A Bootstrap Control Chart for Weibull Percentiles

The problem of detecting a shift of a percentile of a Weibull population in a process monitoring situation 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 percentiles are 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 comparisons are made with an existing Weibull percentile chart. 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. An illustrative example concerning the tensile strength of carbon fibers is presented.