Process capability assessment for univariate and multivariate non-normal correlated quality characteristics

In today's competitive business and industrial environment, it is becoming more crucial than ever to assess precisely process losses due to non-compliance to customer specifications. To assess these losses, industry is extensively using Process Capability Indices for performance evaluation of their processes. Determination of the performance capability of a stable process using the standard process capability indices such as and requires that the underlying quality characteristics data follow a normal distribution. However it is an undisputed fact that real processes very often produce non-normal quality characteristics data and also these quality characteristics are very often correlated with each other. For such non-normal and correlated multivariate quality characteristics, application of standard capability measures using conventional methods can lead to erroneous results. The research undertaken in this PhD thesis presents several capability assessment methods to estimate more precisely and accurately process performances based on univariate as well as multivariate quality characteristics. The proposed capability assessment methods also take into account the correlation, variance and covariance as well as non-normality issues of the quality characteristics data. A comprehensive review of the existing univariate and multivariate PCI estimations have been provided. We have proposed fitting Burr XII distributions to continuous positively skewed data. The proportion of nonconformance (PNC) for process measurements is then obtained by using Burr XII distribution, rather than through the traditional practice of fitting different distributions to real data. Maximum likelihood method is deployed to improve the accuracy of PCI based on Burr XII distribution. Different numerical methods such as Evolutionary and Simulated Annealing algorithms are deployed to estimate parameters of the fitted Burr XII distribution. We have also introduced new transformation method called Best Root Transformation approach to transform non-normal data to normal data and then apply the traditional PCI method to estimate the proportion of non-conforming data. Another approach which has been introduced in this thesis is to deploy Burr XII cumulative density function for PCI estimation using Cumulative Density Function technique. The proposed approach is in contrast to the approach adopted in the research literature i.e. use of best-fitting density function from known distributions to non-normal data for PCI estimation. The proposed CDF technique has also been extended to estimate process capability for bivariate non-normal quality characteristics data. A new multivariate capability index based on the Generalized Covariance Distance (GCD) is proposed. This novel approach reduces the dimension of multivariate data by transforming correlated variables into univariate ones through a metric function. This approach evaluates process capability for correlated non-normal multivariate quality characteristics. Unlike the Geometric Distance approach, GCD approach takes into account the scaling effect of the variance-covariance matrix and produces a Covariance Distance variable that is based on the Mahanalobis distance. Another novelty introduced in this research is to approximate the distribution of these distances by a Burr XII distribution and then estimate its parameters using numerical search algorithm. It is demonstrates that the proportion of nonconformance (PNC) using proposed method is very close to the actual PNC value

Mathematical model of interactions immune system with Micobacterium tuberculosis

Tuberculosis (TB) remains a public health problem in the world, because of the increasing prevalence and treatment outcomes are less satisfactory. About 3 million people die each year and an estimated one third of the world's population infected with Mycobacterium Tuberculosis (M.tb) is latent. This is apparently related to incomplete understanding of the immune system in infection M.tb. When this has been known that immune responses that play a role in controlling the development of M.tb is Macrophages, T Lymphocytes and Cytokines as mediators. However, how the interaction between the two populations and a variety of cytokines in suppressing the growth of Mycobacterium tuberculosis germ is still unclear. To be able to better understand the dynamics of infection with M tuberculosis host immune response is required of a model.One interesting study on the interaction of the immune system with M.tb mulalui mathematical model approach. Mathematical model is a good tool in understanding the dynamic behavior of a system. With the mediation of mathematical models are expected to know what variables are most responsible for suppressing the growth of Mycobacterium tuberculosis germ that can be a more appropriate approach to treatment and prevention target is to develop a vaccine. This research aims to create dynamic models of interaction between macrophages (Macrophages resting, macrophages activated and macrophages infected), T lymphocytes (CD4 + T cells and T cells CD8 +) and cytokine (IL-2, IL-4, IL-10,IL-12,IFN-dan TNF-) on TB infection in the lung. To see the changes in each variable used parameter values derived from experimental literature. With the understanding that the variable most responsible for defense against Mycobacterium tuberculosis germs, it can be used as the basis for the development of a vaccine or drug delivery targeted so hopefully will improve the management of patients with tuberculosis. Mathematical models used in building Ordinary Differential Equations (ODE) in the form of differential equation systems Non-linear first order, the equation contains the functions used in biological systems such as the Hill function, Monod function, Menten- Kinetic Function. To validate the system used 4th order Runge Kutta method with the help of software in making the program Matlab or Maple to view the behavior and the quantity of cells of each population