A comparative study of some EWMA schemes for simultaneous monitoring of mean and variance of a Gaussian process

In this paper, we introduce four different combinations of EWMA schemes, each based on a single plotting statistic for simultaneous monitoring of the mean and variance of a Gaussian process. We compare the four schemes and address the problem of adopting the best combining mechanism. We consider that the actual process parameters are unknown and estimated from a reference sample. We take into account the effects of estimation of unknown parameters in designing the proposed schemes. We consider the maximum likelihood estimators based pivot statistics for monitoring both the parameters and combine them into a single statistic through the 'max' and the 'distance' type combining functions. Also, we examine two different adaptive approaches to introduce pivot statistics into the EWMA-structure. Results show that the distance-type schemes outperform the max-type schemes. Generally, the proposed schemes are useful in detecting small-to-moderate shifts in either or both of the process parameters. Computational studies reveal that the proposed schemes can identify a process shift more quickly compared to some of the existing schemes. We illustrate the implementation strategies of the schemes using two industrial datasets.