A review on fuzzy control charts for monitoring attribute data

Up to now, several methods have been proposed for monitoring processes with attribute data. These methods can be categorized into two major group; statistical methods and fuzzy methods. In this paper current fuzzy methods are introduced and the performance of fuzzy methods and statistical methods are compared together based on the Average Run Length (ARL). The comparison shows that the statistical method has the best performance. We show the necessity of using fuzzy method in case of attribute data. Then the critiques towards fuzzy methods are reviewed which show the usage of fuzzy set theory in these methods have some restriction. As a result we indicate a study gap about the usage of fuzzy set theory for monitoring processes with attribute data and at the end some guideline for the next study are proposed

Fuzzy mean and range control charts for monitoring fuzzy quality characteristics: a case study in food industries using chicken nugget

Organizations must improve or at least maintain the quality of their products to be competitive in today's market. Thus, developing a new approach which could utilize more information from the production process has become an inevitable quality improvement program for each organization. In current study, a fuzzy mean and range control charts were developed to monitor the production process. Fuzzy control charts could handle the uncertainty due to vagueness, ambiguity and/or incomplete information in addition to the inherent uncertainty due to randomness in quality characteristic measurements. The proposed fuzzy control charts were validated through a case study at the chicken nugget production company by collecting data from the factory floor and comparing it to the traditional Shewhart control charts which have been already applied by the factory for monitoring the process. The results reveal that the proposed fuzzy control charts could detect abnormal shifts in the production process more accurately than the traditional Shewhart control charts, as they had used more information from the process. The proposed approach has several benefits for the company by improving the quality and increasing the productivity

Fuzzy based approach for monitoring the mean and range of the products quality

Due to competition in the market, organization must have quality improvement program. Statistical quality control and especially control charts are proven quality improvement techniques. 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. The purpose of this article is to develop a fuzzy Mean and Range (X - R) control charts and monitor the process condition without any transformation techniques (directly). In this approach, observations and control limits are in case of triangular fuzzy numbers. The process condition is determined based on the percentage of area of the sample mean which remains outside the control limits. A numerical example in food industry is presented to illustrate the proposed approach. The result shows that the proposed approach is capable to detect even small shifts in the process quickly without any transformation techniques

Development of fuzzy control charts for monitoring manufacturing process with uncertain and vague observations

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