Monitoring Tools for Autocorreleated Data

Whenever there are inertial elements (capacity) in a process such as storage tanks, reactors or separation columns, the observations from such processes exhibit serial correlation over time. Successive observations are related to 

The process mean p,(A ) at time k varies over time with respect to the target or nominal value for the mean t  

The strength of correlation dies out as the number of sampling intervals between observations increases. In other words, as the sampling interval increases, the correlation between successive samples decreases. In some industrial monitoring systems, a large sampling interval is selected in order to reduce correlation. The penalty for this mode of operation is loss of information about the dynamic behavior of the process. Such policies for circumventing the effects of autocorrelation in data should be avoided. 

The correlation between observations made at different times (autocorrelation) is described mathematically by computing the autocorrelation function, the degree of correlation between observations made k time units apart k = 1,2, ). The correlation coefficient is a measure of the linear association between two variables. It does not describe a cause-and-effect relation. The autocorrelation depends on sampling interval. Most statistical and mathematical software packages include routines for computing correlation and autocorrelation. 

The sample correlation function between two variables x and y is denoted hy Vx,y and it is equal to  

---

Since yMst is a random variable, SPM tools can be used to detect statistically significant changes. histXk) is highly autocorrelated. Use of traditional SPM charts for autocorrelated variables may yield erroneous results. An alternative SPM method for autocorrelated data is based on the development of a time series model, generation of the residuals between the values predicted by the model and the measured values, and monitoring of the residuals [1]. The residuals should be approximately normally and independently distributed with zero-mean and constant-variance if the time series model provides an accurate description of process behavior. Therefore, popular univariate SPM charts (such as x-chart, CUSUM, and EWMA charts) are applicable to the residuals. Residuals-based SPM is used to monitor lhist k). An AR model is used for representing st k) ... 

---