Monitoring the Weibull Shape Parameter by Control Charts for the Sample Range

摘要

In this paper, we propose control charts for monitoring changes in the Weibull shape parameter β. These charts are based on the range of a random sample from the smallest extreme value distribution. The control chart limits depend only on the sample size, the desired stable average run length (ARL), and the stable value of β. We derive control limits for both one- and two-sided control charts. They are unbiased with respect to the ARL. We discuss sample size requirements if the stable value of β is estimated from past data. The proposed method is applied to data on the breaking strengths of carbon fibers. We recommend one-sided charts for detecting specific changes in β because they are expected to signal out-of-control sooner than the two-sided charts.