Cold Standby System Research Articles

Contribution to ECDIS Reliability using Markov Model

An Integrated Bridge System (IBS) contains a fully duplicated Electronic Chart Display and Information System (ECDIS). Although duplication should increase system reliability, reliability and availability are not improved. Proper ECDIS maintenance includes updating both: the information system and the provided chart system. This procedure, in practice, tends to decrease reliability and availability. A Markov ECDIS simulation model is given. A new design concept is presented and proposed. The entire ECDIS system is improved by adding a cold standby system preventing the occurrence of errors due to updating and upgrading of the system device.

English

India was the 7th largest producer of hydroelectric power in 2008 after Norway: 114 TWh and 3.5% the world total in 2008.The potential for hydroelectric power in India is one of the greatest in the world. India is endowed with economically exploitable and viable hydro potential assessed to be about 84,000 MW at 60% load factor. In addition, 6,780 MW in terms of installed capacity from Small, Mini, and Micro Hydel schemes have been assessed. Also, 56 sites for pumped storage schemes with an aggregate installed capacity of 94,000 MW have been identified. It is the most widely used form of renewable energy. India is blessed with immense amount of hydro-electric potential and ranks 5th in terms of exploitable hydro-potential on global scenario. The present installed capacity is approximately 39,788.40 MW which is 17.39% of total electricity generation in India. The public sector has a predominant share of 97% in this sector. Water plays an important and pivotal role in producing hydroelectric power. Non-availability of water results failure to produce hydroelectric power. Reliability is a measure of how well a system performs or meets its design requirements. It is hence the prime concern of all scientists and engineers engaged in developing such a system.. In this paper we have taken two types of failures (1) FNAWnon- availability of water resulting failure to produce Hydroelectric Power (2) FHA-failure due to High acoustics When the main unit fails due to High Acoustics then cold standby system becomes operative . High acoustics cannot occur simultaneously in both the units and after failure the unit undergoes very costly repair facility immediately. Applying the regenerative point technique with renewal process theory the various reliability parameters MTSF, Availability, Busy period, Benefit-Function analysis have been evaluated.

Semi Markov Approach for Asymptotic Performance Analysis of a Standby System with Server Failure

this paper the asymptotic performance of a cold standby system with two identical units is analyzed. When a unit fails it is inspected by a server to check the feasibility of repair or replacement. If repair is not feasible, unit is replaced by new. The server is subjected to failure while performing its job. The system model is developed using semi-Markov approach of Markov processes. The regenerative point technique is used to derive expressions for various measures of system performance. The random variables associated with the system (failure time, inspection time, repair time, treatment time) are assumed to follow arbitrary distribution with different probability density functions. A numerical study is also presented to demonstrate the practical importance of the research.

Energy consumption modelling and optimisation in heterogeneous cold-standby systems

In a 1-out-of-n: G cold-standby system, one component is online and working with the remaining (n – 1) components being unpowered and waiting in the standby mode. The system fails when all the components have failed. In the case of non-identical system components, the sequence of putting the cold-standby components into operation can affect the system energy consumption greatly. Therefore, in this paper, we consider the optimal standby element sequencing (OSES) problem for the 1-out-of-n: G heterogeneous cold-standby systems with the objective to minimise the expected total system energy consumption. An analytical method is first proposed for obtaining approximate estimates of the total energy consumption of the considered cold-standby system. The method also provides a solution for evaluating the reliability of the 1-out-of-n: G heterogeneous cold-standby systems without the limitation on the type of time-to-failure distributions. Based on the proposed energy consumption analysis method, the OSES problem is solved. The brute force approach is used for obtaining the optimal initiation sequence for systems with a small number of standby units; an optimisation methodology based on genetic algorithm is implemented for systems with a relatively large number of standby units. Application of the proposed methodology is illustrated through several case studies.

Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. When failures occur, the repair of both component 1 and component 2 are not ‘as good as new’. The consecutive operating times of component 1 after repair constitute a decreasing geometric process, while the repair times of component 1 are independent and identically distributed. For component 2, its failure is rectified by minimal repair, and the repair time is negligible. Component 1 has priority in use when both components are good. The replacement policy N is based on the failure number of component 1. Under policy N, we derive the explicit expression of the long-run average cost rate C(N) as well as the average number of repairs of component 2 before the system replaced. The optimal replacement policy N*, which minimises the long-run average cost rate C(N), is obtained theoretically. If the failure rate r(t) of component 2 is increasing, the existence and uniqueness of the optimal policy N* is also proved. Finally, a numerical example is given to validate the developed theoretical model. Some sensitivity analyses are provided to show the influence of some parameters, such as the costs for replacement and repair, and the parameters of the lifetime and repair time distributions of both components, to the optimal replacement policy N* and corresponding average cost rate C(N*).

English

Present paper investigates a two-unit cold standby system with three accidental effects. On the failure of a unit, a repairman comes to repair it. During its repair, an accident may take place which may or may not affect the repairman. If it affects, it may be minor or major. Two models have been discussed. In Model 1, it is assumed that when the repairman gets minor injury with an accident, he goes for treatment/rest for some time. After recovery, he comes back and resumes the repair. If major injury takes place, another repairman is called to complete the repair. In Model 2, it is assumed that whenever minor or major accident takes place, another repairman is called. In both the models, it is assumed that after accident the rest of the repair is done with more attention so that no further accident takes place. Various measures of the system effectiveness are obtained by making use of semi-Markov processes and regenerative point technique. Study through graphs is also made.

A Standby System with Priority to Repair over Preventive Maintenance

A cold standby system of two identical units is analyzed stochastically under priority in repair disciplines. Unit has a constant failure from normal mode. There is a single server who visits the system immediately to carry out repair activities. Server conducts preventive maintenance of the unit after a pre-specific time‘t’ of operation. However, repair of the unit is done by the server at its failure. Priority is given to repair of one unit over preventive maintenance of the other unit. The random variables associated with different rates are statistically independent. The failure time and time by which unit goes for preventive maintenance follow exponential distribution while the distributions of maintenance and repair times are taken as arbitrary with different probability density functions. The expressions for several reliability measures of the system are derived using semi-Markov process and regenerative point technique. Graphs are drawn to depict the behavior of MTSF, availability and profit function for particular values of various parameters and costs.

Optimal component loading in 1-out-of-N cold standby systems

This paper considers the optimal choice of productivity (load) of components in 1-out-of-N non-repairable cold standby systems. It is assumed that each system component can function at different levels of productivity (load) and that the life time acceleration factor as well as operational and replacement costs of each component are affected by its productivity. We present a model for evaluating the standby system reliability and expected mission cost. Furthermore, we formulate and solve the optimal load distribution problems in which the mission cost is minimized subject to system reliability constraint. Both fixed and variable sequences of component initiation are considered. Illustrative examples are provided.

Minimum Mission Cost Cold-Standby Sequencing in Non-Repairable Multi-Phase Systems

This paper considers the optimal cold standby element sequencing problem (SESP) for 1-out-of- n: G heterogeneous non-repairable cold-standby systems that accomplish multi-phase missions. Given a fixed set of element choices, the objective of the optimal system design is to select the initiation sequence of the system elements so as to minimize the expected mission cost while providing a desired level of system reliability. It is assumed that during different mission phases the elements are exposed to different stresses, which affects their time-to-failure distributions. The startup and exploitation costs of system elements are also phase dependent. We suggest an algorithm for evaluating the mission reliability and expected mission cost based on a discrete approximation of time-to-failure distributions of the system elements. A genetic algorithm is used as an optimization tool for solving the formulated SESP for multi-phase cold-standby systems. Examples are given to illustrate the considered problem and the proposed solution methodology.

Analysis of a Cold Standby System with an Unreliable Repair Facility and Vacation under Poisson Shocks

This paper analyzes the reliability of a cold standby system with an unreliable repair facility and one repairman who can take multi-vacation. The system can fail due to intrinsic or external factors such as shocks. The shocks arrive according to a Poisson process. Whenever the magnitude of a shock is larger than a pre-specified threshold of the operating component, the operating component fails. The paper assumes that the life of facility is subject to the exponential distribution, and the other distributions are general continuous. By using the geometric process theory, the supplementary variable method and Laplace transform tool, availability and reliability of the system and other reliability indices are obtained.

Bayesian estimation of reliability indexes for cold standby system under general progressive Type II censored data

Purpose – This paper aims to deal with the estimation of the empirical Bayesian exact confidence limits of reliability indexes of a cold standby series system with (n+k−1) units under the general progressive Type II censoring scheme. Design/methodology/approach – Assuming that the lifetime of each unit in the system is identical and independent random variable with exponential distribution, the exact confidence limits of the reliability indexes are derived by using an empirical Bayes approach when an exponential prior distribution of the failure rate parameter is considered. The accuracy of these confidence limits is examined in terms of their coverage probabilities by means of Monte-Carlo simulations. Findings – The simulation results show that accuracy of exact confidence limits of reliability indexes of a cold standby series system is efficient. Therefore, this approach is good enough to use for reliability practitioners in order to improve the system reliability. Practical implications – When items are costly, the general progressive Type II censoring scheme is used to reduce the total test time and the associated cost of an experiment. The proposed method provides the means to estimate the exact confidence limits of reliability indexes of the proposed cold standby series system under this scheme. Originality/value – The application of the proposed technique will help the reliability engineers/managers/system engineers in various industrial and other setups where a cold standby series system is widely used.

Mathematical Modeling Approach to Analyzing Mean Time to System Failure of Two Unit Cold Standby System with A Supporting Device and Repairable Service Station

This paper studies the mean time to system failure (MTSF) of two unit cold standby system operating with the help of a standby external supporting device. A repairable service station is set aside to repair any failed unit. The system is analyzed using first order linear differential equation to develop the explicit expression for mean time to system failure. Special cases such as the cold standby system with a supporting device and repairable standby repairable service stations, and the cold standby system with a supporting device and a repairable service station are treated. Some numerical experiments are conducted in order to illustrate the effects of failure and repair rates on mean time to system failure. Furthermore, we compare the mean time to system failure of the systems under study and found that the MTSF of two cold standby systems with standby supporting device and a repairable service station is better.

Reliability Analysis of a Cold Standby System with Imperfect Repair and under Poisson Shocks

This paper considers the reliability analysis of a two-component cold standby system with a repairman who may have vacation. The system may fail due to intrinsic factors like aging or deteriorating, or external factors such as Poisson shocks. The arrival time of the shocks follows a Poisson process with the intensityλ>0. Whenever the magnitude of a shock is larger than the prespecified threshold of the operating component, the operating component will fail. The paper assumes that the intrinsic lifetime and the repair time on the component are an extended Poisson process, the magnitude of the shock and the threshold of the operating component are nonnegative random variables, and the vacation time of the repairman obeys the general continuous probability distribution. By using the vector Markov process theory, the supplementary variable method, Laplace transform, and Tauberian theory, the paper derives a number of reliability indices: system availability, system reliability, the rate of occurrence of the system failure, and the mean time to the first failure of the system. Finally, a numerical example is given to validate the derived indices.

Reliability Analysis of Random Fuzzy Unrepairable Systems

The lifetimes of components in unrepairable systems are considered as random fuzzy variables since randomness and fuzziness are often merged with each other. Then we establish the fundamental mathematical models of random fuzzy unrepairable systems, including series systems, parallel systems, series-parallel systems, parallel-series systems, and cold standby systems with absolutely reliable conversion switches. Furthermore, the expressions of reliability and mean time to failure (MTTF) are given for the above five random fuzzy unrepairable systems, respectively. Finally, numerical examples are given to show the application in a lighting lamp system and a hi-fi system.

Comparative analysis of some reliability characteristics between two dissimilar redundant systems with replacement at common cause failure

In this paper, probabilistic models for two dissimilar redundant systems with replacement at each common cause failure have been developed to analyze and compare some reliability characteristics. Two configurations are studied under the assumption that each system is replaced at the occurrence of common cause failure. Configuration I is a 3-out-of-4 cold standby system, while configuration II is 3-out-of-5 cold standby system. Explicit expressions for mean time to system failure (MTSF), steady-state availability, busy period and profit function for the three models are analyzed using Kolmogorov’s forward equations method. Comparisons are performed for specific values of system parameters. Furthermore, we compare these reliability characteristics for the two configurations and find that configuration II is more reliable and efficient than configuration I.

RELIABILITY MEASURES OF A COLD STANDBY SYSTEM WITH PREVENTIVE MAINTENANCE AND REPAIR

The purpose of the present study is to determine reliability measures of a two-unit cold standby system with preventive maintenance and repair. The units are identical in nature subject to constant failure from normal mode. Preventive maintenance of the operative unit is carried out after a pre-specific time "t" up to which no failure occurs. However, repair of the unit is done at its failure. The unit works as new after repair and preventive maintenance. The switch devices are perfect. The distributions of failure time and the time by which unit undergoes for preventive maintenance are taken as negative exponential while that of preventive maintenance and repair times are assumed as arbitrary with different probability density functions. The random variables associated with failure, preventive maintenance and repair times are statistically independent. The semi-Markov process and regenerative point technique are adopted to derive the expressions for system performance measures in steady state. The graphical behavior of MTSF, availability and profit function have been observed with respect to preventive maintenance rate for particular values of other parameters and costs.

Sequencing Optimization in k-out-of-n Cold-Standby Systems Considering Mission Cost

The k-out-of-n: G heterogeneous cold-standby system structure is a widely used fault-tolerant system design method, where the sequence in which the different system elements are initiated can greatly affect the system reliability and mission cost. This paper considers the optimal standby element sequencing problem (SESP) for such systems. Given the desired cold-standby redundancy level and fixed set of element choices, the objective of the optimal system design is to select the initiation sequence of the system elements so as to minimize the expected system mission cost while meeting a certain level of system reliability constraint. Based on a discrete approximation of time-to-failure distributions of the system elements, the system reliability and expected mission cost are evaluated simultaneously using a numerical method. A genetic algorithm is used as an optimization tool for solving the formulated SESP problem for k-out-of-n: G heterogeneous cold-standby systems. Examples are given to illustrate the considered problem and the proposed solution methodology.

A preventive maintenance policy for a standby system subject to internal failures and external shocks with loss of units

In many situations, serious damage and considerable financial losses are caused by non-repairable failures of a system. Redundant systems and maintenance policies are commonly employed to improve reliability. This paper is focused on the modelling of a complex cold standby system by analysing the effectiveness and costs of preventive maintenance, always in an algorithmic form. The online unit of the system is subject to wear failures and external shocks. The online unit can go through an indeterminate number of degradation levels before failure. This one is observed when inspections occur. Inspections are performed at random intervals, and when one takes place, the unit is taken to the preventive maintenance facility if it is necessary. The preventive maintenance time and cost is different depending on the degradation level observed. If only one unit is performing, a minimal maintenance policy is adopted in order to optimise system behaviour. Reliability measures such as the conditional probability of failure are worked out in a well-structured and algebraic form in transient and stationary regimes by using algorithmic methods. The stationary distribution is calculated using matrix analytic methods, and rewards are included in the model. An optimisation example shows the versatility of the model presented.

A novel optimal preventive maintenance policy for a cold standby system based on semi-Markov theory

A novel optimal preventive maintenance policy for a cold standby system consisting of two components and a repairman is described herein. The repairman is to be responsible for repairing either failed component and maintaining the working components under certain guidelines. To model the operational process of the system, some reasonable assumptions are made and all times involved in the assumptions are considered to be arbitrary and independent. Under these assumptions, all system states and transition probabilities between them are analyzed based on a semi-Markov theory and a regenerative point technique. Markov renewal equations are constructed with the convolution of the cumulative distribution function of system time in each state and corresponding transition probability. By using the Laplace transform to solve these equations, the mean time from the initial state to system failure is derived. The optimal preventive maintenance policy that will provide the optimal preventive maintenance cycle is identified by maximizing the mean time from the initial state to system failure, and is determined in the form of a theorem. Finally, a numerical example and simulation experiments are shown which validated the effectiveness of the policy.

A Bivariate Replacement Policy for a Cold Standby System Under Poisson Shocks

SYNOPTIC ABSTRACT This study considers a repair-replacement problem for a repairable cold standby system that is composed of two similar components with preventive maintenance. The system may fail because of intrinsic or extrinsic factors such as shocks. The shocks arrive according to a Poisson process. Whenever the magnitude of a shock exceeds a prespecified threshold of the operating component, the operating component fails. We assume that the intrinsic lifetime, the threshold, and the repair time of the operating component are geometric processes. A bivariate repair-replacement policy ( T,N) is adopted for the system, where T is the interval length between preventive maintenances and N is the number of failures of component 1. The explicit expression of the expected long-run cost-per-unit time is derived and the corresponding optimal bivariate policy ( T,N) can be determined analytically or numerically. Finally, three numerical examples are given to validate the theoretical results of the proposed model.