation of reliability of a component subjected to bivariate exponential stress , 1999 .

[13]  David D. Hanagal.  Estimation of system reliability , 1999 .

[14]  N. L. Johnson,et al.  Continuous Multivariate Distributions: Models and Applications , 2005 .

[15]  William S. Griffith,et al.  Optimal Reliability Modeling: Principles and Applications , 2004, Technometrics.

[16]  Filippo Domma,et al.  A copula-based approach to account for dependence in stress-strength models , 2013 .

[17]  Jean-Paul Chilès,et al.  Wiley Series in Probability and Statistics , 2012 .

[18]  Jorge Navarro,et al.  A note on comparisons among coherent systems with dependent components using signatures , 2005 .

[19]  Timothy M. Young,et al.  Applying Novel Mean Residual Life Confidence Intervals , 2006 .

[20]  Laura Ventura,et al.  Robust inference for the stress–strength reliability , 2011 .

[21]  S. Kotz,et al.  The stress-strength model and its generalizations : theory and applications , 2003 .

[22]  Timothy M. Young,et al.  Using Mean Residual Life Functions for Unique Insights into Strengths of Materials Data , 2005 .

[23]  Serkan Eryilmaz,et al.  Multivariate stress-strength reliability model and its evaluation for coherent structures , 2008 .

[24]  F. Samaniego.  On Closure of the IFR Class Under Formation of Coherent Systems , 1985, IEEE Transactions on Reliability.

[25]  Filippo Domma,et al.  A stress–strength model with dependent variables to measure household financial fragility , 2012, Statistical Methods & Applications.

[26]  Serkan Eryilmaz,et al.  A new perspective to stress–strength models , 2011 .

[27]  N. Balakrishnan,et al.  Study of some measures of dependence between order statistics and systems , 2010, J. Multivar. Anal..

[28]  Characterization of symmetry and exceedance models in multivariate FGM distributions , 2004 .

[29]  Serkan Eryilmaz.  On system reliability in stress-strength setup , 2010 .

[30]  Moshe Shaked,et al.  Ordering conditional lifetimes of coherent systems , 2007 .

[31]  Majid Asadi,et al.  The mean residual life function of a k-out-of-n structure at the system level , 2006, IEEE Transactions on Reliability.

[32]  Majid Asadi,et al.  A Note on the Mean Residual Life Function of a Parallel System , 2005 .

[33]  ON SYSTEM RELIABILITY UNDER STRESS-STRENGTH MODELING , 2001 .

[34]  U. U. Mueller,et al.  The Stress-Strength Model and Its Generalizations: Theory and Applications , 2004 .

[35]  Jorge Navarro,et al.  Reliability and expectation bounds for coherent systems with exchangeable components , 2007 .