The Harris Index is an Often Cited Measure of Control Loop Performance. Even So, Its Complexity Could Mean that Other KPIs Are a Better Alternative.
Predicting the weather is difficult – just ask a meteorologist. Even with the help of advanced analytics few seem to get it right with consistency – just ask any parent who has dealt with an unplanned snow day. In addition to more advanced tools meteorologists rely on basic measures such as Temperature, Wind Speed, and Atmospheric Pressure. Their continued reliance on these simpler metrics provides food for thought. Descriptive statistics used in assessing control loop behavior fall into one of three categories: 1) Central tendency, 2) Shape and 3) Spread. Whereas measures of central tendency provide insight into a process’ center or average state of operation and measures of shape describe the distribution of data values, measures of spread indicate the degree to which individual values are clustered or to which they deviate from the mean value in a distribution. Each can provide unique value in terms of understanding a given control loop’s performance.
The Harris Index is a frequently mentioned measure of spread. Calculation is based on a process’ current control relative to a known minimum variance control (MVC) value. In calculating the MVC value an auto-regressive moving average model must be fit to the process data. This is a predictive model that represents the action a minimum variance controller would take. As a result the reliability of the Harris Index depends on the efficacy of that model and its estimation of a process’ Dead-Time.
While the Harris Index is thoroughly documented, consider the following:
- Simple Statistics
Once the Harris Index is configured values can be computed automatically with the help of software. The index’s output is relative to a minimum variance value of one (1) and it can vary significantly from day to day. As such, the value can be difficult to interpret – so wrote Horch and Heiber.
- Model Maintenance
Processes are subject to time-variant behavior and their dynamics steadily change. As a result, the predictive model on which the Harris Index is based will decrease in its efficacy over time. The values will cease to provide an accurate measurement of the associated process’ spread.
- Assessment Alternatives
There are numerous and alternative descriptive statistics for measuring spread. Among them are Average Absolute Error and Standard Variation. While not normalized, both metrics track how well a controller is able to maintain Set Point. Since they are not model-based each can provide an accurate assessment of performance in spite of evolutionary changes in process dynamics.
As with predicting the weather, it’s often worthwhile to start with basic metrics. While the Harris Index is a proven descriptive statistic and offers unique insight into process performance, it is more complex than other available metrics. Indeed, there are numerous others that are simpler to both calculate and interpret. Given the breadth of control loops at a typical production facility, simpler may be better.