Statistical inference of a time-to-failure distribution derived from linear degradation data

In the study of semiconductor degradation, records of transconductance loss or threshold voltage shift over time are useful in constructing the cumulative distribution function (cdf) of the time until the degradation reaches a specified level. In this article, we propose a model with random regression coefficients and a standard-deviation function for analyzing linear degradation data. Both analytical and empirical motivations of the model are provided. We estimate the model parameters, the cdf, and its quantiles by the maximum likelihood (ML) method and construct confidence intervals from the bootstrap, from the asymptotic normal approximation. and from inverting likelihood ratio tests. Simulations are conducted to examine the properties of the ML estimates and the confidence intervals. Analysis of an engineering dataset illustrates the proposed procedures.