Development of fuzzy $$ \bar{X} - S $$ X
- PDF / 766,204 Bytes
- 11 Pages / 595.276 x 790.866 pts Page_size
- 99 Downloads / 178 Views
(0123456789().,-volV)(0123456789(). ,- volV)
METHODOLOGIES AND APPLICATION
Development of fuzzy X -- S control charts with unbalanced fuzzy data Akın O¨zdemir1
Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Statistical process control is an effective quality control technique to monitor a production process with balanced data under certain conditions. However, there are some situations where dealing with uncertainty and unbalanced data is considered. In such situations, the traditional statistical control charts are not effective to obtain control limits. The aim of this paper is fourfold. First of all, the collected unbalanced data are converted to triangular fuzzy numbers for each sample. Second, this paper develops a fuzzy X S control chart while dealing with unbalanced fuzzy data. Third, a proposed approach is presented on how to deal with unbalanced fuzzy data for calculations of control limits. Besides, fuzzy process capability analyses are conducted to measure process performance. Finally, an illustrative example is conducted to show the effectiveness of the proposed fuzzy X S control chart with unbalanced data for uncertainty. Keywords Quality control Fuzzy X S control charts Unbalanced data Triangular fuzzy number Fuzzy process capability indices
1 Introduction In general, the production process is capable of operating with little process variation around the desired target value while meeting the customer’s expectations. To achieve the process stability is a key element to satisfy the customer’s expectations. Therefore, statistical process control (SPC) is a widely used tool to achieve process stability and improving the process capability while minimizing the process variation. Many quality characteristics can be stated based on a numerical measurement. Both the process mean and the process variability are usually monitored when dealing with the numerical measurement. Control of the process mean could be done with the X control chart. The process variability could be monitored with either the S control chart or the R control chart. Particularly, Montgomery (2009) provided a comprehensive review of the statistical control chart under certain conditions.
Communicated by V. Loia. ¨ zdemir & Akın O [email protected] 1
Department of Industrial Engineering, Ondokuz Mayıs University, 55139 Samsun, Turkey
For several situations, fuzzy data widely exist in the production process. There are a few papers on fuzzy statistical control charts based on defuzzification methods (Gu¨lbay and Kahraman 2007). The defuzzification method may not prevent the loss of information from the samples. Based on this awareness, Gu¨lbay and Kahraman (2007) proposed a new approach, which is a direct fuzzy approach (DFA), for fuzzy control charts. This approach does not use the defuzzification method. In the literature, X R and X S are widely used statistical control charts for certain conditions (Montgomery 2009; Sentu¨rk and Erginel 2009). These traditional control charts are
Data Loading...
