| Lifetime data from the field can be complicated due to truncation, censoring, multiple failure modes, and the nonhomogeneity of the population. These complications lead to difficulties in reliability predictions and calibrations of the prediction intervals (PIs). Another trends in field lifetime data is the availability of the dynamic data which give in- formation dynamically on how a product being used and under which environment being used. Incorporating this information (historically not available) into statistical analyses will provide stronger statistical methods. In this dissertation, statistical models and methods motivated by real applications were developed for reliability predictions based on complicated data and dynamic data. In Chapter 2, left truncated and right censored high-voltage power transformer lifetime data are available from an energy company. The company wants to predict the remaining life of transformers and the cumulative number of failures at a future time for their transformer fleet. The population is nonhomogeneous because transformer designs evolved over past decades. The data were stratified into relatively homogeneous groups and regression was done to incorporate the explanatory variables. The random weighted bootstrap was used to overcome the difficulties introduced by the complicated structure of the data in the calibration of the prediction intervals. In Chapter 3, the importance of stratification when the population is nonhomogeneous was analytically studied in the context of reliability predictions. There are two potential pitfalls for fitting a single distribution to nonhomogeneous data, which are misinterpretation of the failure mode and asymptotic biasness in prediction. These results were further illustrated by the high-voltage transformer life data. In Chapter 4, data are available from a product which has four major failure modes. Use-rate information is available for units connected to the network. We use a cycles-to-failure model to compute predictions and prediction intervals for the number failing. We also present prediction methods for units not connected to the network. |
