Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem

The distribution of chilled water flow rate in terminal unit is an important factor used to evaluate the performance of central air conditioning unit. A prototype of A/C unit has been made, which contains three terminal units with a complete set of accessories (3-way valve, 2-way valve, and sensors) to study the effect of the main parameters, such as total water flow rate and chilled water supply temperature with variable valve opening. In this work, 40 tests were carried out. These tests were in two groups, 20 test for 3-way valve case and 20 test for 2-way valve case. These tests were performed at three levels of valve opening, total water flow rate and water supply temperature according to the design matrices establis

In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using   is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast.

Temperature inside the vehicle cabin is very important to provide comfortable conditions to the car passengers. Temperature inside the cabin will be increased, when the car is left or parked directly under the sunlight. Experimental studies were performed in Baghdad, Iraq (33.3 ^oN, 44.4 ^oE) to investigate the effects of solar radiation on car cabin components (dashboard, steering wheel, seat, and inside air). The test vehicle was oriented to face south to ensure maximum (thermal) sun load on the front windscreen. Six different parking conditions were investigated. A suggested car cover was examined experimentally. The measurements were recorded for clear sky summer days started at 8 A.M. till 5 P.M.

In this paper was discussed the process of compounding two distributions using new compounding procedure which is connect a number of life time distributions ( continuous distribution ) where is the number of these distributions represent random variable distributed according to one of the discrete random distributions . Based on this procedure have been compounding zero – truncated poisson distribution with weibell distribution to produce new life time distribution having three parameter , Advantage of that failure rate function having many cases ( increasing , dicreasing , unimodal , bathtube) , and study the resulting distribution properties such as : expectation , variance , comulative function , reliability function and fa