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Testing one-way analysis of variance (ANOVA) is used for experimental data analysis in which there is a continuous response variable and a single independent classification variable. In this paper, we extend one-way ANOVA to a case where observed data are imprecise numbers rather than real numbers. Several fast computable formulas are calculated for symmetric triangular and normal fuzzy data. Similar to the classical testing ANOVA, the total observed variation in the response variable is explained as the sum of observed variation due to the effects of the classification variable and the observed variation due to random error. A real case is given to clarify the proposed method. [ABSTRACT FROM AUTHOR] more...

Process capability indices (PCIs) provide numerical measures on whether a process conforms to the defined manufacturing capability prerequisite. These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. The PCICpcompares the output of a process to the specification limits (SLs) by forming the ratio of the width between the process SLs with the width of the natural tolerance limits which is measured by six process standard deviation units. As another common PCI,Cpmincorporates two variation components which are variation to the process mean and deviation of the process mean from the target. A meaningful generalized version of above PCIs is introduced in this paper which is able to handle in a fuzzy environment. These generalized PCIs are able to measure the capability of a fuzzy-valued process in producing products on the basis of a fuzzy quality. Fast computing formulas for the generalized PCIs are computed for normal and symmetric triangular fuzzy observations, where the fuzzy quality is defined by linear and exponential fuzzy SLs. A practical example is presented to show the performance of proposed indices. [ABSTRACT FROM AUTHOR] more...

Analysis of variance (ANOVA) is an important method in exploratory and confirmatory data analysis. The simplest type of ANOVA is one-way ANOVA for comparison among means of several populations. In this article, we extend one-way ANOVA to a case where observed data are fuzzy observations rather than real numbers. Two real-data examples are given to show the performance of this method. [ABSTRACT FROM AUTHOR] more...

Process capability indices are used to determine whether a production process is capable of producing items within specification tolerance. In practice these indices are estimated using sample data, often with quite small sample sizes. Thus, it is of interest to obtain confidence limits for capability index given a sample estimate. Most of the traditional methods for assessing the capability of manufacturing processes are dealing with crisp quality. In this paper we obtain 100(1 - α)% fuzzy confidence interval for &Ctilde;_p fuzzy process capability index, where instead of precise quality we have two membership functions for specification limits. We present several interpretations for introduced fuzzy confidence interval. Some numerical examples are given to clarify the method. [ABSTRACT FROM AUTHOR] more...