TY - JOUR
T1 - Development of fuzzy process control charts and fuzzy unnatural pattern analyses
AU - Gülbay, Murat
AU - Kahraman, Cengiz
PY - 2006/11/1
Y1 - 2006/11/1
N2 - Many problems in scientific investigation generate nonprecise data incorporating nonstatistical uncertainty. A nonprecise observation of a quantitative variable can be described by a special type of membership function defined on the set of all real numbers called a fuzzy number or a fuzzy interval. A methodology for constructing control charts is proposed when the quality characteristics are vague, uncertain, incomplete or linguistically defined. Fuzzy set theory is an inevitable tool for fuzzy control charts as well as other applications subjected to uncertainty in any form. The vagueness can be handled by transforming incomplete or nonprecise quantities to their representative scalar values such as fuzzy mode, fuzzy midrange, fuzzy median, or fuzzy average. Then crisp methods may be applied to those representative values for control chart decisions as "in control" or "out of control". Transforming the vague data by using one of the transformation methods may result in biased decisions since the information given by the vague data is lost by the transformation. Such data needs to be investigated as fuzzy sets without transformation, and the decisions based on the vague data should not be concluded with an exact decision. A "direct fuzzy approach (DFA)" to fuzzy control charts for attributes under vague data is proposed without using any transformation method. Then, the unnatural patterns for the proposed fuzzy control charts are defined using the probabilities of fuzzy events.
AB - Many problems in scientific investigation generate nonprecise data incorporating nonstatistical uncertainty. A nonprecise observation of a quantitative variable can be described by a special type of membership function defined on the set of all real numbers called a fuzzy number or a fuzzy interval. A methodology for constructing control charts is proposed when the quality characteristics are vague, uncertain, incomplete or linguistically defined. Fuzzy set theory is an inevitable tool for fuzzy control charts as well as other applications subjected to uncertainty in any form. The vagueness can be handled by transforming incomplete or nonprecise quantities to their representative scalar values such as fuzzy mode, fuzzy midrange, fuzzy median, or fuzzy average. Then crisp methods may be applied to those representative values for control chart decisions as "in control" or "out of control". Transforming the vague data by using one of the transformation methods may result in biased decisions since the information given by the vague data is lost by the transformation. Such data needs to be investigated as fuzzy sets without transformation, and the decisions based on the vague data should not be concluded with an exact decision. A "direct fuzzy approach (DFA)" to fuzzy control charts for attributes under vague data is proposed without using any transformation method. Then, the unnatural patterns for the proposed fuzzy control charts are defined using the probabilities of fuzzy events.
KW - Fuzzy probability
KW - Fuzzy process control
KW - Run tests
KW - Unnatural patterns
UR - http://www.scopus.com/inward/record.url?scp=33750375096&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2006.04.031
DO - 10.1016/j.csda.2006.04.031
M3 - Article
AN - SCOPUS:33750375096
SN - 0167-9473
VL - 51
SP - 434
EP - 451
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 1
ER -