Multivariate Fuzzy T2 Hotelling Control Chart with Alpha-Cut Using Trapezoidal Fuzzy Number (TrFN) and Its Application Nur Rezky Safitriani (a*), Muhammad Mashuri (a), Wibawati (a)
a) Department of Statistics : Faculty of Science dan Data Analysis, Institut Teknologi Sepuluh Nopember, Jl. Arief Rahman Hakim, Surabaya, 60111, Indonesia
*rezky.toaba[at]gmail.com
m_mashuri[at]statistika.its.ac.id
wibawati[at]statistika.its.ac.id
Abstract
The quality of a product is the most important factor in the manufacturing industry which can be maintained through statistical monitoring of the production process using the Statistical Process Control (SPC) method. One of them is a control chart which aims to know whether the process is running under controlled conditions or not. Quality control of a product consisting of two or more correlated quality characteristics is more efficient using a multivariate control chart than several univariate control charts. However, there are product qualities that cannot be measured and expressed numerically, so an assessment of linguistic criteria is required. This assessment can cause ambiguity which can be overcome using fuzzy set theory so that multivariate fuzzy control charts are developed. One of the multivariate fuzzy control chart that has ease of application and interpretation is fuzzy T2 Hotelling. This method is sensitive to mean shifts in the production process which is indicated by a decrease in ARL but is not sensitive to small mean shifts. To overcome these shortcomings, alpha-cut is added to improve the tightness of the inspection of each quality control process. Thus, fuzzy T2 Hotelling control chart with alpha-cut can detect small shifts in the mean for linguistic quality characteristics. Statistics fuzzy T2 Hotelling is based on representative values through membership functions where the Triangular Fuzzy Number (TFN) has often been used but rarely uses its development, namely the Trapezoidal Fuzzy Number (TrFN) which provides a better solution. This research developed multivariate fuzzy T2 Hotelling control chart with alpha-cut using TrFN and its application in the manufacturing industry, building materials industry at UD Tiga Beton as a producer of pressed bricks which had never before conducted statistical monitoring of the production process. The results of of the application show that multivariate fuzzy T2 Hotelling control chart with alpha-cut using TrFN can be used to simultaneously monitor the quality characteristics of each process related to multivariate linguistic data and can handle processes sensitive to small mean shifts.
Keywords: Multivariate fuzzy control charts, Fuzzy T2 Hotelling, Alpha-cut, Linguistic, Building materials industry
