About Shewhart control charts to monitor the Weibull mean based on a Gamma distribution

A control chart for the mean of a process whose quality characteristic follows a Weibull distribution is evaluated. In this sense, a transformation that follows an exponential distribution is used involving the parameters of scale and form of a Weibull distribution. Such a transformation allows to obtain analytically the control limits to monitor the mean using the Gamma distribution. Compared with recent results in the literature, lower average run lengths after a change (ARL1) values are measured without the need to use intensive Monte Carlo simulation to obtain the control limits as well as to calculate the ARL1 values. A numerical example is presented in detail to illustrate the efficiency and effectiveness of the developed control chart.