Document Type : Research Manuscript

Authors

• Mohammad Vali Ahmadi
• Hamid Reza Moheghi

University of Bojnord, Bojnord, Iran

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

Main Subjects

• Computational Statistics