Standby Unit Research Articles

Setting and Solving of the Game Problem of Confrontation of the Hardware-Redundant Dynamic System with an Attacking Enemy Operating in the Conflict Process in Conditions of Incomplete Information

The game task of confrontation of the attacked hardware-redundant dynamic system with an attacking enemy operating in conditions of incomplete information about the behavior of the attacked enemy in a conflict was posed and solved numerically and analytically. The attacking party aspires to increase the intensity of failures of the components of the attacked system due to its attack resources, up to its total failure. The attacked party, due to the corresponding strategy of redistribution of the reserve units of the hardware-redundant dynamic system between the failed main units at the appropriate instants of time, strives to maximize the probability of a failure-free operation of the attacked system by the end of the confrontation (game) with the attacking enemy. Behavior of the system under attack in the process of a conflict is approximated by the Markov process, while the number of the operable states is equal to the number of the failed functional units, not exceeding the number of the standby units. As a function of the board in the considered game the probability of a failure-free operation of the attacked system is used by the time the game ends. The solution to the game is the vector of the system setup moments after the corresponding failures of the functional units and a set of the reservation vectors corresponding to the instantaneous settings of the attacked system, which maximize the probability of a system failure during a conflict. The differential game model is reduced to a multi-step matrix model with the given probabilities of the states of the attacking enemy. Numerical algorithms for calculation of the reservation vector for the attacked system are presented, which maximize the probability of its trouble-free operation by the end of the game and for solving of the game problem in a form convenient for its implementation on a personal computer.

Optimizing usage and maintenance decisions for k‐out‐of‐n systems of moving assets

AbstractWe consider an integrated usage and maintenance optimization problem for a k‐out‐of‐n system pertaining to a moving asset. The k‐out‐of‐n systems are commonly utilized in practice to increase availability, where n denotes the total number of parallel and identical units and k the number of units required to be active for a functional system. Moving assets such as aircraft, ships, and submarines are subject to different operating modes. Operating modes can dictate not only the number of system units that are needed to be active, but also where the moving asset physically is, and under which environmental conditions it operates. We use the intrinsic age concept to model the degradation process. The intrinsic age is analogous to an intrinsic clock which ticks on a different pace in different operating modes. In our problem setting, the number of active units, degradation rates of active and standby units, maintenance costs, and type of economic dependencies are functions of operating modes. In each operating mode, the decision maker should decide on the set of units to activate (usage decision) and the set of units to maintain (maintenance decision). Since the degradation rate differs for active and standby units, the units to be maintained depend on the units that have been activated, and vice versa. In order to minimize maintenance costs, usage and maintenance decisions should be jointly optimized. We formulate this problem as a Markov decision process and provide some structural properties of the optimal policy. Moreover, we assess the performance of usage policies that are commonly implemented for maritime systems. We show that the cost increase resulting from these policies is up to 27% for realistic settings. Our numerical experiments demonstrate the cases in which joint usage and maintenance optimization is more valuable. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 418–434, 2017

Availability and cost analysis of an engineering system involving subsystems in series configuration

PurposeThe purpose of this paper is to evaluate various reliability measures like availability, reliability, mean time to failure and profit function.Design/methodology/approachThe authors present a novel method for availability analysis of an engineering system incorporating waiting time to repair. The considered system consists of two subsystems, namely, A and B connected in series. The subsystem B has two identical units in standby arrangement. Each unit of the subsystem has two modes, i.e. normal efficiency or failed. The two standby units of the subsystem B are connected by an imperfect switching. The system is analyzed by supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula.FindingsNumerical examples with a way to highlight the important results have been appended at last. Numerical calculation shows that availability and reliability of the system is decreasing with respect to time when failure rates are fixed at different values. Finally, cost analysis of system reveals that the expected profit decreases with increase in service cost.Originality/valueThis paper presents a mathematical model in which an important aspect of switching has been taken into consideration, which is consistent with actual failures of switching by assuming two different types of failure between adjacent transition. It is evaluated with the help of the Gumbel-Hougaard family of copula.

Availability based operational behavior of B-Pan crystallization system in the sugar industry

In this paper, the B-Pan crystallization system in the sugar industry is analyzed that having three subsystems—crystallizer, centrifugal machine and melter. These subsystems are arranged in series. Subsystem ‘centrifugal machine’ has standby unit, subsystem 'crystallizer' has four parallel units and subsystem ‘melter’ has single unit. The time to failure of the subsystems follows negative exponential distribution while repair time distribution is taken as arbitrary. The differential–difference equations of the system model are developed by using supplementary variable technique and solved to get state transition probabilities of B-Pan crystallization system. A particular case is also considered to show the behavior of availability and expected profit of the B-Pan crystallization system in the sugar industry.

Reliability analysis of a warm standby repairable system with two cases of imperfect switching mechanism

This paper studies a warm standby repairable system including two dissimilar units, one repairman and imperfect switching mechanism. Times to failure and times to repair of active and standby units are assumed to be exponentially distributed. Two cases of unreliable switching mechanism are considered. In case one, the failed active unit will be replaced by the available warm standby unit with coverage probability. However, in case two, the switching mechanism is repairable and its failure time and repair time are also exponentially distributed. Using Markov process and Laplace transforms, the explicit expressions of the mean time to failure, MTTF, and the steady state availability of the two systems are derived analytically. Finally, by solving a numerical example, comparison of the two systems are made based on various reliability and availability characteristics. Moreover, sensitivity analyses of the reliability and availability indexes with respect to the model parameters are accomplished.

One-unit repairable systems with active and standby redundancy and fuzzy parameters

PurposeThe purpose of this paper is to propose a procedure to construct the membership functions for a one-unit repairable system, which has both active and standby redundancy. The coverage factor is the same for the operating and standby unit failure.Design/methodology/approachThe α-cut approach is used to extract a family of conventional crisp intervals from the fuzzy repairable system for the desired system characteristics. This can be determined with a set of non-linear parametric programing using the membership functions.FindingsWhen system characteristics are governed by the membership functions, more information is provided to use by management. On the other hand, fuzzy theory is applied for the redundant system; therefore, the results are more useful for designers and practitioners.Originality/valueDifferent from other studies, the authors’ model provides more accurate estimation compared to uncertain environments based on fuzzy theory. The research would help managers and manufactures to make a better decision in order to have the optimal maintenance strategy based on the desired mean time to failure and availability of the systems.

Stochastic Reliability Analysis of Two Identical Cold Standby Units with Geometric Failure & Repair Rates

The present paper is based on the analysis of an two identical unit system wherein initially one unit is in operative state and other is in cold standby and total failure of the unit is via partial failure mode. Single repairman is always available with the system for any repair of failed unit (partially/ completely). Failure/repair time is considered to be a Geometric distribution. Measures of system effectiveness had also been calculated for the system.

Analysis of Open-Phase Conditions in Korean Standard Nuclear Power Plants and Fault Detection Scheme

Because of partial losses of power known as “open-phase faults”, controlled reactor shutdown has occurred in nuclear power plants around world. Depending on transformer wiring and loading, such conditions can be difficult to detect, because phase voltage measurements can appear to be normal. Many of the identified events went undetected for several weeks. These findings were sufficient for staff to conclude that an open phase condition is a credible event having safety significance and must be considered in the electric power system design for nuclear power plants. This paper elaborates the processes and results of the open-phase fault studies on the standard nuclear power plants in Korea. The ETAP unbalanced load flow module is used for the system analysis. The analysis described in this paper has been performed to determine the response of unit auxiliary transformers and standby auxiliary transformers during open-phase conditions to aid in the development of system protection schemes designed to detect such conditions.

Availability improvement for the successive K-out-of-N machining system using standby with multiple working vacations

This analysis deals with the exact availability evaluation of K-out-of-N machining system with multiple working vacations and standby. The repairman can choose multiple working vacations of random length during its dormant time. The system consists of 'O' operating and 'S' standby machines. Each machine type is characterised by its own failures and repairs. The failure of any operating machine affects the system availability. To cope with this situation, we provide the standby support for increasing the availability of the system. Whenever any operating unit fails, it is immediately replaced by a standby unit if available. Moreover, we provide the transient state equations of governing model with the help of state transition diagram. The machine repair problem is analysed theoretically and numerically by using Runge-Kutta method. At last, the conclusions and future work scope are provided.

Reliability analysis and performance optimisation of the serial process in refining system of a sugar plant

This paper deals with the reliability analysis and performance optimisation of a refining system. The refining system is a complex system and comprises of four repairable subsystems connected in series or parallel configurations. Two subsystems namely filter and sulphonation are supported by standby units with perfect switch over devices. The mathematical modelling of the system based on Markov birth-death process is carried out to derive Chapman-Kolmogorov differential equations with the assumption that the failure and repair rate of each subsystem follows exponential distribution. These equations are solved by using an adaptive step-size control Runge-Kutta method to compute the reliability of the system and steady state availability is calculated using normalising condition, initial boundary conditions and recursive method. The performance of the system is optimised with genetic algorithm. It has been found that the subsystem heater is the most critical and has more impact on performance of the system as compare to other subsystems. The results are highly beneficial to the maintenance personnel for the purpose of effective maintenance planning to enhance the overall performance of the refining system.

Separation of Transformers for Class 1E Systems in Nuclear Power Plants

In order to supply electric power to the safety related loads, safety and reliability of onsite power have to be ensured for the safety function performance in nuclear power plants. Even though the existing electric power system of APR1400 meets the requirements of codes regarding Class 1E system, there is a room for improvement in the design margin against the voltage drop and short circuit current. This paper discusses the amount that the voltage drop and short circuit current occur in the existing electric power system of APR1400. Additionally, this paper studies with regard to the improved model that has the extra margin against the high voltage drop and short circuit current by separation of unit auxiliary transformer (UAT) and standby auxiliary transformer (SAT) for the Class 1E loads. The improved model of the electric power system by separation of UAT and SAT has been suggested through this paper. Additionally, effects of reliability and cost caused by the electric power system modification are considered.

Evaluation of the availability and M.T.T.F. of two unit standby redundant complex systems

Evaluation of the availability and M.T.T.F. of two unit standby redundant complex systems

Fault tolerant system with imperfect coverage, reboot and server vacation

This study is concerned with the performance modeling of a fault tolerant system consisting of operating units supported by a combination of warm and cold spares. The on-line as well as warm standby units are subject to failures and are send for the repair to a repair facility having single repairman which is prone to failure. If the failed unit is not detected, the system enters into an unsafe state from which it is cleared by the reboot and recovery action. The server is allowed to go for vacation if there is no failed unit present in the system. Markov model is developed to obtain the transient probabilities associated with the system states. Runge–Kutta method is used to evaluate the system state probabilities and queueing measures. To explore the sensitivity and cost associated with the system, numerical simulation is conducted.

A multiple warm standby δ-shock system with a repairman having multiple vacations

ABSTRACTIn this article, a warm standby n-unit system is studied. The system is operational as long as there is one unit normal. The unit online, which has a lifetime distribution governed by a phase-type distribution, is also attacked by a shock from some external causes. Assume that shocks arrive according to a Poisson process. Whenever an interarrival time of shock is less than a threshold, the unit online fails. The lifetimes of the units in warm standby is exponentially distributed. A repairman who can take multiple vacations repairs the failed units based on the “first-in-first-out” rule. The repair times and the vacation times of repairman are governed by different phase-type distributions. For this system, the Markov process governing the system is constructed. The system is studied in a transient and stationary regime; the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated. A numerical application is performed to illustrate the calculations.

N-policy for a repairable redundant machining system with controlled rates

The present investigation deals with a multi-component machining system operating under N -policy. There is a provision of k type of mixed standbys units and maintenance crew consisting of permanent repairman as well as removable additional repairmen. The life time and repair time of the units are exponentially distributed with interdependent rates. The permanent repairman can start the repair only when N failed units are accumulated in the system. As soon as a unit fails, it is replaced by an available standby unit. In case when all the standby units are exhausted, the machining system starts to function in a degraded mode due to overload. Markov model is developed by constructing the governing transient state equations which are solved by using Runge−Kutta method. Various performance measures viz. queue size distribution, expected number of failed units, cost function, etc. are evaluated. By taking numerical illustration, numerical results are computed and also depicted with the help of graphs and figures.

English

English

On the survival time of a repairable duplex system sustained by a cold standby unit subjected to a priority rule

ABSTRACTWe analyze the survival time of a general duplex system sustained by a cold standby unit subjected to a priority rule. The analysis is based on advanced complex function theory (sectionally holomorphic functions). As an example, we consider Weibull–Gnedenko and Erlang distributions for failure and repair. Several graphs are displaying the survival function.

Reliability Measures Analysis of an Industrial System under Standby Modes and Catastrophic Failure

The objective of this research paper is, to present the reliability measures of a model by representing an industrial system having three subsystems. Two of the subsystems have standby unit while the third one has n units in parallel configuration. The entire system can fail due to a failure in subsystems or due to the catastrophic failure. The system failure and the repair rates are assumed to be constant. Markov and supplementary variable methodologies have been used to achieve the mathematical analysis of this model. Generalized expressions of state probabilities, system availability, reliability, mean time to failure, mean time to repair, cost analysis and sensitivity analysis are developed. Graphs for the resulting expressions have been shown.

Reliability and sensitivity analysis of the controllable repair system with warm standbys and working breakdown

This paper deals with the reliability and sensitivity analysis of a controllable repair system with M operating units, S warm standby units, and an unreliable service station. Failure times and service times of operating units or standby units are assumed to follow exponential distributions. When the service station normally operates, it is subject to breakdowns; while a breakdown occurs, the service station requires repair at the repair facility. The times to breakdown and repair times of the service station are also assumed to be exponentially distributed. During a breakdown period of the service station, the service station is allowed to provide partial service with lower service rate. A practical justification of the system is also provided. This paper develops the expressions for system reliability, RY(t), as well as the mean time to first failure, MTTFF. The sensitivity and relative sensitivity analyses of RY(t) and MTTFF are performed. Finally, some numerical experiments are designed and performed to demonstrate the effects of system performance measures are affected by the change of each system parameter.

Synthesis of tri-generation systems: Technology selection, sizing and redundancy allocation based on operational strategy

Abstract Tri-generation system is a facility which produces heat, power and cooling simultaneously from a single fuel source. In the industry, such system is commonly operated via two strategies; Following Electrical Load (FEL) or Following Thermal Load (FTL). However, these operating strategies may lead to huge amount of energy that is wasted. In this respect, several works have proposed a switching strategy, whereby tri-generation systems would interchange between FEL and FTL modes depending on energy demand. Unfortunately, the design of tri-generation based on this strategy has received limited attention. Besides, tri-generation operations often face challenges in equipment reliability. As tri-generation systems contain a network of interconnected equipment, equipment failures would disrupt the overall performance of a tri-generation system. As such, this work proposes a novel systematic optimisation approach to design a robust tri-generation system which can operate optimally in its operating strategies. In addition, the proposed approach can simultaneously determine type, size and required equipment redundancy (e.g. operating and standby units) of technologies while considering operating strategies in a tri-generation system. A palm biomass-based tri-generation system (BTS) case study is solved to illustrate the proposed approach.