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On Computing Signatures of k-out-of-n Systems Consisting of Modules

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Abstract

In this paper, we study how to compute the signature of a k-out-of-n coherent system consisting of n modules. Formulas for computing the signature and the minimal signature of this kind of systems based on those of their modules are derived. Examples are presented to demonstrate the applications of our formulas. The main results obtained in this paper generalize some related ones in recent literature.

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References

  • Barlow RE, Proschan F (1981) Statistical theorey of reliability and life testing: probability models. To Begin With, Silver Spring, Maryland,

  • Boland PJ (2001) Signatures of indirect majority systems. J Appl Probab 38:597–603

    Article  MATH  MathSciNet  Google Scholar 

  • Chiang DT, Niu SC (1981) Reliability of consecutive k-out-of-n:F systems. IEEE Trans Reliab R30:87–89

    Article  MATH  Google Scholar 

  • Da G, Zheng B, Hu T (2012) On computing signatures of coherent systems. J Multivar Anal 103:142–150

    Article  MATH  MathSciNet  Google Scholar 

  • Eryilmaz S (2010) Mixture representations for the reliability of consecutive-k systems. Math Comput Model 51:405–412

    Article  MATH  MathSciNet  Google Scholar 

  • Eryilmaz S (2012) On signatures of series and parallel systems consisting of modules with arbitrary structures. Technical Report, Department of Mathematics, Izmir University of Economics, Turkey

  • Gertsbakh I, Shpungin Y, Spizzichino F (2011) Signatures of coherent systems built with separate modules. J Appl Probab 48:843–855

    Article  MATH  MathSciNet  Google Scholar 

  • Kochar S, Mukerjee H, Samaniego FJ (1999) The “signature” of a coherent system and its application to comparison among systems. Nav Res Logist 46:507–523

    Article  MATH  MathSciNet  Google Scholar 

  • Kuo W, Zuo MJ (2003) Optimal reliability modeling, principles and applications. Wiley, New York

    Google Scholar 

  • Marichal J-L, Mathonet P (2011) Extensions of system signatures to dependent lifetimes: explicit expressions and interpretations. J Multivar Anal 102:931–936

    Article  MATH  MathSciNet  Google Scholar 

  • Marichal J-L, Mathonet P, Waldhauser T (2011) On signature-based expressions of system reliability. J Multivar Anal 102:1410–1416

    Article  MATH  MathSciNet  Google Scholar 

  • Navarro J, Eryilmaz S (2007) Mean residual lifetimes of consecutive k-out-of-n systems. J Appl Probab 44:82–98

    Article  MATH  MathSciNet  Google Scholar 

  • Navarro J, Rubio R (2010) Computation of signatures of coherent systems with five components. Commun Stat, Simul Comput 39:68–84

    Article  MATH  MathSciNet  Google Scholar 

  • Navarro J, Ruiz JM, Sandoval CJ (2005) A note on comparisons among coherent systems with dependent components using signatures. Stat Probab Lett 72:179–185

    Article  MATH  MathSciNet  Google Scholar 

  • Navarro J, Ruiz JM, Sandoval CJ (2007) Properties of coherent systems with dependent components. Commun Stat, Theory Methods 36:175–191

    Article  MATH  MathSciNet  Google Scholar 

  • Navarro J, Rychlik T (2007) Reliability and expectation bounds for coherent systems with exchangeable components. J Multivar Anal 98:102–113

    Article  MATH  MathSciNet  Google Scholar 

  • Navarro J, Rychlik T (2010) Comparisons and bounds for expected lifetimes of reliability systems. Eur J Oper Res 207:309–317

    Article  MATH  MathSciNet  Google Scholar 

  • Navarro J, Samaniego FJ, Balakrishnan N (2010) The joint signature of coherent systems with shared components. J Appl Probab 47:235–253

    Article  MATH  MathSciNet  Google Scholar 

  • Navarro J, Samaniego FJ, Balakrishnan N (2011) Signature-based representations for the reliability of systems with heterogeneous components. J Appl Probab 48:856–867

    Article  MATH  MathSciNet  Google Scholar 

  • Navarro J, Samaniego FJ, Balakrishnan N, Bhattacharya D (2008) On the application and extension of system signatures in engineering reliability. Nav Res Logist 55:313–327

    Article  MATH  MathSciNet  Google Scholar 

  • Samaniego FJ (1985) On closure of the IFR class under formation of coherent systems. IEEE Trans Reliab R-34:69–72

    Article  MATH  Google Scholar 

  • Samaniego FJ (2007) System signatures and their applications in engineering reliability. Springer, New York

    Book  MATH  Google Scholar 

  • Triantafyllou IS, Koutras MV (2008) On the signature of coherent systems and applications. Probab Eng Inf Sci 22:19–35

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Taizhong Hu.

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T. Hu is supported by the NNSF of China (Nos. 11071232, 70821001, 71090401).

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Da, G., Xia, L. & Hu, T. On Computing Signatures of k-out-of-n Systems Consisting of Modules. Methodol Comput Appl Probab 16, 223–233 (2014). https://doi.org/10.1007/s11009-012-9308-5

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  • DOI: https://doi.org/10.1007/s11009-012-9308-5

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