Comparison of change-points in multivariate statistical process control using the performance of Lapage-type (nonparametric)

The inability of the Shewhart‟s, the EWMA, and the CUSUM, Hotelling‟s T2 and many other control charts to indicate the time of shift poses great problems in production, Medicine, etc. To overcome the problems the need to identify the period of change (shift) in the process becomes inevitable. The study used Lapage-type Change-point (LCP) to detect the simultaneous shift in both mean and variance. In the study we compare the performance of generalized likelihood ratio change-point (GLRCP) a parametric-base with our proposed method (LCP) at different varying start-ups using real life data. We run the data on Normal, Laplace and Lognormal distributions and also Average Run Length (ARL0) to assess the performance of the methods. Evaluating in-control ARLs (IC-ARLs) for each of the methods at change-point 250 and ARL0 500 indicates the same performance irrespective of the start-up value; LCP and GLR methods have rather a similar performance IC-ARLs at change-point 50 and change-point 100 under the normality assumptions, but under non-normal distributions, LCP has substantially higher IC-ARLs compared to GLRCP at 20. The LCP outperformed the GLRCP when applied to children bronchial pneumonia status. We therefore recommend that new method be used in short-run situations and also when underlying distributions are usually unknown

Analyzing the transmission dynamics of tuberculosis in Kaduna Metropolis, Nigeria

A mathematical model for the transmission dynamics of tuberculosis in Kaduna metropolis, is formulated and analysed. For the prevalence of the disease, the model was considered in proportions of susceptible, exposed, infectious and recovered compartments. The disease-free equilibrium (DFE) and Endemic Equilibrium (EE) states of the model in proportions were obtained and DFE state was used to compute the basic reproduction number 0, as important threshold whose values allow to establish whether an infection will spread in a population or not. The stability analysis shows that the disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than unity using Routh – Hurwitz stability criterion and Lyapunov function respectively. It is further proved using Routh-Hurwitz that the endemic equilibrium state is locally asymptotically stable whenever the basic reproduction number is greater than unity. The computed results of the basic reproduction number 0 estimated to be 1.0623, as well as the stability analysis revealed that tuberculosis infection will remain endemic (persist) in Kaduna metropolis. Furthermore, effective control measures such as expanded and regular immunization campaign will decrease the infection burden

The trade-off between the PLSR and PCR methods for modeling data with collinear structure

This paper investigates the partial least squares regression (PLSR) and principal component regression (PCR) methods as versatile alternative regression techniques when the use of the ordinary least squares method breaks down. Emphasis is more on the situation where the predictor variables are evidently correlated. Data sets with Gaussian non-orthogonal predictor variables were simulated at different sample sizes ranging from 20 to 1000 to examine the performance of the two regression types under varying situations. The data were randomly partitioned into training and test sets with both PLSR and PCR models constructed on the training sets while their performances were evaluated on the test sets using themean square error of predictions and other indices. At each fit of the models, the leave-one-out cross-validation technique was employed to enhance the efficiency and stability of the fitted models. Results from the simulation studies revealed the goodness of the two regression methods but at varying degrees of accuracy. More importantly, it is evident from the results that though, both the PLSR and PCR techniques yielded good regression models, the PLSRtechniqueis consistently more efficient on the test datain terms of good predictions than the PCR method irrespective of sample sizes. Also in terms of model parsimony, the PLSR technique yielded efficient regression models with relatively fewer latent components than the PCR method. Data sets on the performance of M.Sc. graduates from the Department of Statistics, University of Ilorin, Nigeria during the 2012 academic session were used to validate the results from the Monte Carlo studies