# Fuzzy Supplier Selection Method Based on Smaller-The-Better Quality Characteristic
## 1 Introduction  
Many important parts of tool machines all have important smaller-the-better (STB) quality characteristics, such as roundness, concentricity and verticality of gears, bearings and axle centers, etc. The important smaller-the-better (STB) quality characteristics will decide the quality of the end product [1; 2; 3]. Process capability indices (PCIs) are commonly adopted by companies to measure process quality. PCIs not only help manufacturers evaluate process quality during production, but are also viewed as a useful tool of communication between engineers working for the same company. This has been confirmed by extensive research [4; 5; 6; 7; 8; 9; 10].  
The project of six sigma quality improvement led by Motorola can effectively help companies enhance quality as well as reduce defect rates for production processes [11; 12]. According to [PERSON] et al. [13], six sigma assessment helped Motorola achieve its quality-control target of only 3.4 defects per million opportunities. Thus, six sigma quality levels have also been widely applied to manufacturing, in order to measure process quality [14; 15; 16; 17; 18].  
Many researchers, such as [PERSON] et al. [19], [PERSON] et al. [20], [PERSON] et al. [21], and [PERSON] and [PERSON] [22], have attempted to derive relationships between capability indices and six sigma quality levels. This wasaimed at determining whether process quality meets specified requirements. In order to directly determine quality levels based on index values, [PERSON] et al. [11] came up with the six sigma index of quality characteristics to assess the process quality of STB quality characteristics.  
According to [PERSON] and [PERSON] [23] and [PERSON] and [PERSON] [24], obtaining parts from suppliers has become a trend in business strategy to enhance competitiveness and operational flexibility. [PERSON] and [PERSON] [25] also pointed out that forming partnerships with suppliers can help companies increase product quality, as well as the competitiveness of the industry chain as a whole. [PERSON] and [PERSON] [26] and [PERSON] et al. [27] indicated that the quality of raw materials, components, and equipment should be taken into consideration when selecting suppliers, because they can affect end products' quality. The six sigma index can straightly display process quality levels as well as process yield. Consequently, we chose this index as our instrument for supplier selection in this study. Since this index contains unidentified parameters, sample data are required for estimation [28; 29]. Numerous researchers have come up with fuzzy testing methods using confidence intervals to improve the precision of estimation and solve the problem of uncertainty found in the measured data [30; 31]. A smaller size of the sample leads to a larger length of the interval, whereas a larger size of the sample results in a smaller length of the interval [28]. Consequently, applying confidence intervals to the statistical testing method can lead to inconsistencies or different sizes of the sample. Considering practicality, the sample size is rarely large. As a result, this study developed a two-tailed fuzzy testing method to select a proper supplier, which is more reasonable than the statistical testing method and more consistent with the discussions made in several studies [12; 28; 29; 30; 31; 32]. The proposed method can help companies increase product quality, as well as the competitiveness of the industry chain as a whole.  
The other sections of this paper are organized as follows. Section 2 is literature review. Section 3 is related to research design and methods including the confidence interval of the six sigma index and the two-tailed confidence-interval-based fuzzy testing method for the supplier selection. In Section 4, a numerical example is taken to illustrate the efficacy of the proposed method. Last but not least, conclusions are made in Section 5.