Stochastic comparisons of series and parallel systems with randomized independent components

Abstract Consider a series or parallel system of independent components and assume that the components are randomly chosen from two different batches, with the components of the first batch being more reliable than those of the second. In this note it is shown that the reliability of the system increases, in usual stochastic order sense, as the random number of components chosen from the first batch increases in increasing convex order. As a consequence, we establish a result analogous to the Parrondo’s paradox, which shows that randomness in the number of components extracted from the two batches improves the reliability of the series system.

[1]  Harshinder Singh,et al.  Preservation of partial orderings under the formation of k-out-of-n:G systems of i.i.d. components , 1991 .

[2]  Fabio Spizzichino,et al.  Comparisons of series and parallel systems with components sharing the same copula , 2010 .

[3]  Laurence A. Baxter,et al.  On the optimal assembly of series-parallel systems , 1992, Oper. Res. Lett..

[4]  Ming J. Zuo,et al.  Preservation of stochastic orders for random minima and maxima, with applications , 2004 .

[5]  M. Raghavachari,et al.  Optimal allocation of interchangeable components in a series-parallel system , 1998 .

[6]  J. Shanthikumar,et al.  Multivariate Stochastic Orders , 2007 .

[7]  A. Müller,et al.  Comparison Methods for Stochastic Models and Risks , 2002 .

[8]  Moshe Shaked,et al.  Stochastic comparisons of random minima and maxima , 1997 .

[9]  Improving series and parallel systems through mixtures of duplicated dependent components , 2011 .

[10]  Derek Abbott,et al.  Parrondo's paradox , 1999 .

[11]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[12]  Way Kuo,et al.  An annotated overview of system-reliability optimization , 2000, IEEE Trans. Reliab..

[13]  David Malon.  When is greedy module assembly optimal , 1990 .

[14]  Antonio Di Crescenzo.  A PARRONDO PARADOX IN RELIABILITY THEORY , 2007 .

[15]  Jarosław Bartoszewicz,et al.  Stochastic comparisons of random minima and maxima from life distributions , 2001 .

[16]  José E. Valdés,et al.  On the optimal allocation of two active redundancies in a two-component series system , 2006, Oper. Res. Lett..

[17]  Maw-Sheng Chern,et al.  On the computational complexity of reliability redundancy allocation in a series system , 1992, Oper. Res. Lett..

[18]  D. Abbott.  Developments in Parrondo’s Paradox , 2009 .

[19]  Xiaohu Li,et al.  Some new stochastic comparisons for redundancy allocations in series and parallel systems , 2008 .

[20]  Hazard rate ordering of k-out-of-n systems , 1995 .