Non-Invasive Statistical Approach to Evaluate Processes Variability Using Fuzzy Process Capability Indices and Fuzzy Individual Control Charts

Rodríguez-Álvarez, José L.

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Date

2022-02

Author

Rodríguez-Álvarez, José L.

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URI

https://hdl.handle.net/11117/8448

Description

The statistical thinking and monitoring of the quality of product characteristics, either of a variable or attribute type, plays a key role in a successful quality improvement to reduce process or product variation. For this purpose, the control charts techniques and the process capability indices are widely used in a variety of manufacturing and service industries to carry out an overall evaluation of the process performance. However, it should be noted that the results obtained using these techniques, given that they operate under certain assumptions, generally show variation over time, mainly in complex processes in which it is difficult to collect sufficient data on the quality variables and in processes with uncertainty in the measurements. Therefore, special care must be taken in choosing the appropriate technique to have an evaluation close to the reality of the process. Firstly, in this doctoral dissertation is presented an alternative fuzzy individual and moving range control charts based on the 𝛼-cut fuzzy midrange approach. The proposed method to generate the fuzzy numbers is based on the sigma level of the process, and the observed variation in each sample. Thus, these fuzzy control charts are more flexible, because the amplitude between the upper and lower control limits is greater than those shown in the traditional control charts. In the second proposal is presented an alternative method to estimate the process capability indices under a fuzzy approach. This alternative uses a coupled applications of modeling + experimental designs, which are presented as a non-invasive approach. The application has a double purpose: first, to know the process variability, and second, to reduce variability in the quality control variable. When a process performance evaluation based on control charts and capability indices is carried out, it is necessary to use the interest quality variables data. Generally, the data are recorded by the quality control department or the measuring instruments that are part of the process. In the proposed method, the used data set to evaluate the process capability corresponds to values predicted by a trained model with reasonable accuracy. This imply that the measures will include the variability shown in each independent variable that affect the response, in addition to the model error. The method was validated using a real basis weight dataset. The findings showed that the overall process capability indices estimated with the proposed method are closer to the process reality than the existing traditional and fuzzy methods.

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