Reliability evaluation with limited and censored time-to-failure data based on uncertainty distributions

Limited and censored time-to-failure data are common in practical life testing, which may lead to a lack of knowledge, i.e., epistemic uncertainties, and makes it difficult to evaluate product reliability accurately. Under this situation, the large-sample based probability theory is not appropriate anymore. To deal with such problem, in this paper, the uncertainty theory based reliability evaluation is proposed to cope with the limited and censored time-to-failure data, where two types of life testing censoring (type-I and type-II censoring) and two types of time-to-failure data (precise and interval data) are considered. Firstly, the lifetime model and reliability evaluations based on uncertainty theory are presented. Then, the uncertain statistics method is presented for each combination of censoring types and data types in life testing, which includes four steps: order statistics construction, belief degree construction according to the Laplace principle of indifference, parameter estimation based on the uncertain principle of least squares, and uncertain hypothesis testing. Two simulation studies and two practical cases with comprehensive and in-depth discussion are conducted to illustrate the practicability and effectiveness of the proposed method. The results show that the proposed method can quantify epistemic uncertainties properly and provide more stable and accurate mean time to failure results under limited and censored time-to-failure data compared with probability and Bayesian probability methods.