An Extended Lindley Poisson Distribution with Applications
Mavis Pararai, Gayan Warahena-Liyanage, Broderick O. Oluyede
Abstract: The Extended Lindley Poisson (ELP) distribution which is an extension of the extended Lindley distribution  is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density, hazard rate functions, moments, Bonferroni and Lorenz curves are explored. Entropy measures and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and a simulation study is conducted to investigate the performance of the maximum likelihood estimates. Finally, we present applications of the model with a real data set to illustrate the usefulness of the proposed distribution.
Keywords: Lindley distribution, Lindley Poisson distribution, Lifetime data, Maximum likelihood estimation.
Pages: 167 – 198 | Full PDF Paper
Optimal Control Problems of Systems Governed by Elliptic Operators of Infinite Order with Pointwise Control Constrants
S. A. El-Zahaby and Samira El-Tamimy
Abstract: In this paper, we obtain the necessary and sufficient optimality conditions for elliptic control problem with pointwise control constraints generated by elliptic operators infinite order with finite dimensional and discussion of pointwise optimality conditions.
Keywords: Optimal Control of PDE, Infinite order operator, Pointwise control, Constrants.
Pages: 199 – 212 | Full PDF Paper
Response Surface Methodology for Process Monitoring of Soft Drinks: A Case of Delta Beverages in Zimbabwe
Edwin Rupi and Romeo Mawonike
Abstract: Experimentation plays a crucial role in the manufacturing industry. Observing and gathering information about a process helps define how an input variable transforms into a response variable of particular interest to the company. We applied both the first-order and second-order types of Response Surface Methodology (RSM) to analyze the total quantity of Sparkling Beverages produced, revenue collected and the cost of raw materials. A model for minimizing the variability in the monthly quantities of the Sparkling Beverages was developed. In addition a discussion of a Univariate Statistical process control (USPC) scheme based on general linear profile monitoring of process quality was done. Phase I and II linear profile monitoring schemes were discussed in monitoring the slope and intercepts of the profiles. The control scheme helped to identify out of control profiles and hence the in-control process in the sparkling beverages business. The method of Steepest Ascend was useful in building up a model for maximizing the total quantity of sparkling beverages produced with optimal settings for the revenue and cost of raw materials. A Modified Central Composite Design was used to find operating conditions that minimized the variability in the volumes of sparkling beverages. In addition linear profile monitoring procedures were applied to detect shifts in the slope, intercept and error variance for the volumes of sparkling beverages considering the revenue and cost of raw materials.
Keywords: Response Surface Methodology, steepest ascent and steepest decent, Design of Experiments and linear profiles.
Pages: 213 – 233 | Full PDF Paper