Forecast Accuracy in Weibull Analysis Based on Now Risk

Abstract

In an engineering risk analysis, where variable data are being used to measure a product’s failure time, a statistical model is often used to predict future failures. The Weibull distribution is frequently used as an appropriate model for this function. There has been considerable study in the estimation of Weibull parameters relative to the known value, but perhaps more important in this case is to assess how well we believe the model can predict for the event of interest. First, does the model predict the number of failures we see right now? Second, how do we measure this correctly and how do we know if the model is adequate or in need of adjustment, based on this assessment? If the model does not predict what we see happening right now (the Now Risk), it is assumed likely to not accurately predict future failures. This paper explains and examines the Now Risk calculation and derives some of its important properties with an emphasis on the Weibull distribution as the failure time model. The results of Monte Carlo simulations used to derive various properties of this statistic are presented. A real example is shown for demonstration of calculation and use of the statistic. Best practices for use of the Now Risk calculation are also shared with additional insight offered into what estimation methods are best to use for this type of analysis.