Two-unit System Research Articles

An integrated quality and maintenance model for two-unit series systems

Statistical process monitoring and maintenance are two major concepts to increase system reliability and conforming products. To simplify mathematical modeling, the most of existing researches in the literature suffer from three significant disadvantages: (1) statistical process monitoring and maintenance often have been implemented on the single unit systems, in spite of the fact that most of real production processes consists of multiple units; (2) they apply control charts with fixed parameters that are slow in detecting small and moderate shifts; and (3) they design control charts by minimizing the quality cost ignoring statistical properties that decreases extremely the power of control chart. To overcome these drawbacks, this research integrates the economic-statistical design of a VP-Shewhart chart with condition-based maintenance for two-unit series systems. The particle swarm optimization algorithm is applied to minimize the expected total cost per time unit subject to specific statistical constraints. Eventually, the cost savings from monitoring the system with the flexible VP-Shewhart chart are compared to the FP-Shewhart chart through several instances based on a case study. Also, a sensitivity analysis is implemented on the decision variables to extend insights into the matter. The attained results demonstrate that applying the VP-Shewhart chart instead of FP-Shewhart chart leads to a significant increase in the cost savings.

Modelling and analysis of two-unit hot standby database system with random inspection of standby unit

Stochastic model for a two-unit hot standby database system comprising of one operative (primary unit) and one hot standby unit has been developed. The primary unit acts as production unit which is synchronised with hot standby unit through online transfer of archive redo logs. The data being saved in the primary unit gets simultaneously stored in the hot standby unit. The different modes of failure of primary database have been considered. To avoid loss of data, random inspection of the standby unit is carried out by a database administrator (DBA) to see as to whether redo log files are created/updated in standby unit or not. The repair of the failed unit and creation/updation of redo log files are also done by the DBA. The system is analysed using semi-Markov process and regenerative point technique. Mathematical expressions for various performance measures of the system have been obtained along with cost-benefit analysis of the system. Numerical analysis has been done to validate the derived results. Bounds for various parameters have also been obtained with regard to profitability of the system.

Availability of a two-unit warm standby system with different fuzzy Rayleigh failure rates

In the present paper, analysis of a two-unit warm standby system is introduced where the life and repair times of the components of the system are assumed to be fuzzy variables follow fuzzy Rayleigh distribution. Fuzzy Rayleigh distribution is the Rayleigh distribution with fuzzy parameters. Markov models are used to construct the mathematical model of the system. Analysis of the availability function of the model is introduced. A general expression for steady state availability is deduced. A numerical example is introduced for illustration.

The Mathematical Model and Numerical Solution of Instantaneous Availabilities for the Two-Unit Series Repairable System and Parallel Repairable System with Three States

This paper is aimed to obtain the instantaneous availabilities (IAs) for the two-unit series system and parallel system with three states. By the compound S i m p s o n formula and the compound trapezoidal formula, we get the numerical solution of IA for the two-unit series system with three states based on the renewal process. With four-order R u n g e - K u t t a formula, the numerical solution of IA for the two-unit parallel system with three states is obtained based on the Markov process.

Reliability and Profit Analysis of a Two-unit Non-identical Standby System in Snowstorm Weather Conditions

This paper express reliability measures of a cold standby system which have two units. In cold standby system one unit operative and other unit kept as a spare. In the system both the unit kept as non-identical. The each operative unit fails due to snowstorm with different failure rate. The system completely failed when the both two units are failed. The failed unit cannot be operative directly by the repairman. The failed unit under the snow, first digging out from the snow then hospitalize (repair) the unit after that the unit becomes operative. Some properties of reliability system such as mean time to system failure, availability and profit have been computed. At last particular cases have been taken to explain the model.

An optimal inspection and replacement policy for a two-unit system

We study a preventive maintenance policy for a system composed of two units, a binary state unit and a three-state unit. Failures of both units are hard and self-announcing. The intermediate, defective state for the second unit can be regarded as a signal of pending failures. Unit 2 is inspected when its age attains integral multiples of interval [Formula: see text] and when unit 1 fails, and preventive replacement is immediate once the defective state is revealed. This strategy could be extended by further providing preventive replacement for the first unit. A case study on an offshore wind turbine is presented for illustration. We find that opportunistic maintenance schemed for both units could effectively reduce the maintenance cost.

Comparative Analysis of Two-Unit Hot Standby Hardware-Software Systems with Impact of Imperfect Fault Coverages

Comparative Analysis of Two-Unit Hot Standby Hardware-Software Systems with Impact of Imperfect Fault Coverages

Stochastic analysis of a two-unit system with standby and server failure subject to inspection

It is not necessary that the server can perform its duty without failure/tiredness. While, a common man also know the importance of water supply system that works punctually without any delay. The same situation simulated here, with two unit cold standby system with the facility that the server inspects the failed unit before repair/replacement of the unit and refreshment is provided to server whenever required has been discussed. This model is applicable in the water supply system. In this model, operative unit may fail, directly from normal mode and the cold standby unit may get failed owing to remaining unused for a longer period of time or any other reason. There is a single server who visits the system immediately whenever required for the dual purpose of inspection and repair activities. Also, after having refreshment, the server may eventually perform the better service efficiently. It is assumed that time for refreshment and repair activity follows negative exponential distribution whereas the distributions of unit failure and server failure are taken as arbitrary with different probability density functions. For concluding the study of such model, various stochastic measures are analyzed in steady state using semi-Markov process and regenerative point technique. The tables are structured for arbitrary values of the parameters to exhibit the behaviour of some important performance measures to check the efficacy of the system model under such situations.

A bivariate optimal replacement policy with cumulative repair cost limit for a two-unit system under shock damage interaction

In this paper, a bivariate $(n,k)$ replacement policy with cumulative repair cost limit for a two-unit system is studied, in which the system is subjected to shock damage interaction between units. Each unit 1 failure causes random damage to unit 2 and these damages are additive. Unit 2 will fail when the total damage of unit 2 exceed a failure level $K$, and such a failure makes unit 1 fail simultaneously, resulting in a total failure. When unit 1 failure occurs, if the cumulative repair cost till to this failure is less than a predetermined limit $L$, then unit 1 is corrected by minimal repair, otherwise, the system is preventively replaced. The system is also replaced at the $n$th unit 1 failure, or at damage level $k$ (${<}K$) of unit 2, or at total failure. The explicit expression of the long-term expected cost per unit time is derived and the corresponding optimal bivariate replacement policy can be determined analytically or numerically. Finally, a numerical example is given to illustrate the theoretical results for the proposed model.

Analysis of a two-unit automatic power factor controller system with priority to inspection over repair/replacement

Analysis of a two-unit automatic power factor controller system with priority to inspection over repair/replacement

Analysis of a two-unit automatic power factor controller system with priority to inspection over repair/replacement

For the present paper, a reliability model of automatic power factor controller working in industrial companies has been developed using regenerative point technique. The system for the study consists of two cold standby identical units. Initially, the system is operative with controlled power factor. The inspection is carried out to detect the type of failure which can be due to fuse blown off, transformer burnt, programming problem, output relay faulty. But different type of failure requires different time to repair/replacement. Priority is given to repair/replacement based on estimated values of repair/replacement rates for different type of failure. Hence it is required to detect the type of failure as soon as possible which can be done by inspection only. In view of this, inspection is given priority over repair/replacement also. The various reliability indices of system effectiveness are obtained and graphs have been plotted for economic analysis of the system.

Optimal preventive and opportunistic maintenance policy for a two-unit system

This paper presents a new optimal opportunistic and preventive maintenance policy for a two-unit model with economic dependency applicable to the electric power distribution systems. Unlike the previous optimal maintenance policies which considered mainly single unit systems or no opportunistic maintenance for two-unit systems, we consider a two-unit system with economic dependency, where unit 1 is subject to condition monitoring and soft failure and unit 2 is subject to hard failure. Unit 1 is gradually deteriorating and unit 2 has a general life time distribution. Condition of unit 1 is monitored periodically and it is considered as failed when its deterioration level reaches a critical level N. At the failure time of unit 2 system is considered as failed, although unit 1 is working, and unit 2 will be correctively replaced by the next inspection epoch. Units 1 or 2 are preventively replaced when deterioration level of unit 1 or age of unit 2 reaches or exceeds the related PM levels. At the time of corrective or preventive replacement of a unit, there is an opportunity to replace also the other unit. A mathematical model is derived to find the preventive and opportunistic replacement levels for units 1 and 2 that minimize the long run expected average cost per unit time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. Numerical example is provided to illustrate the performance of the proposed model and a comparison of the proposed model with other policies is carried out.

A new mixed bivariate geometric-exponential life distribution with applications to series systems

ABSTRACTIn this paper, a new mixed bivariate geometric-exponential distribution is introduced. We present the properties and numerical characteristics of the distribution. In addition, the applications of this new bivariate distribution are given in a two-unit series system. Through an intensive Monte-Carlo simulation study, we assess the precision of the proposed estimation methods for the parameter inference. A real data is analysed for illustrative purpose.

Dependability and performance stochastic modelling of a two-unit repairable production system with preventive maintenance

In this paper, a two-unit multistate repairable production system is considered in which preventive maintenance (PM) is implemented in order to improve its dependability and performance. A general model is provided for the production system using a semi-Markov process, for examining system’s limiting behaviour. Apart from combining redundancy with PM, we introduce scenarios like imperfect and failed maintenance which are usually met in real life production systems. For the proposed model, we calculate the availability, the mean time to failure and the total operational cost and we formulate optimisation problems settled with respect to the system’s inspection times. The main aim of our work is to determine the optimal inspection times and consequently the optimal PM policies to be adopted in order to optimise system’s dependability and performance.

Joint optimization of lot-sizing and maintenance policy for a partially observable two-unit system

In this paper, we present a new model to find the jointly optimal economic manufacturing quantity (EMQ) and preventive maintenance (PM) policy for a complex production facility. Unlike the previous joint models which dealt with EMQ and maintenance policy considering a single unit production facility and traditional maintenance approaches, we consider a production facility which consists of two modules with economic dependence. The more expensive module (unit 1) is subject to condition monitoring (CM), and only the age information of the second module (unit 2) is available, which follows a general distribution. The deterioration process of unit 1 is modeled as a continuous time hidden-Markov process. CM data is available at the end of each production run, and it provides only partial information about the hidden state of unit 1. The failure state of unit 1 is observable at any time. The objective is to develop a jointly optimal lot sizing and maintenance policy for a two-unit production facility using multivariate Bayesian control approach by minimizing the long-run expected average cost per unit time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. Also, a formula for the mean residual life (MRL) of the production facility is derived, which is an important statistic for practical applications. A practical example of the wind turbine CM and maintenance is provided and a comparison with other policies shows an outstanding performance of the new model and the control policy proposed in this paper.

Optimal two-threshold replacement policy in a cumulative damage model

In this paper, a two-unit system with failure interactions is studied. The system is subject to two types of shocks (I and II) and the probabilities of these two shock types are age-dependent. A type I shock, rectified by a minimal repair, causes a minor failure of unit A and type II shock causes a complete system failure that calls for a replacement. Each unit A minor failure also results in an amount of damage to unit B. The damages to unit B caused by type I shocks can be accumulated to trigger a preventive replacement or a corrective replacement action. Besides, unit B with cumulative damage of level z may become minor failed with probability \(\pi (z)\) at each unit A minor failure and rectified by a minimal repair. We consider a more general replacement policy. Under this policy, the system is preventively replaced at the Nth type I shock, or at the time when the total damage to unit B exceeds a pre-specified level Z (but less than a failure level K where \(K>Z\)) or is replaced correctively at first type II shock or when the total damage to unit B exceeding a failure level K, whichever occurs first. To minimize the expected cost per unit time, the optimal replacement policy \((N^{*}\), \(Z^{*})\) is derived analytically and determined numerically. We also show that several previous maintenance models in the literature are special cases of our model.

Optimal Maintenance Modeling for Systems with Multiple Non-Identical Units Using Extended DSSP Method

In the optimal maintenance modeling, all possible maintenance activities and their corresponding probabilities play a key role in modeling. For a system with multiple non-identical units, its maintenance requirements are very complicated, and it is time-consuming, even omission may occur when enumerating them with various combinations of units and even with different maintenance actions for them. Deterioration state space partition (DSSP) method is an efficient approach to analyze all possible maintenance requirements at each maintenance decision point and deduce their corresponding probabilities for maintenance modeling of multi-unit systems. In this paper, an extended DSSP method is developed for systems with multiple non-identical units considering opportunistic, preventive and corrective maintenance activities for each unit. In this method, different maintenance types are distinguished in each maintenance requirement. A new representation of the possible maintenance requirements and their corresponding probabilities is derived according to the partition results based on the joint probability density function of the maintained system deterioration state. Furthermore, focusing on a two-unit system with a non-periodical inspected condition-based opportunistic preventive-maintenance strategy; a long-term average cost model is established using the proposed method to determine its optimal maintenance parameters jointly, in which “hard failure” and non-negligible maintenance time are considered. Numerical experiments indicate that the extended DSSP method is valid for opportunistic maintenance modeling of multi-unit systems.

A study of MTTF in two-unit standby redundant system with priority under limited information about failure and repair times

We consider a two-unit standby redundant system with priority. In the previous literature, the theoretical formulae for the MTTF of such a system have been obtained using the renewal theory in the condition that the probability distributions about failure and repair times have the respective explicit functions. However, it is sometimes impossible to calculate the MTTF of the system depending on the probability distributions in the case of using the theoretical formulae in the previous literature. In this paper, we consider the situation that the probability distributions about failure and repair times can be approximated as a mixed Erlang distribution. Under this situation, we develop a new approximation procedure for computing the MTTF of the system by combining some results of the Markov analysis based on Erlang distributions. Then, we investigate the validity of our proposed approximation by simulation.

Stochastic Analysis of a Two-Unit Cold Standby System with Arbitrary Distributions for Life, Repair and Waiting Times

Stochastic Analysis of a Two-Unit Cold Standby System with Arbitrary Distributions for Life, Repair and Waiting Times

Extended preventive replacement policy for a two-unit system subject to damage shocks

We consider a system consisting of two units (A and B), which is subject to two types of shocks (I and II) that occur according to a non-homogeneous Poisson process. The probabilities of these two shock types are age-dependent. Each type-I shock causes a minor failure of unit A, which can be corrected by a minimal repair. Meanwhile, this type of shock results in a certain amount of damage to unit B. These damages to unit B are accumulated to trigger a preventive replacement (PM) or a corrective replacement (CM) action. In addition, a minor failure for unit B with the cumulative damage of z will occur with probability at a type-I shock instant. Type-II shock is a major one that causes system replacement. We consider a two-dimensional PM policy, which prescribes that the system is preventively replaced at age T, or at the time when the total damage to unit B exceeds a prespecified level Z (but less than the failure level K where K > Z) or is replaced correctively at first type-II shock or when the total damage to unit B exceeds a failure level K, whichever occurs first. Thus, both PM and CM actions may be performed in our model. To minimise the expected cost per unit time, the optimal policy (, ) is derived analytically and determined numerically. We also show that our model is a generalisation of many previous maintenance models in the literature.