The Continuous Non-parametric Tolerance Limits

Tolerance limits form an interval within which at least a certain proportion of a population lies with a given confidence level. Usually, they are used to make sure that the production will not be outside of specifications. For non-normal populations, nonparametric tolerance limits are constructed at the beginning of the process. Being calculated just one time, these tolerance limits cannot reflect changes of tolerance level over the lifetime of the process. This article proposes a non-parametric method of constructing tolerance limits continuously over time. A simulation study is conducted to compare the average lengths and standard deviations of the tolerance intervals for both the snapshot and the continuously constructed non-parametric tolerance limits.