Analyzing Attribute Control Charts for Defectives Based on Intuitionistic Fuzzy Sets

Abstract

Control charts (CCs) are one of the most used statistical quality control (SQC) techniques to determine the process' situation is under control or not. The CCs can be classified into two groups based on the quality characteristics such as “variable” or “attribute”. Two well--known attribute control charts (ACCs) named $p$ and $np$ control charts are designed to measure the defectives during the manufacturing stages. If the process is deal with the number of defectives, then $np$ control chart is used. Similarly, if the process deals with the defective rate, the $p$ control chart is used. In the traditional CCs, one of the most important issues is to represent the available data with the highest rate. Since the handled data may consist of uncertain information, ordinary $p$ and $np$ CCs have remained incapable of the ability to reflect the data. Moreover, the operators or the observers of the system can be hesitant while measuring these values during the data gathering process. Therefore, dealing with these problems can be realized by extending the ordinary CCs with useful tools. In the literature, classical fuzzy sets are used to extend $p$ an $np$ control charts. This paper aims to extend these CCs by using Intuitionistic fuzzy sets (IFSs). Comparing with the existed studies, the usage of IFSs enables to represent the hesitancy in their design stages. For this aim, two types of ACCs have been re-designed based on IFSs to improve their sensitiveness and flexibility. In this paper, the extensions of $p$ and $np$ control charts with IFs are proposed and the design of these CCs based on IFs has also been represented in detail. Additionally, control limits and center lines have been re-formulated by using IFs. Moreover, a descriptive example is introduced to analyze the applicability of the proposed method.

Keywords

• Fuzzy logic
• intuitionistic fuzzy sets
• np control chart
• p control chart

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