IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 17, Issue 3 Ser. II (May – June 2021), PP 33-40 www.iosrjournals.org DOI: 10.9790/5728-1703023340 www.iosrjournals.org 33 | Page Continuous-Time Markov Chain Model of Repairable Machine: Application to Asalaya Sugar Factory Hussein Nassreldeen Eltahir 1 , Khalid Rahamtalla Khedir 2 , Mohammedelameen Eissa Qurashi 3 * 1, 2,3 Sudan University of Science & Technology, Faculty of Science, Department of Statistics, Po Box 407, Khartoum, Sudan Abstract: This study aims at dealing with continuous time Markov chain model application on the fault time of two machines (Mill troup -Boiler), important machine in Asalaya Sugar Factory in season (January/2019– Decmber/2019), which affiliated to Sudanese Sugar Company.The study conduces that the failure time of machines follows Exponential distribution estimation fault distribution.Failure time represent transition matrix in the Continuous time Markov chain. The probability of the machine in operating state is greater than the probability of the machine in a fail state.The high probability of the machine in operating state and the mean time of a machine stay estimated by 4 hours in state (1) (operating state) meanwhile the machine stay in state (0) (fail state) estimated by one hour which indicates the efficiency of the maintenance unit, it is clear that, the probability of available time to repair machines when it fault approximately (0.80), this indicates that the machines has high availability. Keywords: Continuous time Markov chain, Generator Matrix, Repairable Machine, Availability --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 29-05-2021 Date of Acceptance: 12-06-2021 --------------------------------------------------------------------------------------------------------------------------------------- I. Introduction: The use of quantitative and mathematical methods provide an insight into the actual reality of the operational state of machinery and equipment. In addition, they are powerful tools in the final evaluation (Norman, 2012). Maintenance is one of the main factors that help in maintaining machines and prolonging their life. For this reason, most companies strive for maintenance management to have a high degree of planning, organization, and control. Maintenance aims to ensure that all production machinery and equipment are kept in good condition for optimum operational. And stand on the actual operational condition of the machines. There are many quantitative and mathematical models that help the industrial facility to achieve this. The objective of the study is to apply Continuous time Markov chain (CTMC) Model monthly failure time for the season (January/2019–December/2019) of two machines (Mill troup -Boiler) important machine in the Asalaya Sugar Factory, which affiliated to Sudanese Sugar Company to measure the transitions probability machines from an operational state to other the probabilities of the machine can be one of two states state (1) machine operating state and state (0) machine is a fail state. In addition to the availability machines. The data of this study have been collocated for monthly failure time for the season (January/2019– December/2019) of two machines (Mill troup -Boiler), and important machine in the Asalaya Sugar Factory. Based on mechanical faults; the study seeks to achieve the following hypotheses:  The failure time distribution pattern is exponential distribution.  The failure time transition matrices represented the continuous time Markov chain.  The machines have high availability. II. Continuous Time Markov Chain Process of Repairable Machine Continuous Time Markov Chain Process is used to represent and calculate the transition probabilities of the machine from being in operating to being down at specific points in time. In addition to calculating the long run (stationary) probability for a machine to be state operating / state down, the mean sojourn time in state operating / state down. 2.1 The Model Consider the machine has two possible states, state (1) a machine is operating , state (0) a machine is down .Assume a machine status Markov Chain    0 ,  t t X with the state machine taken   1 , 0  S . A transition matrix is defined as: