Product reliability analysis based on heavily censored interval data with batch effects

In many industries including engineering, biology, and medical science, etc, interval failure data commonly exist. Utilizing the data to estimate product lifetime is often confounded with both heavy censoring and batch effects. To deal with the two characteristics, in this paper, we propose a novel two-stage method called fractional-random-weight bootstrap to help make interval estimation for both model parameters and future failure numbers. By carrying out various simulation studies, our method demonstrates the superiority over two other commonly-used bootstrap methods in terms of the relative bias, root mean squared error, and width of confidence intervals. When extremely heavy censoring is present, the advantage is more significant. In addition, we illustrate the application of the proposed methodology using a real dataset from experiments on printed circuit boards. By comparison, we show that misconsidering the batch effects in the interval data could lead to inaccurate predicted number of failures.