On multivariate Lupa 3 operators
This paper is primarily concerned with multivariate Lupa3 operator. We demonstrate that multivariate Lupa3 operator preserves the properties of the general function of modulus of continuity, Lipschitz's constant and order of a Lipschitz continuous function. Moreover, we obtain monotonicity of the multivariate Lupa3 operator under the condition that the original function is convex. Lastly, two modi ed extensions are constructed.
On multivariate Baskakov operator
Abstract In this paper, we study multivariate Baskakov operator B n , d ( f , x ) . We first show that the operator can retain some properties of the original function f , such as monotony, semi-additivity and Lipschitz condition, etc. Secondly, we discuss the monotony on the sequence of multivariate Baskakov operator B n , d ( f , x ) for n when the function f is convex. Then, we propose, for estimating the rate of approximation, a new modulus of smoothness and prove the modulus to be equivalent to certain K -functional. Finally, with the modulus of smoothness as metric, we establish a strong direct theorem by using a decomposition technique for the operator.
Distribution-free monitoring of univariate processes
We consider statistical process control (SPC) of univariate processes when observed data are not normally distributed. Most existing SPC procedures are based on the normality assumption. In the literature, it has been demonstrated that their performance is unreliable in cases when they are used for monitoring non-normal processes. To overcome this limitation, we propose two SPC control charts for applications when the process data are not normal, and compare them with the traditional CUSUM chart and two recent distribution-free control charts. Some empirical guidelines are provided for practitioners to choose a proper control chart for a specific application with non-normal data.