Applications of survival functions to continuous semi-Markov processes for measuring reliability of power transformers

Abstract

The reliability of power transformers is subject to service age and health condition. This paper proposes a practical model for the evaluation of two reliability indices: survival function (SF) and mean residual life (MRL). In the proposed model, the periodical modeling of power transformers are considered for collecting the information on health conditions. The corresponding health condition is assumed to follow a continuous semi-Markov process for representing a state transition. The proportional hazard model (PHM) is introduced to incorporate service age and health condition into hazard rate. In addition, the proposed model derives the analytical formulas for and offers the analytical evaluation of SF and MRL. SF and MRL are calculated for new components and old components, respectively. In both cases, the proposed model offers rational results which are compared with those obtained from comparative models. The results obtained by the contrast of the proposed analytical method and the Monte Carlo method. The impact of different model parameters and the coefficient of variation (CV) on reliability indices are discussed in the case studies.

A Data Mining Approach for Transformer Failure Rate Modeling Based on Daily Oil Chromatographic Data

“…The SDs in state 2 at time t1 and t2 are equal, and the failure rates at time t1 and t2 calculated by formula (16) and are also the same. The reason for equal SDs at times t1 and t2 is that the Markov model always assumes that the transformer can return to the initial state after the maintenance is performed at time t3 [22].…”

“…Obviously, the values of SD ti used in the Markov model are determined only by the current state and the corresponding state duration at time t. As along as the transformer is under the same state and has the same state duration, the values of SD remain the same. However, the maintenance might not return the transformer to its original condition [22]. The SD at time t2 after maintenance should be no longer the same as that at time t1.…”

“…However, the transformer failure rates obtained by those models are still equal as long as the state and the state duration are the same although operating at different operation time. That is these models cannot describe the impact of maintenance on the transformer failure rate [22]. The reason for this defect is that those models ignored the actual operating conditions of the day when calculating the real-time failure rate of the transformer.…”

“…The reason for this defect is that those models ignored the actual operating conditions of the day when calculating the real-time failure rate of the transformer. To overcome this problem, some improved models introduced more covariates so as to describe the operating conditions and quantify the impact of maintenance when modeling the failure rates [22]. [23] proposed a transformer failure rate model based on Proportional hazard model.…”

Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems

“…Examples of discrete-time semi-Markov processes with the associated reliability measures and statistical topics can be found in, e.g., [7][8][9][10], who proposed a semi-Markov chain usage model in discrete time and provided analytical formulas for the mean and variance of the single-use reliability of the system. The evaluation of reliability indicators for continuous-time semi-Markov processes and statistical inference can be found in [11][12][13][14][15]. The readers interested in solving numerically continuous-time semi-Markov processes by using discrete-time semi-Markov processes for solving continuous ones are referred to [16][17][18][19].…”