Theory of Approximation and Applications
Volume:13 Issue: 2, Summer and Autumn 2019

Control charts are one of the most important tools in statistical process control that lead to improve quality processes and ensure required quality levels. In traditional control charts, all data should be exactly known, whereas there are many quality characteristics that cannot be expressed in numerical scale, such as characteristics for appearance, softness, and color. Fuzzy sets theory is a powerful mathematical approach to analyze uncertainty, ambiguous and incomplete that can linguistically define data in these situations. Fuzzy control charts have been extended by converting the fuzzy sets associated with linguistic or uncertain values into scalars regarded as representative values. In this paper, we study two different approaches to construct X ̅ control chart, when the observations are fuzzy number. Two methods of defuzzification for calculating the value representing sample means and for determining the control chart limits are presented. In the second approach α-cut control chart for variable are developed using upper control limits and lower control limits. The article also presents a fuzzy decision for in control or out of control of the process, in which membership degrees of in and out of control states of process mean is computed.

This paper is concerned with a technique for solving Volterra integro-dierential equationsin the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernelmethod, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series. An iterative method is given toobtain the approximate solution. The convergence analysis is established theoretically. Theapplicability of the iterative method is demonstrated by testing some various examples.