Process Quality Evaluation Model with Taguchi Cost Loss Index

Process Capability Indices (PCIs) are not only a good communication tools between sales departments and customers but also convenient tools for internal engineers to evaluate and analyze process capabilities of products. Many statisticians and process engineers are dedicated to research on process capability indices, among which the Taguchi cost loss index can reflect both the process yield and process cost loss at the same time. Therefore, in this study the Taguchi cost loss index was used to propose a novel process quality evaluation model. After the process was stabilized, a process capability evaluation was carried out. This study used Boole’s inequality and DeMorgan’s theorem to derive the (1 – α) ×100% confidence region of (δ,γ2) based on control chart data. The study adopted the mathematical programming method to find the (1 – α) ×100% confidence interval of the Taguchi cost loss index then employed a (1 – α) ×100% confidence interval to perform statistical testing and to determine whether the process needed improvement.

Analyzing of Process Capability Indices based on Neutrosophic Sets

Process capability analysis (PCA) is an important statistical analysis approach for measuring and analyzing the ability of the process to meet specifications. This analysis has been applied by producing process capability indices (PCIs). \({C}_{p}\) and \({C}_{pk}\) are the most commonly used PCIs for this aim. Although they are completely effective statistics to analyze process’ capability, the complexity of the production processes based on uncertainty arising from human thinking, incomplete or vague information makes it difficult to analyze the process capability with precise values. When there is uncertain, complex, incomplete and inaccurate information, the capability of the process is successfully analyzed by using the fuzzy sets. Neutrosophic sets (NSs), one of the new fuzzy set extensions, have a significant role in modeling uncertainty, since they contain the membership functions of truth, indeterminacy, and falsity definitions rather than an only membership function. This feature provides a strong advantage for modeling uncertainty. In this paper, PCA has been performed based on NSs to overcome uncertainties of the process. For this purpose, specification limits (SLs) have been reconsidered by using NSs and two of the well-known process capability indices (PCIs) named \({C}_{p}\) and \({C}_{pk}\) have been reformulated. Finally, the neutrosophic process capability indices (NPCIs) named \({C}_{p}\) \(\left({\tilde{\stackrel{⃛}{C}}}_{p}\right)\) and \({C}_{pk}\) \(\left({\tilde{\stackrel{⃛}{C}}}_{pk}\right)\) have been derived for three cases that are created by defining SLs. Additionally, the obtained NPCIs have also been applied and confirmed on real case problems from automotive industry. The obtained results show that the NPCIs support the quality engineers to easily define SLs and obtain more flexible and realistic evaluations for PCA.

Process design and capability analysis using penthagorean fuzzy sets: surgical mask production machines comparison

Process capability analysis (PCA) is a tool for measuring a process’s ability to meet specification limits (SLs), which the customers define. Process capability indices (PCIs) are used for establishing a relationship between SLs and the considered process’s ability to meet these limits as an index. PCA compares the output of a process with the SLs through these capability indices. If the customers’ needs contain vague or imprecise terms, the classical methods are inadequate to solve the problem. In such cases, the information can be processed by the fuzzy set theory. Recently, ordinary fuzzy sets have been extended to several new types of fuzzy sets such as intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets. In this paper, a new extension of intuitionistic fuzzy sets, which is called penthagorean fuzzy sets, is proposed, and penthagorean fuzzy PCIs are developed. The design of production processes for COVID-19 has gained tremendous importance today. Surgical mask production and design have been chosen as the application area of the penthagorean fuzzy PCIs developed in this paper. PCA of the two machines used in surgical mask production has been handled under the penthagorean fuzzy environment.