PROGRESSIVE MEAN CONTROL CHARTS FOR PHASE II MONITORING OF MULTIVARIATE SIMPLE LINEAR PROFILES

In some statistical quality control applications, the process outcome is better expressed by a functional relationship among several correlated response variables and one independent variable called multivariate simple linear prole. Monitoring such proles without taking the correlation structure among the response variables into account leads to misleading interpretations. Specically, monitoring each prole 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 memorytype 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 MPMa, MPMe and MPMae charts are developed for Phase II monitoring of multivariate simple linear proles. 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 is compared with competing ones in the literature including MEWMA, MEWMA/x2 and MEWMA-3 schemes. The results conrm that under dierent correlation coe cient values, when the intercept parameter of one pro- le 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 coecient. Concerning the sustained shifts in slope parameter, it is observed that by increasing the correlation coecient and shift magnitude, the MPMa and MPMae charts perform better than the other ones. Besides, under standard deviation disturbances, the proposed charts have almost the same sensitivity to react to small and moderate changes. The results indicate that under simultaneous shifts in model parameters of both proles, the proposed PM based schemes have better detectability than their competing ones. Finally, the applicability of the best proposed chart is illustrated using a real life example from automotive industry.