Some quality characteristics are well defined when treated as response variables and are related to some independent variables. This relationship is called a profile. Parametric models, such as linear models, may be used to model profiles. However, in practical applications due to the complexity of many processes it is not usually possible to model a process using parametric models.In these cas...

  Although control charts are very common to monitoring process changes, they usually do not indicate the real time of the changes. Identifying the real time of the process changes is known as change-point estimation problem. There are a number of change point models in the literature however most of the existing approaches are dedicated to normal processes. In this paper we propose a novel app...

‎Let $R$ be a commutative ring with non-zero identity. ‎We describe all $C_3$‎- ‎and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. ‎Also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎Finally, ‎we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...

Sometimes the quality of a process or product is described by a functional relationship between a response variable and one or more explanatory variables referred to as profile. In most researches in this area the response variable is assumed to be normally distributed; however, occasionally in certain applications, the normality assumption is violated. In these cases the Generalized Linear Mod...

The idea of a finite collection of closed sets having " strongly regular intersection " at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically, we consider the case of two sets, one of which we assume to be suitably " regular " (special cases being convex sets, smooth manifolds, or feasible regions...

This paper addresses the problem of obtaining a consistent estimate (or upper bound) of the covariance matrix when combining two quantities with unknown correlation. The combination is defined linearly with two gains. When the gains are chosen a priori, a family of consistent estimates is presented in the paper. The member in this family having minimal trace is said to be “family-optimal”. When...

The process personnel always seek the opportunity to improve the processes. One of the essential steps for process improvement is to quickly recognize the starting time or the change point of a process disturbance. Different from the traditional normally distributed assumption for a process, this study considers a process which follows a gamma process. In addition, we consider the possibility o...