## 2 Related Work  
It is well known that the effectiveness of individual control loops results in more efficient, reliable and profitable operations. This is true regardless of the industry. Despite this, many industrial control loops exhibit poor performance that may result from improper design and/or tuning. It is this industry fact that is the motivation for the methods and techniques for assessing the performance and quality of an individual control loop.  
As mentioned earlier, there are two fundamental methodologies to this problem. One methodology is model-based and utilizes a model for the benchmarking evaluation process [8]. The second methodology is data-driven and only utilizes data from the normal operation of the process. Some of the methods use specific experiments, while the others do not. As mentioned earlier, the success of any given CPA methodology depends largely on simplicity--i.e., the required a priori knowledge and the steps needed to obtain this information. The following paragraphs briefly describe some of the factors affecting simplicity [6; 9]:  
1. Methods necessitating an experiment [7; 8; 10; 11]: * measures that use a setpoint step response: overshoot, undershoot, rise, peak and settling time, decay ratio, offset, peak value; * indexes that require a disturbance step response: idle index, area index, output index, R-index.
2. Model-based methods [12; 13; 14]: * minimum variance Harris index, control performance index or variance benchmarking methods; * all types of model-based measures derived from close loop identification, such as aggressive/oscillatory and sluggishness indexes; * frequency methods starting from classical Nyquist, Bode or Nichols charts with phase and gain margins using further investigations, such as Fourier transform, sensitivity function, singular spectrum analysis, reference to disturbance ratio index, etc.; * alternative indexes using neural networks or support vector machines.
3. Data-driven methods [15; 16; 17; 18; 19]: * integral time measures: mean square error, integral absolute error, integral (square) time absolute value, integral of square time derivative of the control input, amplitude index, and total squared variation; * correlation measures, such as the relative damping index or the oscillation detection index; * statistical factors for various probabilistic distribution functions or variance band indexes; * benchmarking methods; * alternative indexes using orthogonal functions, wavelets, persistence measures, entropy, multi-fractals or fractional-order.
4. Hybrid or mixed approaches [20; 21]: * fusion CPA measures with sensor combinations or the exponentially weighted moving averages calculated for various indexes; * pattern recognition and graphic visualization methods; * case-specific business key performance indicators, such as the number of alarms or human interventions, the time in manual mode and other currency-based indexes.  
The research reported in the literature describes common industrial CPA (control performance assessment) applications [10], e.g., pulp and paper plants and other process industries, mechanical engineering systems or heating ventilation and air conditioning units. Industrial applications introduce a new context of non-linearities, complexities, non-stationarities, and unknown properties with frequent outliers that result in time series distribution tails of the data.  
The problem of monitoring the quality of regulation forms the basis for the optimization task, widely described in the literature [22; 23].