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Control Chart for Process Average Based on Generalized Intuitionistic Fuzzy Number

Ali Shabani, Gholamhossein Yari, Ezzatulleh Baloui Jamkhaneh

Abstract



Control charts are based on the quality characteristics measurement in the course of time. There are some situations such as measurement error, sophisticated measurement instruments, costly skilled inspectors, environmental condition and imprecise specification limits that the quality characteristics of the products cannot be measured precisely. Fuzzy set theory is a well-known and proven technique in the case of imprecise, vague and uncertain situations. In the literature of control charts, there are also some research used fuzzy set theory that construct fuzzy control charts, determines the process condition by using transformation and defuzzification techniques (indirectly) which may reduce some useful information from the process. In this paper, we study constructing ̅X control charts, when the observations are generalized intuitionistic fuzzy number. First, we introduce generalize trapezoidal intuitionistic fuzzy number (GTrIFNB). In this situation, control charts are constructed by using GTrIFNB, which are developed using upper and lower control limits. The article also presents a fuzzy decision for in control or out of control of the process, in which membership and non-membership degrees of in and out of control states of process mean is computed. An application is presented for the proposed fuzzy control charts.

Keywords


Statistical process control, control charts, fuzzy set theory, fuzzy control charts, generalized intuitionistic fuzzy number, (α ,β )-cut control limits.

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