Stochastic quantile-filling augmentation algorithm to censored and accurate reliability data

•A new inspection strategy on units to get failure data is given.•Interval-censored data and some accurate data are detected simultaneously.•An imputation algorithm of stochastic quantile augmentation is proposed.•Algorithm is executed under ME and MLE which have good performance on estimations.

During the operating lifetime of products, an inspection strategy is discussed to get both censored data and some accurate data embedded in censoring intervals here. To obtain the parameter estimates of lifetime model, an iterative single-point imputation (SPI) algorithm is proposed under stochastic quantile probabilities, called stochastic quantile-filling augmentation (SQFA). By the algorithm, stochastic conditional quantiles are imputed as the virtual failure time data from doubly transacted distributions in interval-censored intervals; and the virtual right-censored data are obtained by equipartition conditional quantiles in right-censored interval, respectively. It has iterative thoughts of stochastic multiple imputations to obtain the virtual data. And its convergence is verified through the examples both under the criterion of moment estimation (ME) and maximum likelihood estimation (MLE). Especially, closed-form estimates for Weibull distribution and Gamma distribution are given through some transformations. Furthermore, numerical examples and simulations show that the proposed augmentation algorithm performs better on parameter estimations than the iterative SPI algorithm under equipartition quantile probabilities.