Monitoring the Shape Parameter of a Weibull Regression Model in Phase II Processes

In this paper, the interest is focused on monitoring profiles with Weibull distributed‐response and common shape parameter γ in phase II processes. The monitoring of such profiles is completely possible by taking the natural logarithm of the Weibull‐distributed response. This is equivalent to characterize the correspondent process by an extreme value linear regression model with common scale parameter σ = γ⁻¹. It was found out that from the monitoring of the common log‐scale parameter of the extreme value linear regression model, with the help of a simple scheme, it can be obtained important information about the deterioration of the entire process assuming the β coefficients as nuissance parameters that do not have to be known but stable. Control charts are based on the relative log‐likelihood ratio statistic defined for the log‐scale parameter of the log‐transformation of the Weibull‐distributed response and its respective signed square root. It was also found out that some existing adjustments are needed in order to improve the accuracy of using the distributional properties of the monitoring statistics for relatively small and moderate sample sizes. Simulation studies suggest that resulting charts have appealing properties and work fairly acceptable when non‐large enough samples are available at discrete sampling moments. Detection abilities of the studied corrected control schemes improve when sample size increases.