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Properties of System Lifetime in the Classical Model with I.I.D. Exponential Component Lifetimes

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Advances in Statistics - Theory and Applications

Part of the book series: Emerging Topics in Statistics and Biostatistics ((ETSB))

Abstract

We consider coherent and mixed systems composed of components with independent identically exponentially distributed lifetimes. We describe sufficient conditions assuring specific properties of the system lifetime density and failure rate functions expressed in terms of the system Samaniego signature. In particular, we determine conditions which guarantee monotonicity, unimodality, and strong unimodality of the density function, and monotonicity of the failure rate and mean residual life.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland

    Tomasz Rychlik

  2. Institute of Automation and Robotics, Poznan University of Technology, Poznań, Poland

    Magdalena Szymkowiak

Authors
  1. Tomasz Rychlik
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  2. Magdalena Szymkowiak
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Corresponding author

Correspondence to Tomasz Rychlik .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of North Carolina Wilmington, Wilmington, NC, USA

    Indranil Ghosh

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

    N. Balakrishnan

  3. Department of Statistical Science, Southern Methodist University, Dallas, TX, USA

    Hon Keung Tony Ng

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Rychlik, T., Szymkowiak, M. (2021). Properties of System Lifetime in the Classical Model with I.I.D. Exponential Component Lifetimes. In: Ghosh, I., Balakrishnan, N., Ng, H.K.T. (eds) Advances in Statistics - Theory and Applications. Emerging Topics in Statistics and Biostatistics . Springer, Cham. https://doi.org/10.1007/978-3-030-62900-7_3

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