Journal of Data Science and Modeling

A goodness-of-fit test for progressively first-failure-censored data from a proportional hazard rate model

Articles in Press

Document Type : Research Manuscript

Authors

Mohammad Vali Ahmadi
Hamid Reza Moheghi

University of Bojnord, Bojnord, Iran

https://doi.org/10.22054/jdsm.2026.88330.1076
Abstract
Progressive first-failure censoring schemes are potentially useful in practical applications where budget constraints exist or rapid testing is required. Moreover, several common sampling schemes such as first-failure censoring, progressive Type-II censoring, Type-II censoring, and complete sampling can be viewed as special cases of the progressive first-failure censoring scheme.
In this article, we propose a goodness-of-fit test statistic to assess whether a progressively first-failure-censored sample originates from a distribution belonging to the proportional hazard rate model. This model encompasses several well-known lifetime distributions, including the exponential, Rayleigh, Lomax, Burr Type-XII, Weibull, Gompertz, and Pareto distributions, among others.
We derive the null distribution of the proposed test statistic. Through Monte Carlo simulations, we evaluate the power of the proposed test under a range of different alternative distributions, assuming the null distribution to be exponential, Rayleigh, or Pareto. Finally, we present several numerical real-world examples to demonstrate the practical applicability of the proposed goodness-of-fit test. We also summarize the main findings and provide concluding remarks.

Keywords

Goodness-of-fit test
Proportional hazard rate model
Progressive first-failure censoring
Monte Carlo simulation
Power study
Subjects
Journal of Data Science and Modeling

Articles in Press, Accepted Manuscript
Available Online from 23 July 2026

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