Optimisation of K-Out-Of-N systems subject to common-cause failures with repair provision

This paper considers K-Out-Of-N systems that is subject to two modes of failures, Common cause failures (CCFs) and Random failures, We assure that the system is repaired after each system failure. We develop an optimality criterion leading to the optimal number of units N^* for a K-Out-Of-N system, based on cost considerations. Numerical examples are included to illustrate the procedure.     

Optimal number of uses for an intermittently-used system

This paper studies an intermittently-used system which fails by continuous deterioration with age or by discrete deterioration with use. The system is replaced before failure at number N of uses. The optimal number N^* to minimize the expected cost rate is discussed for three particular cases. The case where the system deteriorates with both operating time and use time is considered.     

An economic discrete replacement policy for a shock damage model with minimal repairs

A discrete replacement model for a repairable system which is subject to shocks and minimal repairs is discussed. Such shocks can be classified, depending on its effect to the system, into two types: Type I and Type II shocks. Whenever a type II shock occurs causes the system to go into failure, such a failure is called type II failure and can be corrected by a minimal repair. A type I shock does damage to the system in the sense that it increases the failure rate by a certain amount and the failure rate also increases with age due to aging process without external shocks; furthermore, the failure occurred in this condition is called type I failure. The system is replaced at the time of the first type I failure or the n-th type Il failure, whichever occurs first. Introducing costs due to replacement and mininal repairs, the long-run expected cost per unit time is derived as a criterion of optimality and the optimal number n∗ found by minimizing that cost. It is shown that, under certain conditions, there exists a finite and unique optimal number n∗.     

Optimal redundancy of K-out-of-n:G system with two kinds of CCFs

This paper considers the problem of optimal redundancy of K-out-of-n:G systems. The model highlights the occurrence of two types of common-course failures, namely, lethal and non-lethal CCFs, in addition to random failures. The optimum number of redundant components (n^*) in K-out-of-n: G systems are derived with two types of CCF. The optimization is approached by a minimization of the mean cost rate (C₁(n^*)) which is established to be finite and unique. Numerical evidence indicates the reduction of optimal redundancy with two types of CCF when compared to random failures alone.     

Three replacement models with two kinds of damage

This paper proposes three replacement policies for a modified cumulative damage model. An item receives shocks and suffers two kinds of damage: one is produced by shocks and the other increases with time at constant rate a. It fails only when the total damage exceeds a failure level K at some shock and is replaced before failure at time T, at shock N, or at damage k. The expected cost rates of three replacement policies are obtained. When shocks occur in a Poisson process, optimal T^*, N^* and k^* which minimize them are computed numerically. Finally, two extended cases where a is a function of time and K is a random variable are also considered.     

The study of a maintenance float model with gamma failure and two repair centres

This paper considers an operational system made up of a number of independent and identical units. A given number N must be in service and is supported by a maintenance float. Here, an attempt has been made to model and analyse the maintenance float problem assuming two types of repairs, namely minor and major repairs. For the sake of simplicity, the failure distributions are taken to be exponential and gamma while the repair distributions are exponential and lognormal.     

Periodic replacement when minimal repair costs depend on the age and the number of minimal repairs for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for a multi-unit system which has a specific multivariate distribution. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed for any intervening component failure. The cost of a minimal repair to the component is assumed to be a function of its age and the number of minimal repairs. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. The necessary and sufficient conditions for the existence of an optimal replacement interval are found.     

On the optimization of VLSI allocation in high-level synthesis

Allocation is one of main tasks in the high-level synthesis. It includes module , functional unit allocation, storage allocation and interconnection allocation. This paper models the allocation problem as cluster analysis and applies a new algorithm, neighbor state transition (NST) algorithm, for cluster optimization. It is proved that the algorithm produces an asymptotically global optimal solution with the upper bound on the cost function (1 O(1/n)2-ε)F*, When F" is the cost of the optimum solution, n is the problem size and e is a positive parameter arbitrarily close to zero. The numerical examples show that the NST algorithm produces better results compared to the other known methods.     

Reliability analysis and optimization applications of a two-unit standby redundant system with spare units

Consider a two-unit standby redundant system with two main units, one repair facility, and n spare units. When the main unit has failed and the other is under repair, a spare unit takes over the operation and if it fails, it is replaced by a new one until the repair of the failed unit is completed. The system fails when the last spare unit fails while one main unit is under repair and the other has failed. In this paper, we derive expressions for 1) the distribution function of the first time to system failure, 2) the probability that the total number of failed spare units during the time interval (0,t] is n and 3) the mean of the total number of failed spare units in (0,t] and its asymptotic behaviour. Introducing costs incurred for each failed main unit and each failed spare unit, the expected cost per unit of time of the system was also derived. Finally an optinmization problem is discussed in order to compare the expected cost of the system with both main units and spare units with that of spare units only, and particular cases are considered.     

Analysis of 1-server n-unit parallel system subject to different service strategies

This paper deals with the cost-benefit analysis of 1-server n-unit parallel system subject to different service strategies. At t = 0, all the n units are switched on. The repair times of the units are arbitrarily distributed, while the failure rates of the units are constants. The system is analysed by writing integral equations for the probabilities of the system being found in various states by identifying the system at suitable regeneration epochs. These equations are solved using integral transforms. The following system characteristics, namely,

1. (1) expected duration in [0, t] k units are operating, 0 ≤ k ≤ n

2. (2) expected duration in [0, t] the server is busy with the repair of the units

3. (3) expected number of repairs in the interval [0, t], and

4. (4) expected number of times the system enters down-state

are evaluated to carry out the cost-benefit analysis of the system.     

Cost optimal, parallel reliability systems with fixed repair sanction

Optimisation methods under varied criteria for different parameters in stochastic reliability systems are being increasingly developed and have been reported in recent literature. The large interest evinced in this fascinating area is primarily due to its applicational value and operational role in the decision making process. Recently a parallel system has been considered and the optimal number of units discussed, as well as optimal replacement times for the system based on acquisition and replacement costs.In this paper we consider an improved version of the model formulation, by bringing in additionally the maintenance and per unit repair time costs, and develop a procedure to obtain the optimal number of components in the system with the condition that the system is allowed to undergo a prefixed maximum number of repairs, after which the system is to be replaced.The applicational use of the results is illustrated through numerical work, specialising to some known laws governing the system parameters and corresponding to different fixed number of repair sanctions.     

Fusion function placement for Active Networks paradigm in wireless sensor networks

Active Networks paradigm integrated with distributed data fusion has the potential to significantly reduce energy dissipation in wireless sensor networks, where energy conservation is the most challenging issue. This work aims to minimize energy cost when distributed data fusion is deployed for the Active Networks computing paradigm. First we propose an optimal solution for mapping task graph of distributed data fusion application into network. Optimal solution uses an exhaustive search algorithm for finding the placements with minimized power consumption. However, optimal solution has high computational complexity—O(mn ^k ), where n denotes the number of network nodes, m is the number of fusion functions, and k is the maximum number of children a fusion function has in task graph and its children are also fusion functions. Then, an approximate solution with low complexity (O(mlog n + log² m)) is proposed called P2lace, which includes two phases, task graph partition and task graph placement. Finally, an extensive evaluation compares approximate solution with optimal solution. The results show that approximate solution is scalable with different task graph characteristics and network size and only causes slightly more transmission cost than optimal solution. And the algorithm without optimizing is shown to be applicable to the network, where the sink node does not have global information of entire network.     

Optimal control of a removable server in an M/Ek/1 queueing system with finite capacity

This paper deals with the economic behavior of a removable server in the N policy M/E_k/1 queueing system with finite capacity. Expressions for the probability mass functions of the number of customers in the system are derived and taken in closed-form. As special cases, the probability mass functions of the number of customers for the N policy M/M/1 queueing system, the ordinary M/K_k/1 queueing system, and the ordinary M/M/1 queueing system are obtained. The cost structure includes a holding cost per unit time spent in the system for each customer, costs per unit time for keeping the server on or off, a server start-up cost, a server shut-down cost, and fixed cost for every lost customer. Following the construction of the total expected cost per unit time, we determine the optimal operating policy at minimum cost.     

Stochastic behaviour of a three-state complex repairable system with three types of failures

This paper deals with the operational availability of a three-state complex repairable system consisting of n distinct units arranged in series. Single service facility is available for three types of failures of the complex system. A mathematical model for the complex system under severe restrictions has been developed for exponential failures and general repairs. Laplace transforms of various state probabilities have been evaluated and availability is then obtained by the inversion process. Few graphical illustrations are also given in the end so as to explain the practical utility of the model.     

Efficient architectures for modulo 2n − 2 arithmetic units

Moduli of the 2ⁿ and 2ⁿ ± 1 forms are usually employed in designs that adopt the residue number system. However, in several cases such as in finite impulse response filters and communication components, a modulo value equal to 2ⁿ ? 2 can be used. So far, modulo 2ⁿ ? 2 arithmetic units have been based either on look-up tables or on generic modulo arithmetic units. In this work, by taking advantage of the properties of modulo 2ⁿ ? 2 arithmetic, we propose efficient modulo 2ⁿ ? 2 multi-operand adder, multiplier as well as squarer architectures. The proposed circuits are based on the corresponding ones for modulo 2^n?1 ? 1 arithmetic and some simple logic. Experimental results validate that the proposed circuits achieve significant area and delay savings compared to those previously presented.     

A Distributed Algorithm for Dynamic Channel Allocation

Recent demand for mobile telephone service has been growing rapidly while the electro-magnetic spectrum of frequencies allocated for this purpose remains limited. Any solution to the channel assignment problem is subject to this limitation, as well as the interference constraint between adjacent channels in the spectrum. Channel allocation schemes provide a flexible and efficient access to bandwidth in wireless and mobile communication systems. In this paper, we present an efficient distributed algorithm for dynamic channel allocation based upon mutual exclusion model, where the channels are grouped by the number of cells in a cluster and each group of channels cannot be shared concurrently within the cluster. We discuss the algorithm and prove its correctness. We also show that the algorithm requires at most (worst case) O(N _gN _n logN _n) messages, where N _g is the number of groups and N _n is the number of neighbors. This is compared to Choy's algorithm which requires O(N _g ²N _n), where N _g is the number of groups and N _n is the number of neighboring cells in the system. We report our algorithm's performance with several channel systems using different types of call arrival patterns. Our results indicate that significant low denial rate, low message complexity and low acquisition time can be obtained using our algorithm.     

Optimal control of a removable and non-reliable server in a markovian queueing system with finite capacity

This paper studies the economic behavior of a removable and non-reliable server in an Markovian queueing system with finite capacity under steady-state conditions. The removable server applies the N policy which turns the server on when the queue length reaches the value N, and turns the server off when the system is empty. The server may break down only if operating and require repair at a repair facility. Interarrival and service times of the customers, and breakdown and repair times of the server, are assumed to follow a negative exponential distribution. A cost model is developed to determine the optimal operating N policy numerically in order to minimize the total expected cost per unit time.     

Analysis of 1-out-of-n: G adjustable operating system

This paper deals with the analysis of a single unit Adjustable Operating system supported by (n ? 1) inactive standbys and a repair facility. Various operating characteristics are studied, viz. transit probabilities, failure time distribution and mean time to failure of the system, availability of the system at time t, s-expected number of failures of the system in (0,t], s-expected number of repairs in (0,t]. Results are obtained in terms of L.S. transforms. A few special cases are studied for n = 3.     

Class of minimax error-corecting codes based on perfect binary arrays

Aregular synthesis method has been developed for synthesizing infinite families of minimax M(N)-classes of perfect binary arrays having order N = 2 ^k , where k is arbitrary natural number. This method enabled us to construct a new class of four-parameter minimax error-correcting M(n)-codes having length n = N ² that possess many practically attractive properties; in this case the task of decoding is reduced to the effective procedure of majority estimation of parameters of the received code words     

Estimation of parameters of a model of a complex repairable system

This paper deals with estimation of parameters of a model of a complex repairable system with 3ne unit on operation and the remaining (N − 1) units as inactive standbys and having a repair facility. Various operating characteristics, namely, reliability, availability, mean time to failure of the system, s-expected numbers of repairs in (0, t], s-expected numbers of failures of the system in (0, t] are estimated under two censoring schemes namely, the type-I censoring and type-II censoring schemes.