Expressions For System Reliability Research Articles

Time dependent performance analysis of a Smart Trash bin using state-based Markov model and Reliability approach

In this paper, the authors have developed a quantitative mathematical model to assess the performance of a smart trash bin. This model takes into account six hardware components of the trash bin, including Arduino Uno, ultrasonic sensor, servo motor, switch, battery, jumper wires utilizing Markov modelling and reliability-based approach. The objective of this model is to facilitate timely planning of repair and maintenance activities, ensuring prolonged availability of the smart trash bin after identifying the weakest component/components of the system.The efficient functioning of all components in the smart trash bin is imperative for the timely transmission of the garbage level data to the municipal corporation. To achieve this, the paper focuses on evaluating key reliability metric for smart trash bin system, specifically reliability, unreliability, and Mean time to Failure (MTTF). The modelling approach employs a state-based Markov model, from which Kolmogorov differential equations are derived and subsequently solved using Laplace transformation. After collecting data from organization and experts of the field explicit expression for system reliability, unreliability and MTTF have been obtained.Furthermore, this study includes sensitivity analysis of the system to pinpoint critical components which is switch and servo motor, requiring attention for proper maintenance. The research finding indicates that reliability and MTTF of the system diminish as the failure rate of the components increase under certain conditions.

System Performance Analysis of Sensor Networks for RF Energy Harvesting and Information Transmission

This paper investigates the problem of RF energy harvesting in wireless sensor networks, with the aim of finding a suitable communication protocol by comparing the performance of the system under different protocols. The network is made up of two parts: first, at the beginning of each timeslot, the sensor nodes harvest energy from the base station (BS) and then send packets to the BS using the harvested energy. For the energy-harvesting part of the wireless sensor network, we consider two methods: point-to-point and multi-point-to-point energy harvesting. For each method, we use two independent control protocols, namely head harvesting energy of each timeslot (HHT) and head harvesting energy of dedicated timeslot (HDT). Additionally, for complex channel states, we derive the cumulative distribution function (CDF) of packet transmission time using selective combining (SC) and maximum ratio combining (MRC) techniques. Analytical expressions for system reliability and packet timeout probability are obtained. At the same time, we also utilize the Monte Carlo simulation method to simulate our system and have analyzed both the numerical and simulation solutions. Results show that the performance of the HHT protocol is better than that of the HDT protocol, and the MRC technology outperforms the SC technology for the HHT protocol in terms of the energy-harvesting efficiency coefficient, sensor positions, transmit signal-to-noise ratio (SNR), and length of energy harvesting time.

엔진 유지점검과 정지능력을 고려한 액체로켓 추진시스템의 신뢰도 모형

Purpose: In this paper, we present a reliability model for a liquid rocket propulsion system with the engine out capability.<BR>Methods: Previously, researchers have developed such a reliability model, in which a failure decay function is used to modify time-independent reliability to time-dependent reliability for each engine. In that model, engine reliability at different thrust values was estimated independently, and the check-up time and mission time were fixed. Such a model is not useful for determining the check-up time necessary to achieve the system reliability target. In this paper, we present a system reliability model in terms of the engine check-up time and mission time. We use the cumulative exposure model to relate the lifetime of an engine operating at different thrust values, assuming that the lifetime of each engine follows a general distribution. By using a mixed exponential distribution, we obtain a closed form expression of system reliability and explain how time-independent engine reliability can be transformed to time-dependent engine reliability.<BR>Result: The proposed model is useful for determining the check-up time that provides the target mission reliability.<BR>Conclusion: The reliability of a liquid rocket propulsion system must be expressed explicitly in terms of the engine reliability depending on the check-up time and the mission time if the check-up time must be determined to achieve the system reliability requirement.

Stochastic Multi-phase Modeling and Health Assessment for Systems Based on Degradation Branching Processes

Degradation modeling and health assessment play a critical role in predictive maintenance of engineering systems. In a multi-component system, the degradation of a component may propagate to other components after a random time period, resulting in a multi-phase system-level degradation behavior. Although extensive work has been conducted on system degradation modeling, traditional methods are not adequate to model such degradation and propagation phenomena simultaneously. In this paper, a stochastic multi-phase modeling approach is proposed for such systems based on the degradation branching processes. The statistical properties of general degradation branching processes are analyzed in regards to two common types of system failures. Specially, when each branch of the multi-phase degradation process can be described by a Wiener process, the analytical expressions for system reliability and lifetime distribution are derived after dividing the entire degradation process into multiple phases based on the locations of branching particles. Based on these results, system health assessment can be conducted by incorporating the current degradation state and the importance of each component. Case studies on high-speed train bogie systems and solar panel arrays are provided to demonstrate the effectiveness and practical values of the proposed methods in handling such complex degradation phenomena.

Reliability of n-Cascade Stress-Strength P(X

In this paper, the n-cascade with P(X<Y<Z) is used to find the reliability of stress-strength system, where X and Z are the strengths of a component subjected to stress Y. The n-cascade stress-strength system reliability expression is obtained for four different distributions which are [Exponential Pareto, Inverted Exponential, Exponentiated Invers Rayleigh, Frechet]. For some specific values of the parameters of the distribution, the numerical values of the four different reliabilities have also been computed, provided, and discussed.

Low voltage high current modular DC power supply for solid state RF amplifiers

A low voltage, high current, modular 50 V, 700 A dc power supply has been developed to bias 35 number of 500 W, 505.8 MHz solid state RF amplifiers. This power supply incorporates 7 number of 50 V, 100 A ac-dc power modules, operating in parallel to share the load current. This power supply has two unique attributes namely modular hot swappability and active redundancy. Hot swappable feature incorporated in power modules enables isolation of faulty power modules and facilitates their online replacement without affecting the operation of RF amplifiers and remaining power modules. Active redundancy increases reliability of the power supply significantly. Both these features reduce the down time and increase the availability of the overall system significantly. This paper presents comparison of system reliability of this modular dc power supply with other modular dc power supplies of same output voltage and current rating and having different number of power modules. Suitable mathematical expressions for system reliability of these modular dc power supplies have been evaluated. This power supply also has a digital controller for monitoring the status of 35 number of RF amplifiers and 7 number of power modules as well as controls load current sharing among the power modules. This power supply achieves current THD ≤ 6.2%, input power factor ≥ 0.98, output voltage stability ≤ 0.4% and peak to peak output ripple ≤ 0.2% with overall system reliability and availability approaching near 100%.

Model niezawodności dla systemów typu k-z-n z podziałem obciążenia podlegających uszkodzeniom parametrycznym i katastroficznym, w których zachodzi zależność między obciążeniem pracą a skutkami obciążeń losowych

A component in a k-out-of-n system may experience soft and hard failures resulting from exposure to natural degradation and random shocks. Due to load-sharing characteristics, once a component fails, the surviving components share an increased workload, which increases their own degradation rates. Moreover, under the larger workload, random shocks may cause larger abrupt degradation increments and larger shock sizes. Therefore, the system experiences the dependent workload and shock effects (DWSEs). Such dependence will cause the load-sharing system to fail more easily, though it is often not considered in existing methods. In this paper, to evaluate the system reliability more accurately, we develop a novel reliability model for load-sharing k-out-of-n systems with DWSEs. In the model, the joint probability density function of shock effects to soft and hard failures is developed to describe the DWSEs on a component. To derive an analytical expression of system reliability with load-sharing characteristics and DWSEs, conditional probability density function is used to model the random component failure times. A load-sharing MicroElectro-Mechanical System (MEMS) is then utilized to illustrate the effectiveness of the reliability model

Reliability and Sensitivity Analysis of the Controllable Repair System with Warm Standbys under the Recovery Threshold Policy

Abstract This article performs reliability and sensitivity analyses of a controllable repair system with M operating units, S warm standby units, and an unreliable repair server under the recovery threshold policy. Failure times and service times of an operating unit or a standby unit are assumed to follow exponential distributions. When the repair server normally operates, it is subject to breakdowns; while a breakdown occurs, the repair server requires repair at another repair facility, and the repair of the breakdown server cannot be initiated until there are more than or equal to q failed units. The times to breakdown and repair times of the server are also assumed to be exponentially distributed. A server during a breakdown period can provide partial service with lower service rates. This article derives expressions for system reliability as well as the mean time to failure. The sensitivity analyses of both system performance measures are performed. Finally, some numerical experiments are designed and performed to demonstrate how the system performance measures are affected by the change of each system parameter.

Reliability analysis for a Wiener degradation process model under changing failure thresholds

Wiener degradation processes with fixed failure threshold have recently received extensive applications due to their desirable mathematical properties. However, a system may experience various environments during the overall degradation life cycle. This may lead to abrupt changes of both the failure thresholds and drift parameters due to the fluctuation of endurance of the deterioration system. Motivated by the practical needs of such multi-phase degradation systems, in this paper, a multi-phase degradation model based on the Wiener process is developed to describe the phenomenon of abrupt changes of failure thresholds and drift parameters. Both the two-phase and multi-phase (n ≥ 3) cases are considered under changing failure thresholds and drift parameters in this paper. Analytical expression of system reliability is given for the Wiener process model with two successive different failure thresholds. Meanwhile, a recursive formula is developed to get the analytical expression of system reliability for the Wiener process model with multiple successive different failure thresholds (n ≥ 3). In addition, simulation procedures are carried out to verify the given results. And some numerical examples are presented to illustrate the proposed model.

Complex System Reliability Optimisation: Further Assessment of a Multicriteria Approach

Optimal allocation of reliability to components of a system is one of the several ways of ensuring high system reliability in design. The problem which is typically formulated as single criterion optimisation encounters difficulty when the analytic system reliability expression is intractable usually as a result of complex system configuration. The current work re-examines a novel approach previously developed by the authors which takes a multicriteria view of the problem on the basis of the minimum cut sets of a system, and thus avoids finding the top level system reliability before optimisation. The model and methodology was applied to two complex system reliability allocation problems: a classical one and one associated with electricity transmission. The results were consistent with previously obtained ones by the authors and with the reliability importance of some notable components.

Reliability Analysis and Redundancy Allocation for a One-Shot System Containing Multifunctional Components

Enabling more than one function in a component provides a new cost-effective way to develop a highly reliable system. In this paper, we study the reliability of a one-shot system containing multifunctional components. Such systems have attracted increasing attention in many areas, such as ad hoc sensor networks. We derive the expressions for system reliability and reliability of each function, and formulate a redundancy allocation problem (RAP) with the objective of maximizing system reliability. Unlike constructing a system with single-functional components, the number of copies of a specific function to be included in each multifunctional component (i.e., functional redundancy) needs to be determined as part of the design. Moreover, a start-up strategy for turning on specific functions in these components must be decided prior to system operation. We develop a heuristic algorithm and include it in a two-stage genetic algorithm (GA) to solve the new RAP. We also apply a Tabu search (TS) method for solving such NP-hard problems. Our numerical studies illustrate that the two-stage GA and the TS method are quite effective in searching for high-quality solutions.

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.

Reliability evaluation and analysis of CNC cam shaft grinding machine

Purpose – Reliability assessment does require an effective structural modelling approach for systems, in general and manufacturing systems are no exception. This paper aims to develop it for large manufacturing systems using graph models, a systems approach. Design/methodology/approach – Structural graph models for reliability at various hierarchical levels are developed by considering a CNC cam shaft grinding machine. The system reliability expression is obtained by converting the reliability graphs into equivalent matrices, which helps to evaluate and analyse system. Findings – Using the obtained reliability expressions at various hierarchical levels of the system, it is possible not only to evaluate its reliability from structure point of view but also to identify weak structural elements from reliability point of view. Research limitations/implications – The approach can be extended to include the influence of other parameters, such as human, component and environment, etc., on the system reliability. Practical implications – The approach helps to design and develop manufacturing systems from reliability consideration by assessing their possible alternatives among these. Originality/value – The suggested methodology is useful for reliability evaluation of large and complex manufacturing systems.

Complex System Reliability Optimisation: A Multi-Criteria Approach

The optimal allocation of reliability to the components of complex systems to maximise their reliability is posed as multi-criteria optimisation. The minimum cut-sets leading to series-parallel reduction of such systems were constituted into criteria and their reliability maximised while minimising cost of improving the systems reliability. Consequently, the system reliability expression is made redundant, which simplifies the problem. The resultant nonlinear optimisation model was solved by the Weighted Sum method for the Pareto optimal component reliability values. The model was applied to a life support system. The results show that higher components/ systems reliability can be achieved using the approach.

Reliability and sensitivity analysis of a system with multiple unreliable service stations and standby switching failures

This paper presents the reliability and sensitivity analysis of a system with M primary units, W warm standby units, and R unreliable service stations where warm standby units switching to the primary state might fail. Failure times of primary and warm standby units are assumed to have exponential distributions, and service times of the failed units are exponentially distributed. In addition, breakdown times and repair times of the service stations also follow exponential distributions. Expressions for system reliability, R Y ( t ) , and mean time to system failure, MTTF are derived. Sensitivity analysis, relative sensitivity analysis of the system reliability and the mean time to failure, with respect to system parameters are also investigated.

Reliability and sensitivity analysis of a repairable system with warm standbys and R unreliable service stations

This paper deals with the reliability and sensitivity analysis of a repairable system with M operating units, S warm standby units, and R unreliable service stations. Failure times and service times of operating or standby units are assumed to be exponentially distributed. While the service station is working, it is subject to breakdowns according to a Poisson process. When the station breaks down, it requires repair at a repair facility, where repair times follow the negative exponential distribution. This paper provides the expressions for system reliability, R Y (t), and the mean time to system failure, MTTF. We perform a sensitivity analysis for changes in the reliability characteristics, along with changes in specific values of the system parameters. Sensitivity analysis for the MTTF is also investigated.

AN EFFICIENT MULTI-VARIABLE INVERSION ALGORITHM FOR RELIABILITY EVALUATION OF COMPLEX SYSTEMS USING PATH SETS

Reliability evaluation of a large and complex system is quite an involved and time-consuming process and its state-of-art is far from being called as satisfactory. This is mainly due to the fact that unionizing path sets results in large number of terms in the reliability expression. Thereafter, the process of computing numerical value of system reliability from its expression is a task not free from the build up of round-off errors. The entire process also restricts the use of a low-end PC for computing system reliability of such systems. In this paper, we propose an efficient methodology to evaluate reliability of large and complex systems based on minimal path sets; the path sets enumeration procedure used in this paper generates path sets in lexicographic and increasing order of cardinality — a condition, which is helpful in obtaining sum of disjoint products (SDP) of the system reliability expression in a compact form. Although we make use of the system connection matrix but no complicated matrix operations are performed to obtain the results. The paper further presents an improved multi-variable inversion (MVI) algorithm to evaluate system reliability in a compact form. Our approach offers an extensive reduction in the number of mutually disjoint terms and provides a minimized and compact system reliability expression. The procedure not only results in substantial saving of CPU time but also can be run on a low-end PC. To demonstrate this capability, we solve several problems of varied complexities on a low-end PC and also provide a comparison of our approach with earlier techniques available for the purpose.

Modular operational test plans for inferences on software reliability based on a Markov model

This paper considers the problem of assessing the reliability of a software system that can be decomposed into a finite number of modules. It uses a Markovian model for the transfer of control between modules in order to develop the system reliability expression in terms of the module reliabilities. An operational test procedure is considered in which only the individual modules are tested and the system is considered acceptable if, and only if, no failures are observed. The minimum number of tests required of each module is determined such that the probability of accepting a system whose reliability falls below a specified value R/sub 0/ is less than a specified small fraction /spl beta/. This sample size determination problem is formulated as a two-stage mathematical program and an algorithm is developed for solving this problem. Two examples from the literature are considered to demonstrate the procedure.

Some statistical characteristics of a repairable, standby, human and machine system

This paper presents a model for a two-unit s-identical system with one operating-unit (OU) online and the other, warm standby-unit (SU) human machine system. The failure rates for both the OU and SU (common-cause, human error and hardware failures) are constant, whereas the repair times are arbitrarily distributed for a failed system. Linear ordinary differential equations are used to obtain a general expression for system steady-state availability for failed system by taking the repair time distributions as Gamma. Generalized expressions for system reliability, and time-dependent availability are presented. Graphs demonstrate the impact of human error on system steady-state availability for various distributions, and some physical meaning is given. As time increases, the time-dependent availability decreases for exponential repair time distribution for different values of initial human error rate.

Availability analysis of a repairable standby human-machine system

This paper presents a model representing a two units active and one unit on standby human-machine system with general failed system repair time distribution. In addition, the model takes into consideration the occurrence of common-cause failures. The method of linear ordinary differential equation is presented to obtain general expressions for system steady state availability for failed system repair time distributions such as Gamma, Weibull, lognormal, exponential, and Rayleigh. Generalized expressions for system reliability, time-dependent availability, mean time to failure, and system variance of time to failure are also presented. Selected plots are presented to demonstrate the impact of human error on system steady state availability, reliability, time-dependent availability, and mean time to failure.