The Score Statistic in Constancy Testing for a Discrete Hazard Rate

In discrete failure analysis, variable hazard-rate functions can often yield the constant hazard rate as a special case. In many such instances it is of interest to test statistically, using failure data, whether the hazard rate is constant or variable. The purpose of this article is to examine, using examples, the advantages of the score statistic in such tests. While the score statistic is based on the gradient of the log-likelihood function, the complexities often associated with maximum likelihood estimation and testing do not arise when the score statistic is used to test the constancy of the hazard rate. In particular, the appropriate score statistic can be calculated using simple linear least-squares regression techniques. The results are applied to failure data on electrical power transformers.