A failure-time model for infant-mortality and wearout failure modes

Some populations of electronic devices or other system components are subject to both infant-mortality and wearout failure modes. Typically, interest is in the estimation of reliability metrics such as distribution-quantiles or fraction-failing at a point in time for the population of units. This involves: (1) modeling the failure time; and (2) estimating the parameters of the failure-time distributions, for the different failure modes, as well as the proportion of defective units. This paper: (1) proposes GLFP (general limited failure population) for this purpose; (2) uses the ML (maximum likelihood) method of to estimate the unknown model parameters-the formulae for the likelihood contribution corresponding to different types of censoring are provided; (3) describes a likelihood-based method to construct statistical-confidence intervals and simultaneous statistical-confidence bands for quantities of interest; and (4) fits the model to a set of censored data to illustrate the estimation technique and some of the model's characteristics. The model-fitting indicates that identification of the failure mode of at least a few failed units is necessary to estimate model-parameters. Based on the fitting of the data from the lifetime of circuit boards, the GLFP model provides a useful description of the failure-time distribution for components that have both wearout and some infant mortality behavior. However, the data must include the cause of failure for at least a few observations in order to avoid complications in the ML estimation. The more-failed units whose failure mode has been identified, the better model estimates are in terms of model-fitting.