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Testing goodness of fit to the increasing failure rate family

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  • Robert Tenga
  • Thomas J. Santner

Abstract

One branch of the reliability literature is concerned with devising statistical procedures with various nonparametric “restricted family” model assumptions because of the potential improved operating characteristics of such procedures over totally nonparametric ones. In the single‐sample problem with unknown increasing failure rate (IFR) distribution F, (1) maximum‐likelihood estimators of F have been calculated, (2) upper or lower tolerance limits for F have been determined, and (3) tests of the null hypothesis that F is exponential have been constructed. Barlow and Campo proposed graphical methods for assessing goodness of fit to the IFR model when the validity of this assumption is unknown. This article proposes several analytic tests of the IFR null hypothesis based on the maximum distance and area between the cumulative hazard function and its greatest convex minorant (GCM), and the maximum distance and area between the total time on test statistic and its GCM. A table of critical points is provided to implement a specific test having good overall power properties.

Suggested Citation

  • Robert Tenga & Thomas J. Santner, 1984. "Testing goodness of fit to the increasing failure rate family," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(4), pages 617-630, December.
    • Handle: RePEc:wly:navlog:v:31:y:1984:i:4:p:617-630
    DOI: 10.1002/nav.3800310411
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    Cited by:

    1. Lando, Tommaso, 2021. "A test for the increasing log-odds rate family," Statistics & Probability Letters, Elsevier, vol. 170(C).
    2. Tommaso Lando, 2022. "Testing convexity of the generalised hazard function," Statistical Papers, Springer, vol. 63(4), pages 1271-1289, August.
    3. Lando, Tommaso, 2023. "Testing departures from the increasing hazard rate property," Statistics & Probability Letters, Elsevier, vol. 193(C).

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