Evaluation of reliability and availability characteristics of two different systems using linear first order differential equation

Thesis Overview

<p> 1.0 GENERAL INTRODUCTION<br>1.1 Introduction:<br>The role and importance of reliability have been a core of any engineering industry for the<br>last three decades. Reliability is of importance to both manufacturers and consumers. So,<br>the reliability measure is very important, as the improvement of reliability is achieved<br>through quality. While this measure of reliability assumes great importance in industry,<br>there are many situations where continuous failure free performance of the system, though<br>desirable may not be absolutely necessary, Yadavalli and Vanwyk (2012).<br>Several authors have studied a two (or more) similar and dissimilar unit standby redundant<br>system. Haggag (2009a), studied the cost analysis of dissimilar-unit cold-standby system<br>with three state and preventive maintenance using linear first order differential equations.<br>El-sherbeny et al (2009), studied the optimal system for series systems with warm standby<br>components and a repairable service station. Researchers in reliability have shown a keen<br>interest in the analysis of two (or more) component parallel system owing to their practical<br>utility in modern industrial and technological set ups.<br>Two unit warm standby redundant systems have been investigated extensively in the past.<br>The most general model is the one in which both the life time and repair time distributions<br>of the units are arbitrary. However the study of standby system with more than two units,<br>though very important, has received much less attention, possibly because of the built in<br>difficulties in analyzing them. Such systems have been studied only when either the life<br>time or the repair time is exponentially distributed. When both these are general, the<br>21<br>problem appears to be intractable even in the case of cold standby systems. The present<br>contribution is an improvement in the state of art in the sense that a three unit warm<br>standby system is shown to be capable of comprehensive analysis. In particular we show<br>that there are imbedded renewal points that render the analysis possible. Using these<br>imbedded renewal points they obtained the reliability and availability functions,<br>Srinivasan and Subramaniam (2006).<br>But In this research, the reliability and availability characteristics of two different systems<br>are study, where the second system differs from the first system due to the additional<br>feature of preventive maintenance. Each system consisting of one active unit and one warm<br>standby unit with self-reset function and maintenance facility. The failure unit is repaired<br>through self reset or maintenance according to different failure models.<br>1.2: Background to the Study<br>Reliability and availability are very important indices in a substation control protection<br>system. The Station Computer (SC) has important role in the system. Its function is to<br>maintain the central system data base and provide interfaces to the outsider world-locally to<br>station operators through the local Man Machine Interfaces (MMI) subsystem and remotely<br>to system operators and protection engineers through Supervisory Control and Data<br>Acquisition system (SCADA) communication interfaces. So, its reliability directly<br>influences the reliability of Station Computer (SC). Two units warm standby redundancy is<br>taken. Redundancy is one of the ways of improving the reliability of system when the<br>individual unit of the system remains unchanged. Warm standby is essential for two units to<br>switch within the shortest time. So, the active unit and warm standby unit run in different<br>22<br>states, which makes their failure rate different. Commonly, the failure rate of the warm<br>standby unit is smaller than that of the active one. So, compared with a hot standby system,<br>the reliability of the warm standby system is increased. Second, each unit has a self reset<br>function. Each unit performs automatic error detection through self – checking and recovers<br>from some failures, El-Said and El-Hamid (2006).<br>1.3: Reliability Measures<br>Reliability is the analysis of failures, their causes and consequences. It is the most<br>important characteristics of product quality as things have to be working satisfactorily<br>before considering other quality attributes. Usually, specific performance measures can be<br>embedded in to reliability analysis by the fact that if the performance is bellow a certain<br>level, a failure can be said to have occurred.<br>1.3.1: Reliability is the probability that the system will perform its intended function under<br>specified working condition for a specified period of time. Mathematically, the reliability<br>function R(t) is the probability that a system will be successfully operating without failure<br>in the interval from time zero to time t.<br>R(t) = P(T &gt; t), t ≥ o<br>where T is a random variable representing the failure time or time – to failure. The failure<br>probability, or unreliability is then F(t) = 1- R(t), = P(T≤ t) which is known as the<br>distribution function of T.<br>1.3.2: Mean Time to Failure the mean time to failure (MTTF) is defined as the expected<br>value of the lifetime before a failure occurs.<br>23<br>1.3.3: Failure Rate Function and Repair Rate Function<br>The failure rate function, or hazard function, is very important in reliability analysis<br>because it specifies the rate of the system aging.<br>The Failure Rate Function: Is defined as the quantity representing the probability that a<br>device of age t will fail in the small interval from time t, to t + dt. The importance of failure<br>rate function is that it indicates the changing rate in the aging behavior over the life of a<br>population component.<br>Repair Rate Function: Is the expected time to repair the system from failure. This include<br>the time it takes to diagnose the problem, the time it takes to get a repair technician on site,<br>and the time it takes to physically repair the system, Pham (2003).<br>1.3.4: Maintainability and Availability<br>When a system fails to perform satisfactorily, repair is normally carried out to locate and<br>correct the fault. The system is restored to operational effectiveness by making an<br>adjustment or by replacing a component.<br>ï‚· Maintainability: Is defined as the probability that a failed system will be restored to a<br>functioning state within a given period of time when maintenance is performed<br>according to prescribed procedures and resources. Generally, maintainability is the<br>probability of isolating and repairing a fault in a system within a given time.<br>Maintenance personnel have to work with system designers to ensure that the system<br>product can be maintained cost effectively.<br>24<br>ï‚· The Availability Function of a system, denoted by A(t) is defined as the probability<br>that the system is available at time t. Different from the reliability that focuses on a<br>period of time when the system is free of failures, availability concerns at a time<br>point at which the system does not stay at the failed state.<br>Mathematically, A(t) = Pr(system is up or available at time instant t).<br>1.3.5: Mean Time to Failure (MTTF), and Mean Time Between Failure (MTBF) it is<br>important to distinguish between the concepts mean time to failure and mean time between<br>failures (MTBF). The MTTF is the expected time to failure of a component or system. That<br>is, the mean of the time to failure (TTF) for that component or system. The MTBF is the<br>expected time to failure after a failure and repair of the component or system.<br>1.3.6: Preventive Maintenance the maintenance carried out at predetermined intervals or<br>corresponding to prescribed criteria and intended to reduce the probability of failure or the<br>performance degradation of an item. Hoyland and Naws (1994).<br>1.4: Aim and Objectives<br>The main aim of this research work is to investigate and improve upon the existing<br>methodologies for the reliability and availability characteristics of two different systems,<br>where the second system differs from the first system due to the additional feature of<br>preventive maintenance. To achieve the above aim the following objectives are derived.<br>ï‚· To observe the effect of failure rate, repair rate and preventive maintenance on both<br>system, in terms of their MTSF, Steady-State Availability and Profit Function. <br></p>