Component time-to-failure distribution estimation with limited statistical data: A critical survey

In many power systems worldwide, a substantial proportion of the network infrastructure was installed in the 1960s, and is thus approaching its design lifetime (typically 40 years). In order to plan replacement programmes, robust means of estimating the distribution of failure dates for classes of component are required. This paper provides a tutorial description of the methods for time-to-failure distribution estimation where not all components in a class have failed, contrasting methods from the reliability literature with a least-squares approach proposed in the power systems literature. The conclusion is that, while on the basis of the limited examples presented here the least-squares approach should not be dismissed definitively, much further work is required before it can be regarded as competitive with standard maximum-likelihood approaches. The accuracy of extrapolation beyond ages at which actual failures have been observed is also discussed; simulation results provide a demonstration of how this can be highly inaccurate unless one has precise knowledge of the correct form of the time-to-failure distribution.