**1. Introduction**

Nowadays, the problem of increasing reliability of manufacturing process, which represents the core of any industrial enterprise, affects the realization of business goals so that it is an interesting field of research for both researchers and practitioners. According to the results of the best practice, and literature sources [1], it can be said that failures have the greatest impact on the reliability of the manufacturing process. Although there is a significant number of production and organization concepts, such as world class manufacturing (WCM), just-in-time (JIT), the scope of this paper is set to the lean manufacturing and in compliance with that, failures leading to lean waste are identified. According to the lean concept [2], there are seven types of waste found in any process: transportation, inventory, motion, waiting, overprocessing, overproduction, and defect. Later, Liker [3] introduced waste related to underutilization of labor creativity, and it is denoted as Unused employee creativity. Reducing or eliminating the impact of identified failures can be performed by implementing various quality methods.

Quality methods are extremely important, because without reliable and complete information, it is practically impossible to undertake effective measures aimed at improving manufacturing processes [4,5].

There are many quality methods that are defined in the literature [6,7]. Application of these quality methods can lead to the simultaneous elimination or reduction of the

**Citation:** Gojkovi´c, R.; Ðuri´c, G.; Tadi´c, D.; Nesti´c, S.; Aleksi´c, A. Evaluation and Selection of the Quality Methods for Manufacturing Process Reliability Improvement—Intuitionistic Fuzzy Sets and Genetic Algorithm Approach. *Mathematics* **2021**, *9*, 1531. https://doi.org/10.3390/ math9131531

Academic Editors: Jorge de Andres Sanchez and Laura González-Vila Puchades

Received: 29 May 2021 Accepted: 24 June 2021 Published: 29 June 2021

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impact of one or more identified failures of the manufacturing process. Respecting the limited resources (money, time, etc.), it can be concluded that it is almost impossible to implement a number of quality methods at the same time. In practice, the basic task of the reliability manager is how to choose a set of quality methods whose application of the considered problem can be effectively solved in the shortest possible time. Many authors sugges<sup>t</sup> that the choice of quality methods should be based on the priority of failures [8–11]. Experiences of best practice show that decision makers (DMs), when choosing quality methods, respect many criteria besides the priority of failures. In this research, the authors sugges<sup>t</sup> that in determining the set of quality methods, besides the mentioned, it is necessary to consider applicability of methods and implementation costs due to limited financial resources of small and medium enterprises in the manufacturing industry. Prioritization can be seen as a problem in itself. According to [12], the priority assessment under an uncertain environment is based on the failure mode and effect analysis (FMEA) which is combined with fuzzy sets theory [13], as in this research. In other words, evaluation of failures is performed by respecting to risk factors (RFs): severity, occurrence, and detection. According to suggestions of Liu [14], in this research, assumptions were introduced: (i) RFs have not equal the relative importance, and (ii) the relative importance of RFs and their values can be adequately described in linguistic terms, and (iii) the priority of failures is based on the rank of risk priority number (RPN) which is calculated as the product of these three RFs with respects to their weights.

Respecting the nature of human thinking, it can be said that DMs hardly give an accurate evaluation of uncertain data in practical decision problems. Hence, DMs express their assessments easier when using natural language words instead of the precise numbers. The development of theories of mathematics, such as the theory of intuitive fuzzy sets (IFSs) [15] allows vagueness to be represented fairly quantitatively. The advantages of using IFSs are: (1) transient stages during decision making can be rendered by intuitionistic indices, and (2) it is possible to foresee the best and worst results.

As it is known, in the manufacturing process managemen<sup>t</sup> literature, it is almost impossible to find papers where the problem of choosing the quality methods set is considered as a combinatorial optimization problem. Since, in this research, the treated problem is stated as a rubber knapsack problem which represents the version of the classic 0–1 knapsack problem (0–1 KP) with the goal of finding, in a set of items of given values and weights, the subset of items with the highest total value, subject to a total weight constraint [16,17]. This can be marked as one of this paper's novelties. Finding the optimal solution of the considered problem is based on using the genetic algorithm (GA) [18]. By using GAs, perform a search in complex, and large landscapes, and provide near-optimal solutions for objective function an optimization problem. In the literature, GA is a widely used metaheuristic method for solving difficult nondeterministic polynomial time (NP) problems from different domains [19–21], as in this research.

Motivation for this research comes from the fact that there are almost no literature sources that treat the selection of quality methods where uncertainties are given by exact ways.

The wider objective of this research may be interpreted as: (1) identification of failures in manufacturing process in SMEs of the process industry, (2) assessment identified failures based on FMEA, (3) modelling of the existing uncertainties are performed by using triangular intuitionistic fuzzy number (TIFN) [22,23], (4) the priority of failure is determined by applying the RPN with TIFNs with respects to RF weights, (6) selection of quality methods is stated as KP, and obtaining an adequate set of quality methods is based on the application of GA. The authors believe that the solution obtained in this way is significantly less burdened by the subjective attitudes of DMs, and therefore the effectiveness of solving the problem of reliability of the manufacturing process is significantly better.

The paper is organized in the following way: In Section 2, there is a literature review. Methodology is presented in Section 3. The proposed Algorithm is presented in Section 4. The case study is presented in Section 5. Conclusion and discussion are given in Section 6.
