Detecting shift in a Weibull process using bootstrap method

Abstract

Detecting a shift in a Weibull process is considered. The parametric bootstrap method is used to establish lower and upper control limits for monitoring percentiles. When process measurements have a weibull distribution small percentile is of importance when observing tensile strength and it is desirable to detect their downward shift. The performance of the proposed bootstrap percentile charts is considered based on computer simulations, and some comparison is made with the existing Weibull percentile chart. The advantage of the bootstrap method is that they are not restricted by assumptions on the distribution of the process measurements. The bootstrap method uses only the sample data to estimate the sampling distribution of the parameter estimator and then determine appropriate control limit. The new bootstrap chart indicates a shift in the process percentile substantially quicker than the previously existing chart, while maintaining comparable average run lengths when the process is in control.