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Testing goodness of fit to the increasing failure rate family with censored data

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  • Thomas Santner
  • Robert Tenga

Abstract

One important thrust in the reliability literature is the development of statistical procedures under various “restricted family” model assumptions such as the increasing failure rate (IFR) and decreasing failure rate (DFR) distributions. However, relatively little work has been done on the problem of testing fit to such families as a null hypothesis. Barlow and Campo proposed graphical methods for assessing goodness of fit to the IFR model in single‐sample problems. For the same problem with complete data, Tenga and Santner studied several analytic tests of the null hypothesis that the common underlying distribution is IFR versus the alternative that it is not IFR for complete data. This article considers the same problem for the case of four types of censored data: (i) Type I (time) censoring, (ii) Type I1 (order statistic) censoring, (iii) a hybrid of Type I and Type I1 censoring, and (iv) random censorship. The least favorable distributions of several intuitive test statistics are derived for each of the four types of censoring so that valid small‐sample‐size α tests can be constructed from them. Properties of these tests are investigated.

Suggested Citation

  • Thomas Santner & Robert Tenga, 1984. "Testing goodness of fit to the increasing failure rate family with censored data," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(4), pages 631-646, December.
    • Handle: RePEc:wly:navlog:v:31:y:1984:i:4:p:631-646
    DOI: 10.1002/nav.3800310412
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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. Lando, Tommaso, 2023. "Testing departures from the increasing hazard rate property," Statistics & Probability Letters, Elsevier, vol. 193(C).

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