About Shewhart control charts to monitor the Weibull mean

In this paper, a new reparametrization expressed in terms of the process mean for Weibull distribution is studied; thus, the monitoring of the process mean can be made directly. Additionally, we call attention that the asymptotic control limits for X‾ control chart by central limit theorem (CLT) may lead to a serious erroneous decision. Definitively, they can only be used to signal small/medium shifts in the process mean but with a very very large sample size. We present guidelines for practitioners about the minimum sample size needed to match out‐of‐control average run length (ARL1) with the exact and asymptotic control limits in function of the shape parameter after an extensive simulation study. The proposed schemes are applied to monitoring the Weibull mean parameter of the strength distribution of a carbon fibber used in composite materials.