Oliver Thunich, Consultant, STATCON GmbH

In industry production, tolerance intervals are widely used to determine the quality of a process.The commonly used tolerance intervals, however, assume normal distribution of the data, which is problematic for many processes. Following a request of a client, we came up with a possibility to calculate nonparametric tolerance intervals by calculating confidence intervals for quantiles using the nonparametric empirical likelihood approach implemented in JMP. As the desired sample sizes become very small, the traditional nonparametric confidence intervals tend to return unstable results. Therefore, we developed a JSL script that extends the empirical likelihood method and is able to generate stable, nonparametric tolerance intervals for a large proportion of the population even with small samples. A simulation study evaluates the performance of the approach in comparison to existing methods using production data as well as survival analysis data. We found that the proposed method is much more stable than existing methods, especially when the data heavily differs from a normal distribution. Using JMP in combination with the implemented method, we are able to assure quality of processes where measuring quality is very costly and/or time consuming.