Self-starting control chart for simultaneously monitoring process mean and variance

A self-starting control chart, based on the likelihood ratio test and the exponentially weighted moving average procedure, is proposed for monitoring the process mean and variance simultaneously when the process parameters are unknown. A table is presented to assist in the design of the control chart with different parameters. Its in-control average run length can be evaluated by a two-dimensional Markov chain model. Moreover, the diagnostic aids of the proposed chart are given. Monte Carlo simulation results compared with some competing methods in the literature show that the proposed approach has quite satisfactory charting performance across a range of possible shifts when the process parameters are unknown, even including the detection of a decrease in variability. A real data example from industrial manufacturing is used to demonstrate its implementation.