ON MODELING AND ANALYZING CORRUPTED RELIABILITY DATA

This paper is concerned with the effect of various data recording errors on the estimation of parameters in models commonly used in the analysis of reliability data. We start by outlining sources of such errors, and propose some modeling strategies that allow these errors into the framework of our analysis. It is then shown that the estimation of model parameters needs to take into account a mis-specified model, with the consequence that any theoretical advantages nominally enjoyed by estimators are reduced. In particular, the results from a series of simulation experiments show that the maximum likelihood estimator is no longer asymptotically unbiased. We next outline an approach that generalizes the usual asymptotic theory to obtain expressions for both the mean and variance of the maximum likelihood estimator in the present framework; these expressions involve both the underlying distribution and parameters controlling the extent to which recording errors are present in a data set. We then link these expressions to results obtained in a series of simulation experiments, and show that this approach accommodates a general formulation of the effect of data recording errors. We conclude with a discussion of the practical consequences of this work.