عنوان مقاله [English]
In some statistical quality control applications, the process outcome is better expresses by a functional relationship among several correlated response variables and one independent variable called multivariate simple linear profile. Monitoring such profiles without taking the correlation structure among the response variables into account leads to misleading interpretations. Specifically, monitoring each profile by a separate chart increases the probability of Type I error. With increasing customer expectations, detecting small and moderate changes has become important in today’s competitive markets. In this regard, some monitoring schemes including memory-type charts, adaptive charts, and progressive mean (PM) charts have been proposed to enhance the chart sensitivity in reacting to small and moderate disturbances. In this paper, three PM based monitoring schemes including and charts are developed for Phase II monitoring of multivariate simple linear profiles. Extensive simulations in terms of average run length (ARL) metric are carried out to probe the capability of the proposed charts in detecting separate and simultaneous changes in regression model parameters (intercept, slope and standard deviation). Moreover, the sensitivity of the proposed PM based charts are compared with competing ones in the literature including MEWMA, and MEWMA-3 schemes. The results confirm that under different correlation coefficient values, when the intercept parameter of one profile changes from its nominal value, the proposed charts work better than the competing ones. Under the mentioned shift structure, the sensitivity of all charts improves by increasing the value of correlation coefficient. Concerning the sustained shifts in slope parameter, it is observed that by increasing the correlation coefficient and shift magnitude, the and charts perform better than the other ones. Besides, under standard deviation disturbances, the proposed charts have almost a same sensitivity to react to small and moderate changes. The results indicate that under simultaneous changes shifts in model parameters of both profiles, the proposed PM based schemes have better detectability than their competing ones. Finally, the applicability of the proposed chart is illustrated using a real life example from automotive industry.