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Volume 60 - December 2023

Contents

Page 5 of 5

Front Cover (OFC, IFC) and matter

  • JPR volume 60 issue 3 Cover and Front matter

  • Published online by Cambridge University Press:
    07 August 2023, pp. f1-f2
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Original Article

  • On some properties of distributions possessing a bathtub-shaped failure rate average

  • Part of:
  • Ruhul Ali Khan, Dhrubasish Bhattacharyya, Murari Mitra
  • Published online by Cambridge University Press:
    04 January 2023, pp. 693-708

  • The life distribution of a device subject to shocks governed by a homogeneous Poisson process is shown to have a bathtub failure rate average (BFRA) when the probabilities $\bar{P}_k$ of surviving k shocks possess the corresponding discrete property. We prove closure under the formation of weak limits for BFRA distributions and explore related moment convergence issues within the BFRA family. Similar results for increasing and decreasing failure rate average distributions are obtained either independently or as consequences of our results. We also establish some results outlining the positions of various non-monotonic ageing classes such as bathtub failure rate, increasing initially then decreasing mean residual life, new worse then better than used in expectation, and increasing initially then decreasing mean time to failure in the hierarchy. Finally, an open problem is posed and a partial solution provided.

Obituary

Addendum

Original Article

  • Competing risks and shock models governed by a generalized bivariate Poisson process

  • Part of:
  • Antonio Di Crescenzo, Alessandra Meoli
  • Published online by Cambridge University Press:
    15 December 2022, pp. 709-722

  • We propose a stochastic model for the failure times of items subject to two external random shocks occurring as events in an underlying bivariate counting process. This is a special formulation of the competing risks model, which is of interest in reliability theory and survival analysis. Specifically, we assume that a system, or an item, fails when the sum of the two types of shock reaches a critical random threshold. In detail, the two kinds of shock occur according to a bivariate space-fractional Poisson process, which is a two-dimensional vector of independent homogeneous Poisson processes time-changed by an independent stable subordinator. Various results are given, such as analytic hazard rates, failure densities, the probability that the failure occurs due to a specific type of shock, and the survival function. Some special cases and ageing notions related to the NBU characterization are also considered. In this way we generalize certain results in the literature, which can be recovered when the underlying process reduces to the homogeneous Poisson process.

Other

Back Cover (IBC, OBC) and matter

  • JPR volume 60 issue 3 Cover and Back matter

  • Published online by Cambridge University Press:
    07 August 2023, pp. b1-b2
    • Article
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Front Cover (OFC, IFC) and matter

  • JPR volume 60 issue 4 Cover and Front matter

  • Published online by Cambridge University Press:
    22 December 2023, pp. f1-f2
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  • JPR volume 60 issue 2 Cover and Front matter

  • Published online by Cambridge University Press:
    04 May 2023, pp. f1-f2
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  • JPR volume 60 issue 1 Cover and Front matter

  • Published online by Cambridge University Press:
    09 February 2023, pp. f1-f2
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Back Cover (IBC, OBC) and matter

  • JPR volume 60 issue 4 Cover and Back matter

  • Published online by Cambridge University Press:
    22 December 2023, pp. b1-b2
    • Article
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    • PDF
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  • JPR volume 60 issue 1 Cover and Back matter

  • Published online by Cambridge University Press:
    09 February 2023, pp. b1-b2
    • Article
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  • JPR volume 60 issue 2 Cover and Back matter

  • Published online by Cambridge University Press:
    04 May 2023, pp. b1-b2
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Page 5 of 5