Monitoring Correlation Within Simple Linear Profiles for AR(1) Processes

In some statistical process control applications, a relationship between a response variable and an explanatory variable referred to as profile characterize the quality of a process or product and should be monitored over time. Many researches have been done in this area but in most of them, the successive observations in different levels of the explanatory variables are assumed to be independent. This assumption is violated in many real case problems for example when observations are taken in short periods of time. If one neglects the correlation between the observations in different levels of explanatory variable, it leads to misleading results on the Average Run Length (ARL) criterion. In recent years, some researchers have proposed some methods to account for the autocorrelation whitin a simple linear profile. Soleimani et al. [1] proposed a transformation technique to consider the correlation between observations in each profile. This paper specifically concentrates on the autocorrelation whitin simple linear profile in Phase II and proposes the use of real variance of autocorrelated observations to take the autocorrelation into consideration. Our simulation studies show the superiority of the proposed technique over the transformation technique in terms of average run length criterion.