# Response Surface Methodology Using Observational Data: A Systematic Literature Review
###### Abstract  
In the response surface methodology (RSM), the designed experiment helps create interfactor orthogonality and interpretable response models for the purpose of process and design optimization. However, along with the development of data-recording technology, observational data have emerged as an alternative to experimental data, and they contain potential information on design/process parameters (as factors) and product characteristics that are useful for RSM analysis. Recent studies in various fields have proposed modifications to the standard RSM procedures to adopt observational data and attain considerable results despite some limitations. This paper aims to explore various methods to incorporate observational data in the RSM through a systematic literature review. More than 400 papers were retrieved from the Scopus database, and 83 were selected and carefully reviewed. To adopt observational data, modifications to the procedures of RSM analysis include the design of the experiment (DoE), response modeling, and design/process optimization. The proposed approaches were then mapped to capture the sequence of the modified RSM analysis. The findings highlight the novelty of observational-data-based RSM (RSM-OD) for generating reproducible results involving the discussion of the treatments for observational data as an alternative to the DoE, the refinement of the RSM model to fit the data, and the adaptation of the optimization technique. Future potential research, such as the improvement of factor orthogonality and RSM model modifications, is also discussed. classic RSM; observational data; RSM-OD; RSM stages; systematic literature review +
Footnote †: journal: Medical  
and increase the number of nonconforming items, hence, resulting in high costs [2]. When direct experimentation is not feasible, one of the alternative solutions is to use observational data as the input to the RSM [3,4]. Some high-tech industries are often complemented with intelligent data-acquiring systems that allow them to record real-time process/equipment parameter changes. For prediction purposes, these real-time recorded data become the input for a mathematical model to generate outputs, such as a forecasting system for maintenance schedules or product quality [5]. Several pieces of research on chemical engineering and food production [6,7] have demonstrated that observational-data-based RSM (RSM-OD) provided a fitted mathematical model to find an optimal factor setting. Other research used the observed data from a running process or equipment as the input for RSM-OD, as shown in the work of [8] for steel production and [9] with pollutant removal processes. However, observational data and their similarities, including real-time recording data and already conducted experiment data, limits a researcher's control over their factor levels, as the DoE ideally affords. There are presumptions that observational data contain a high volume, high variability, unstructured, and serial-correlated situations [10]. Therefore, some modifications to selecting the observations are required prior to the use of the data in RSM analysis, including the adaptive RSM model and optimization techniques, while still considering the ideal concept of the RSM. The authors of [3] have successfully adopted observational data for the DoE by selecting a subset of observations and identifying stages within the data, similarly, Refs. [2,11,12] also giving alternatives by matching the data with certain DoE to ensure orthogonality. Moreover, the authors of [4,13] apply the RSM to real-time data acquisition for optimization during continuous processes. It is also worth noting that the recent development of big data has accelerated the use of observational data. For instance, Ref. [14] demonstrated real-manufacturing-oriented big data, in which recorded datasets provide information for process improvement and optimization. The data-recording technology provides massive datasets in which huge datasets are recorded along with operations [15,16,17].