Evaluation of Reliability and Availability Characteristics of Two Different Systems Using Linear First Order Differential Equation
Chapter One
Aim and Objectives
The main aim of this research work is to investigate and improve upon the existing methodologies for the reliability and availability characteristics of two different systems, where the second system differs from the first system due to the additional feature of preventive maintenance. To achieve the above aim the following objectives are derived.
- To observe the effect of failure rate, repair rate and preventive maintenance on both system, in terms of their MTSF, Steady-State Availability and Profit
- To evaluate the MTSF, Steady-State Availability and Profit Function of the two systems theoretically and graphically and to also identify which originate better reliability and availability, due to the effect of preventive
- To determine the busy period of the two systems.
CHAPTER TWO
LITERATURE REVIEW
Redundancy plays an important role in enhancing system reliability. Which redundancy has been analyzed for many difference system structures. One of the commonly used forms of the redundancy is the standby redundancy. Standby systems often find applications in various industrial and other set ups. In standby redundant system, some additional paths are created for proper functioning of the system. Standby unit is a support to increase the reliability of the system.
In practice, system do not always fail with major breakdown, it is developed that various mathematical models consisting of two types of failure: major and minor. A maintenance policy that suits a system presenting two types of failure represented by many earlier researchers revealed that minor failures are removed by a minor repair that brings the system back to the operating condition. A major repair is restored the system as good as new,Agarwal et al (2010).
Relationship between Availability, Reliability and Maintainability
Availability: Is defined as the probability that the system is operating properly when it is requested for use. In other words, availability is the probability that a system is not failed or undergoing a repair action when it needs to be used. At first glance, it might seem that if a system has a high availability then it should also have a high reliability. Reliability on the other hand represents the probability of components, parts and system to perform their required functions for a desired period of time without failure in specified environments with a desired confidence. Reliability, in it self does not account for any repair action that may take place. Reliability account for the time that it will take component, part or system to fail while it is operating. It does not reflect how long it will take to get the unit under repair back in to working condition. As stated, availability represents the probability that the system is capable of conducting its required function when it is called upon given that it is not failed or undergoing a repair action. Therefore not only availability a function of reliability, but it is also a function of maintainability, Liao et al (2006).
Availability Classification
Availability is classified by Nelson (1982) as follows:
- Point Availability: Point or instantaneous availability is the probability that a system (component) will be operational at any random time
- Mean Availability: The mean availability is the proportion of time during a mission or time-period that the system is available for use. It represents the mean value of the instantaneous availability function over the period (0,T).
- Steady State Availability: The steady state availability of the system is the limit of the instantaneous availability function as time approaches infinity. The instantaneous availability function approaches the steady value very closely at time approximate to four times the
- Operational Availability: Is a measure of availability that indicates all the experienced sources of downtime, such as administrative downtime, logistic downtime etc,Nelson,(1982).
CHAPTER THREE
RESEARCH METHODOLOGY
Introduction
This research presents reliability and availability analysis of two different systems. Using linear first order differential equations, the second system differs from the first system due to the additional feature of preventive maintenance. Reliability and Availability analysis of system having one active unit and one warm standby unit with self – reset function and one maintenance facility is presented. The failure unit is repaired through self-reset or maintenance according to different failure models. We derived the Mean Time to System Failure (MTSF), Steady State Availability, Busy Period as well as profit function are derived and perform evaluations theoretically and graphically to study the effect of preventive maintenance on system performance.
Model Description and Assumptions
- The system consists of one active unit and one warm standby unit. When the active unit fails, the warm standby unit becomes active without a time delay. One failed unit resets or waits for maintenance and after that it becomes the warm standby unit of the system. When two units fail and need maintenance, the system is in failed state. Only after repairs of two units are completed, will the system start to run again.
- All failure rates are constant. There are two kinds of failure. One causes the self- reset of the failed unit the other needs maintenance by a
- All failures are statistically
CHAPTER FOUR
RESULT AND DISCUSSION
Introduction
This chapter describes the result obtained from chapter three by using MATLAB. It shows that the result of the Mean – Time to System Failure, Steady- State Availability, Profit Function and Busy Period by the use of MATLAB.
CHAPTER FIVE
SUMMARY AND CONCLUSSION
:Summary
This chapter summarizes the work done in the research. The research is a study of reliability and availability characteristics of two different system using system of linear fist order ordinary differential equation. Two systems were considered, where the second system differs from the first system due to addition feature of preventive maintenance. Each system consisting of one active unit and one warn stand-by unit with self reset function and maintenance facility. MTSF, Steady-State Availability, Busy Period Analysis and Profit Function were found by the use of MATLAB.
Conclusion
I this study the performance of two systems were evaluated using Linear First Order Differential Equation. Where the second system differs from the first system due to the additional feature of preventive maintenance. The result shows that increase in failure rate lead to the decrease in MTSF, Steady State Availability and Profit Function of figure 4.1,
4.2 and 4.3. Also increase in repair rate lead to the increase in MTSF, Steady State Availability and Profit Function of figure 4.4, 4.5 and 4.6 then, it was observing that second system has better reliability due to the additional feature of preventive maintenance.
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