Statistical process control methods for monitoring processes with univariate ormultivariate measurements are used widely when the quality variables fit to known probabilitydistributions. Some processes, however, are better characterized by a profile or a function of qualityvariables. For each profile, it is assumed that a collection of data on the response variable along withthe values of the c...

Multivariate receptor modeling is used to estimate profiles and contributions of pollution sources from concentrations of pollutants such as particulate matter in the air. The majority of previous approaches to multivariate receptor modeling assume pollution source profiles are constant through time. In an effort to relax this assumption, this article uses the Dirichlet distribution in a dynami...

In many circumstances, the quality of a process or product is best characterized by a given mathematical function between a response variable and one or more explanatory variables that is typically referred to as profile. There are some investigations to monitor autocorrelated linear and nonlinear profiles in recent years. In the present paper, we use the linear mixed models to account autocorr...

Let V and W be two real vector spaces and let &sim be a relation on both V and W. A linear function T : V → W is said to be a linear preserver (respectively strong linear preserver) of &sim if Tx &sim Ty whenever x &sim y (respectively Tx &sim Ty if and only if x &sim y). In this paper we characterize all linear functions T : M_{n,m} → M_{n,k} which preserve or strongly preserve multivariate an...

In medical research, it is rare that a single variable is sufficient to represent all relevant aspects of epidemiological risk, genomic activity, adverse events, or clinical response. Since biological systems tend to be neither linear, nor hierarchical in nature, the assumptions of traditional multivariate statistical methods based on the linear model can often not be justified on theoretical g...