Representations of the inactivity time for coherent systems with heterogeneous components and some ordered properties

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• 作者：Zhengcheng Zhang ; N. Balakrishnan
• 关键词：Mixture ; Heterogeneous variables ; Stochastic orders ; Signature ; Inactivity time ; Mean reliability function
• 刊名：Metrika
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：79
• 期：1
• 页码：113-126
• 全文大小：443 KB
• 参考文献：Barlow RE, Proschan F (1975) Statistical theory of reliability and life testing. Holt, Rinehart and Winston, New YorkMATH
  Belzunce F, Franco M, Ruiz JM (2001) On partial orderings between coherent systems with different structures. Probab Eng Inf Sci 15:273–293MATH MathSciNet CrossRef
  Boland PJ (2001) Signature of indirect majority systems. J Appl Probab 38:597–603MATH MathSciNet CrossRef
  David HA, Nagaraja HN (2003) Order statistics, 3rd edn. Wiley, HobokenMATH CrossRef
  Esary JD, Marshall AW (1970) Coherent life functions. SIAM J Appl Math 18:810–814MATH MathSciNet CrossRef
  Goliforushani S, Asadi M (2011) Stochastic ordering among inactivity times of coherent systems. Sankhya 73:241–262MATH MathSciNet CrossRef
  Goliforushani S, Asadi M, Balakrishnan N (2012) On the residual and inactivity times of the components of used coherent systems. J Appl Probab 49:385–404MATH MathSciNet CrossRef
  Jasinski K, Navarro J, Rychlik T (2009) Bounds on variances of lifetimes of coherent and mixed systems. J Appl Probab 46:894–908MATH MathSciNet CrossRef
  Khaledi BE, Shaked M (2007) Ordering conditional lifetimes of coherent systems. J Stat Plan Inference 137:1173–1184MATH MathSciNet CrossRef
  Kochar SC, Mukerjee H, Samaniego FJ (1999) The signature of a coherent system and its application to comparisons among systems. Nav Res Logist 46:507–523MATH MathSciNet CrossRef
  Li X, Zhang Z (2008) Some stochastic comparisons of conditional coherent systems. Appl Stoch Models Bus Ind 24:541–549MATH MathSciNet CrossRef
  Navarro J, Rubio R (2010) Comparisons of coherent systems using stochastic precedence. Test 19:469–486MATH MathSciNet CrossRef
  Navarro J, Rychlik T (2007) Reliability and expectation bounds for coherent systems with exchangeable components. J Multivar Anal 98:102–113MATH MathSciNet CrossRef
  Navarro J, Spizzichino F (2010) Comparisons of series and parallel systems with components sharing the same copula. Appl Stoch Models Bus Ind 26:775–791MATH MathSciNet CrossRef
  Navarro J, Ruiz JM, Sandoval CJ (2005) A note on comparisons among coherent systems with dependent components using signatures. Stat Probab Lett 72:179–185MATH MathSciNet CrossRef
  Navarro J, Ruiz JM, Sandoval CJ (2007) Properties of coherent systems with dependent components. Commun Stat Simul Comput 36:175–191MATH MathSciNet
  Navarro J, Balakrishnan N, Samaniego FJ (2008a) Mixture representations of residual lifetimes of used systems. J Appl Probab 45:1097–1112MATH MathSciNet CrossRef
  Navarro J, Samaniego FJ, Balakrishnan N, Bhattacharya D (2008b) On the application and extension of system signatures in engineering reliability. Nav Res Logist 55:313–327MATH MathSciNet CrossRef
  Navarro J, Samaniego FJ, Balakrishnan N (2010) The joint signature of coherent systems with shared components. J Appl Probab 47:235–253MATH MathSciNet CrossRef
  Navarro J, Balakrishnan N, Samaniego FJ (2011) Signature-based representations for the reliability of systems with heterogeneous components. J Appl Probab 48:856–867MATH MathSciNet CrossRef
  Parvardeh A, Balakrishnan N (2013) Conditional residual lifetimes of coherent systems. Stat Probab Lett 83:2664–2672MATH MathSciNet CrossRef
  Samaniego FJ (1985) On closure of the IFR class under formation of coherent systems. IEEE Trans Reliab 34:69–72MATH CrossRef
  Samaniego FJ (2007) System signatures and their applications in engineering reliability. Springer, New YorkMATH CrossRef
  Satyanarayana A, Prabhakar A (1978) A new topological formula and rapid algorithm for reliability analysis of complex networks. IEEE Trans Reliab R–27:82–100MathSciNet CrossRef
  Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New YorkMATH CrossRef
  Shaked M, Suarez-Llorens A (2003) On the comparison of reliability experiments based on the convolution order. J Am Stat Assoc 98:693–702MATH MathSciNet CrossRef
  Zhang Z (2010a) Ordering conditional general coherent systems with exchangeable components. J Stat Plan Inference 140:454–460MATH CrossRef
  Zhang Z (2010b) Mixture representations of inactivity times of conditional coherent systems and their applications. J Appl Probab 47:876–885MATH MathSciNet CrossRef
  Zhang Z, Li X (2010) Some new results on stochastic orders and aging properties of coherent systems. IEEE Trans Reliab 59:718–724CrossRef
  Zhang Z, Meeker WQ (2013) Mixture representations of reliability in coherent systems and preservation results under double monitoring. Commun Stat Theory Methods 42:385–397MATH MathSciNet CrossRef
  
• 作者单位：Zhengcheng Zhang (1)
  N. Balakrishnan (2)
  
  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, 730070, China
  2. Department of Mathematics and Statistics, McMaster University, Hamilton, L8S 4K1, Canada
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1435-926X

文摘

In this paper, we present several useful mixture representations for the reliability function of the inactivity time of systems with heterogeneous components based on order statistics, signatures and mean reliability functions. Some stochastic comparisons of inactivity times between two systems are discussed. These results form nice extensions of some existing results for the case when the components are independent and identically distributed.