Investigation of maximum likelihood percentile estimates for transformer asset management

To achieve a suitable balance between investment and reliability, it is necessary for utilities to be able to understand the long-term behaviour of asset populations in association with the `wear-out´ stage of the so called `bathtub curve´. For the case of power transformers this is made difficult due to the presence of excessive amounts of censored data. Censored data presents partial information only, e.g. transformer survival times, inhibiting the ability of asset managers to correctly identify the long-term behaviour of the population through the use of traditionally statistical methods such as the Maximum Likelihood Estimation (MLE) procedure. This paper investigates the ability of the MLE to estimate strategic percentiles of asset populations that are used to assist asset management decisions. The analytical study is performed through a series of Monte Carlo simulations and statistical measures to determine the `quality´ of estimates of the 2.5 and 97.5 percentiles of the Normal and Weibull distributions, under scenarios with different sample size and percentages of censored data. The results demonstrate the ability of the MLE procedure to identify percentiles in the near tail of the distribution with reasonable accuracy, and the pessimistic nature of percentiles in the far tail when the dataset contains levels of censoring normally found in transformer populations. The results are further verified through the calculation of approximate 95% confidence intervals.