Reliability engineering tools: bootstrapping and extreme value statistics

Abstract

Summary form only given. This tutorial provides practical information on two techniques that are of use to anyone doing statistical data analysis and making statistical inferences. Reliability engineers often base their decisions on fitting lifetime data to a particular type of distribution (e.g. lognormal, exponential, Weibull). Statistical bootstrapping is a tool that allows us to explore data and make useful inferences (e.g. mean, confidence intervals) about it without the need for assuming that the data is from a particular underlying distribution. Bootstrapping was introduced in the late 1970's and is a computationally intensive Monte-Carlo procedure that is simple to understand and implement. To bootstrap a statistic (e.g. the sample mean), we draw for example 1000 random resamples with replacement from the original sample data, calculate the statistic of interest (sample mean) for each resample, then estimate the overall sample mean by taking the average of all the 1000 resampled means. Inferences about our statistic can then be made by inspecting the resulting bootstrap distribution of our 1000 resampled values of the statistic of interest. The key idea here is that the bootstrap distribution approximates the sampling distribution of the statistic and we use it as a way to estimate the variation in a statistic based on the original data. The second topic of discussion in this tutorial was an introduction to extreme value statistics. Extreme values statistics have proven useful in ocean engineering (e.g. highest wave height), meteorology (highest amount of rainfall, maximum wind speed), and in investigating fatigue strength and corrosion. Here the focus was on the extremes of a measured parameter instead of the typical focus on centralized tendencies such as the mean or median. I believe that they could also prove useful in exploring electrical reliability issues such as the highest (lowest) use temperature for a metal line, maximum use current flow through a specific device, or the highest use voltage across a capacitor.