*5.2. Case Study*

In this section, to demonstrate the applicability and capability of the proposed model, a case study in a plaster-producing company is presented. In a traditional statistical process control system, after gathering the data, the following steps are done:


The proposed ISPC model, designed in Matlab, can adequately perform the above operations (Figure 13). Here, pursuant to the plaster-producing experts' opinion, if "Cpk > 1", the chart is considered as the baseline for interpreting the process. As can be seen in the ISPC implementation flow chart, after collecting the process data, the baseline chart should be set by eliminating and replacing points beyond the control limits of new data. As shown in Figure 14, the normality test was done, where the normality assumption was valid, and "Cpk > 1" in control mode. After drawing the baseline chart, the actual data of the process were inserted and checked and analyzed by the desired control charts. As illustrated in Figure 15, although there is no "out of control" mode within the "R-chart", the process was unable to meet specifications due to "Cpk < 1", being equal to 0.81 (Figure 16). On the other hand, by choosing the "X-bar chart" (Figure 17), the user receives the following error message: "X-bar chart is out of control" (Figure 18). Then, the ES using "Western Electric tests" announces that "out of control" modes may have the following reasons: "carelessness in the measurement, machinery stop, or off-spec materials". Later, the user receives a suggestion message from ES to check the unnatural patterns identified by NN (Figure 19). As can be seen in Figure 20, not only was the "downward shift pattern" in the "X-bar chart" identified by the NN, but the "starting point" of the unnatural pattern was estimated (point 6). The "shift magnitude parameter" (−0.161) was also determined. In this scenario, because of the appearance of a "downward shift pattern" and based on user observation, which was "kiln body scarlet", the reason for the deviation was recognized as the "temperature exchange of kiln with the environment due to the loss of refractory and thickness". "Establishment of maintenance and inspection of refractory" was also recommended as corrective or preventive activities. In this scenario, by making corrective actions and following re-sampling the process (Figure 21), "out of control" modes did not appear in the control charts anymore (Figure 22) and, furthermore, "process capability" increased from Cpk = 0.81 to Cpk = 1.15 (Figure 23). The experimental results show that corrective actions could significantly contribute to process recovery. Thus, the proposed fault diagnosis system could be used to support decision-makers of the plaster production.

**Figure 13.** ISPC implementation flow chart.

**Figure 14.** Normality test and process capability calculation.

**Figure 15.** X-bar chart in "out of control" mode.

**Figure 16.** Process capability calculation.

**Figure 17.** Request for analyzing the X-bar chart.

**Figure 18.** X-bar chart reasoning by Western Electric tests.

**Figure 19.** Pattern recognition in X-bar chart by NN.

**Figure 20.** Determining Cpk, unnatural pattern, parameters, and recovery actions.

**Figure 21.** Inserting new dataset.

**Figure 22.** X-bar and R charts in control mode.

**Figure 23.** Capability of the process after performing corrective actions.
