Belief reliability evaluation with uncertain right censored time-to-failure data under small sample situation

Uncertain right censoring (URC) which describes the situation that the censoring settings of test units are unrelated to their failure time often occurs in practical life testing. Besides, in practical life testing, the small sample situation is also common since the test resources are usually limited, which brings epistemic uncertainties to reliability evaluations due to the lack of information. Under such situation, the large sample-based probability theory is not appropriate anymore to conduct reliability evaluations. In this paper, the belief reliability evaluation is conducted with uncertain right censored time-to-failure (TTF) data under the small sample situation based on the belief reliability theory. Firstly, to deal with epistemic uncertainties, a truncated normal uncertainty distribution of lifetime is given, and the belief reliability evaluation is presented using the uncertain measure. Then, the corresponding uncertain statistics method for unknown parameter estimation is provided with objective measures. Finally, a simulation study and a practical case are used to illustrate the proposed method. The results show that the proposed method is suitable to deal with epistemic uncertainties and can achieve more accurate and stable mean time-to-failure (MTTF) results with uncertain right censored TTF data under the small sample situation compared to classical probability and Bayesian reliability methods.