Development of fuzzy control charts for monitoring manufacturing process with uncertain and vague observations - Jahromi, Seyed Mojtaba Zabihinpour (2015)
Quality characteristics measurement may include uncertainty due to randomness and fuzziness. Conventional control charts only consider the uncertainty due to randomness. Therefore, the application of fuzzy control charts becomes inevitable when quality characteristics are measured with vagueness, or affected by uncertainty, incomplete information or human subjectivity. To date, several researches have been directed to develop various types of fuzzy control charts, but the application of fuzzy X-S control charts for monitoring mean and variability of the process is restricted to biased estimation of population standard deviation. A review of the literature on fuzzy control charts also shows that the application of fuzzy set theory to develop fuzzy cumulative sum control charts has not been considered. In this research, unbiased estimation of population standard deviation for a triangular fuzzy random variable was introduced followed by the development of fuzzy X-S and FCUSUM control charts. Percentage of area as a methodology to determine the process state directly when the observations are in the form of triangular fuzzy random variable was developed and optimum γ-level when applying percentage of area to determine the process state in fuzzy X-S control charts for various sample was find using a simulation study based on average run length. Transformation techniques to determine the process state indirectly were modified and the optimum transformation techniques was introduced using a comparison study based on average run length when applying fuzzy X-S and FCUSUM charts. A simulation study was then made to verify the proposed technique by comparing its performance based on average run length with previous techniques in the literature. Finally, the proposed fuzzy control charts were validated in a case study that monitored the cooking quality characteristic of chicken nuggets in B.A. Food Production Group and texture quality of noodle preparation in a food laboratory. The proposed fuzzy control charts detected the shift in the process immediately after changing the raw material (wheat) in preparing the noodles, while, conventional control could not detect this shift. From this study, it was observed that the proposed fuzzy X-S and FCUSUM charts could improve the quality through reduction of the variability from 0.1% to as much as 68% compare to the conventional Shewhart control charts and previous techniques in the literature. Fuzzy median is the optimum transformation technique when applying fuzzy X-S control charts, while fuzzy median and fuzzy average are the optimum transformation techniques when applying FCUSUM control chart.