Optimal monitoring strategies for slowly deteriorating repairablesystems

A simple model for determination of an optimal limit on taking corrective action in a slowly deteriorating repairable system is presented. The performance of such a system is assumed to be characterized by a single parameter which is continuously being monitored. The underlying deterioration process is assumed to be governed by a Brownian motion process with a positive drift. When the measured value of the parameter reaches the action limit, the repair/replacement procedure is initiated. The optimal action limit is derived so that the expected long run average total cost is minimized. Some simple numerical examples illustrate the model and the optimization     

Optimal maintenance policy for systems that experience state degradations

The states of the system studied consist of good (state 0), degraded (states 1,2,…,n?1) and failed (state n). Renewal theory was used to obtain the hazard rate of the system with the assumption that the transition rate from one state to the next (including the failure state) is equal at any state. An optimal preventive maintenance policy was obtained by maximizing the availability of the system, i.e., the fractional amount of the up-time over a long total time interval.     

Optimal channel assignment strategies for forced channel hopping in CDPD systems

To provide an acceptable call blocking probability in circuit-switched cellular networks, such as the Advanced Mobile Phone System (AMPS) networks, a significant fraction of the channel capacity in each cell is normally unused. This “free” capacity can be effectively used for packet data transmissions that yield to voice traffic when necessary. Cellular Digital Packet Data (CDPD) is a packet-switched data service which may share radio channels with the AMPS service on a secondary basis to tap this “free” capacity. The length of time that a CDPD stream can occupy a channel is greatly influenced by the channel assignment strategies of both the AMPS and the CDPD systems. This paper investigates these channel assignment strategies and their effects on the CDPD channel holding times, in comparison with the optimal channel assignment strategy that interrupts the CDPD service only when a new AMPS call finds no other idle channels in the cell site. One such optimal strategy is the cooperative strategy in which the CDPD and AMPS networks actively communicate with each other. It is shown that other optimal strategies exist without the need of communications between the two systems. The effects of AMPS traffic levels, number of channels, and number of CDPD streams at the cell site on the CDPD channel holding time and channel utilization are also considered. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal channel assignment strategies for forced channel hopping in CDPD systems

To provide an acceptable call blocking probability in circuit-switched cellular networks, such as the Advanced Mobile Phone System (AMPS) networks, a significant fraction of the channel capacity in each cell is normally unused. This “free” capacity can be effectively used for packet data transmissions that yield to voice traffic when necessary. Cellular Digital Packet Data (CDPD) is a packet-switched data service which may share radio channels with the AMPS service on a secondary basis to tap this “free” capacity. The length of time that a CDPD stream can occupy a channel is greatly influenced by the channel assignment strategies of both the AMPS and the CDPD systems. This paper investigates these channel assignment strategies and their effects on the CDPD channel holding times, in comparison with the optimal channel assignment strategy that interrupts the CDPD service only when a new AMPS call finds no other idle channels in the cell site. One such optimal strategy is the cooperative strategy in which the CDPD and AMPS networks actively communicate with each other. It is shown that other optimal strategies exist without the need of communications between the two systems. The effects of AMPS traffic levels, number of channels, and number of CDPD streams at the cell site on the CDPD channel holding time and channel utilization are also considered. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal maintenance schedules of systems subject to stochastic failure

Almost all operational and standby systems need maintenance, yet this is often overlooked in the stages of design and development. Lately, maintenance has been emphasized by several factors such as rising costs of labor and material, increased complexity of systems and increased quality requirements. The aim of this paper is to develop new algorithms and analysis techniques that can be used in a general way to handle optimization of various types of inspection and maintenance schedules of systems subject to stochastic failure. Physical problems of systems in active operation with increasing failure rate are treated. Examples of such systems are: airborne electronic equipment, radio receivers, aircraft engines, etc. The optimal maintenance schedule incorporates the effects of inspection, maintenance, delayed detection, uptime and downtime costs. The techniques of classical differential calculus and dynamic programming are applied for the development of the optimal maintenance schedule.     

Optimal replacement of improving and deteriorating repairablesystems

System improvement and deterioration are defined in terms of partial orderings between life distributions. The effects of ageing of `the distribution of time to first failure' on improvement and deterioration of a repairable system subject to minimal repairs, are investigated. Under various types of life distributions we derive explicitly the times at which the system should be condemned (replaced by a new one) to minimize the total cost of maintenance and replacement in terms of parameters of the distribution and of the cost function     

A geometric-process maintenance model for a deteriorating system under a random environment

This paper studies a geometric-process maintenance-model for a deteriorating system under a random environment. Assume that the number of random shocks, up to time t, produced by the random environment forms a counting process. Whenever a random shock arrives, the system operating time is reduced. The successive reductions in the system operating time are statistically independent and identically distributed random variables. Assume that the consecutive repair times of the system after failures, form an increasing geometric process; under the condition that the system suffers no random shock, the successive operating times of the system after repairs constitute a decreasing geometric process. A replacement policy N, by which the system is replaced at the time of the failure N, is adopted. An explicit expression for the average cost rate (long-run average cost per unit time) is derived. Then, an optimal replacement policy is determined analytically. As a particular case, a compound Poisson process model is also studied.     

Reliability analysis : Optimal inspection and maintenance schedules of failing systems

Inspection and maintenance schedules involve planned and unplanned actions carried out to retain a system in, or restore it to an acceptable condition. Optimal maintenance schedules aim to minimize downtime, while providing for the most effective use of systems in order to secure the desired results at the lowest possible costs. This paper is a state-of-the-art review of the literature related to optimal inspection and maintenance schedules of failing systems.     

Fuzzy-set approach to select maintenance strategies for multistateequipment

Maintenance of any equipment based on its condition is unavoidable. The condition of the equipment can be represented using fuzzy sets. This paper details a fuzzy-set model for maintenance policy of multistate equipment; the model is based on: (a) equipment condition and remaining life, and (b) maximizing a known detailed utility function. The model is extended to maintenance planning for the entire life of the equipment. The results are useful for replacement decisions as well as for inventory control     

Optimal strategies for scheduling checkpoints and preventivemaintenance

At checkpoints during the operation of a computer, the state of the system is saved. Whenever a machine fails, it is repaired and then reset to the state saved at the latest checkpoint. In the present work, save times are known constants and repair times are random variables; failures are the epochs of a given renewal process. In scheduling the checkpoints, the cost of saves must be traded off against the cost of work lost when the computer fails. It is shown how to schedule checkpoints to minimize the mean total time to finish a given job. Similar optimization results are obtained for the tails of the distribution of the finishing time. Two variants of the basic model are considered. In one of the computer receives maintenance during each save; in the other it does not. Applications to the M/G/1 queuing system are touched on     

Optimal coding strategies for certain permuting channels

We give optimal coding strategies for nonprobabilistic permuting (especially, "trapdoor") channels and also for a permuting relay channel. Our results open the door to a coding theory for nonprobabilistic (or deterministic) channels with memory.     

Optimal filtering for multirate systems

For a multirate system where the output sampling is slower than the input updating, this brief aims at designing filters for fast state estimation in the H/sub 2/ and H/sub /spl infin// settings. Because of the multirate nature, linear matrix inequality solutions to the design problems involve a nonconvex constraint, which is numerically tackled by the product reduction algorithm. Finally, a design example is given and the effectiveness of the approach is illustrated.     

Optimal preventive maintenance with repair

A minimal preventive-maintenance model is developed for repairable, continuously-operating devices whose conditions deteriorate with the time in service. The times to preventive maintenance have an Erland distribution and can be, in a limiting case, deterministic. The optimal value of the mean time a preventive maintenance is determined by minimizing the unavailability of the device due to preventive maintenance, to Poisson-distributed failures, and to deterioration failures. The model is useful for many devices, including electric power-system components such as coal pulverizers, circuit breakers, and transformers     

Marginally monotonic maintenance policies for a multi-state deteriorating machine with probabilistic monitoring, and silent failures

We characterize the structure of optimal policies for maintenance & replacement actions over a finite horizon. The context is machine monitoring when the following are true: 1) The machine can operate in one of N states in S/spl isin/{0,1,...,N-1} where 0 is good, 1 to N-2 represent increasing levels of deterioration (i.e., the system becomes increasingly worn, but is still able to produce usable parts), and N-1 is bad (or failed). 2) Observations are related probabilistically to the state of the process. 3) The machine's state is known with certainty only immediately after a replacement. The last assumption, consistent with "silent" failures, distinguishes our results from others. We prove [using the theory & results of partially observable Markov decision processes (POMDP)] that the policy that minimizes the total expected cost of system maintenance has a "marginally monotonic" structure. The concept of "marginal monotonicity", which requires a component-wise partial ordering, and monotonicity of the expected total cost function with respect to each component of the state space, allows characterization of the policy that minimizes the total expected cost. This feature allows us to represent the optimal policy by a collection of decision rules characterized by at most N functions.     

ARQ strategies for relay cooperative systems

We propose two novel automatic repeat request (ARQ) strategies for relay cooperative systems over Rayleigh fading channel one uses relay ARQ and the other destination ARQ. The BER performance of these two strategies is derived in fast block fading. Numerical analysis and simulation show the systems can get more performance gain when the inter-channel (the source to the relay) quality is bad in the relay ARQ strategy. In the destination ARQ strategy, when the uplink qualities of the source and relay to the destination are poor, the average received SNR of the destination is much low, the systems performance can be improved efficiently.     

Optimal design for cellular mobile systems

Cellular zone design parameters for a land mobile communication system are clarified. System parameters having a strong influence on cellular system performance are discussed and some problems encountered when system parameters are changed are examined.     

Optimal waveform selection for tracking systems

Investigates adaptive waveform selection schemes where selection is based on overall target tracking system performance. Optimal receiver assumptions allow the inclusion of transmitted waveform specification parameters in the tracking subsystem defining equations. The authors give explicit expressions for two one-step ahead optimization problems for a single target in white Gaussian noise when the tracker is a conventional Kalman filter. These problems may be solved to yield the most improvement possible in tracking performance for each new transmitted pulse. In cases where target motion is restricted to one dimension, closed-form solutions to the local (one step ahead) waveform optimization problem have been obtained. The optimal waveform selection algorithms in the paper may be included with conventional Kalman filtering equations to form an enhanced Kalman tracker. Simulation examples are presented to illustrate the potential of the waveform selection schemes for the optimal utilization of the capabilities of modern digital waveform generators, including multiple waveform classes. The extension of the basic waveform optimization scheme to more complex tracking scenarios is also discussed     

Optimal block-type-decodable encoders for constrained systems

A constrained system is presented by a finite-state labeled graph. For such systems, we focus on block-type-decodable encoders, comprising three classes known as block, block-decodable, and deterministic encoders. Franaszek (1968) gives a sufficient condition which guarantees the equality of the optimal rates of block-decodable and deterministic encoders for the same block length. We introduce another sufficient condition, called the straight-line condition, which yields the same result. Run-length limited RLL(d,k) and maximum transition run MTR(j,k) constraints are shown to satisfy both conditions. In general, block-type-decodable encoders are constructed by choosing a subset of states of the graph to be used as encoder states. Such a subset is known as a set of principal states. For each type of encoder and each block length, a natural problem is to find a set of principal states which maximizes the code rate. We show how to compute the asymptotically optimal sets of principal states for deterministic encoders and how they are related to the case of large but finite block lengths. We give optimal sets of principal states for MTR(j,k)-block-type-decodable encoders for all codeword lengths. Finally we compare the code rate of nonreturn to zero inverted (NRZI) encoders to that of corresponding nonreturn to zero (NRZ) and signed NRZI encoders.     

Optimal decision strategies for paging in mobile cellular networks

A high‐level technical survey of paging in mobile cellular communication networks is presented in this paper. We view paging as an optimal decision problem and explore different strategies based on sequential decisions. The examined schemes concentrate on different perspectives of the problem, depending on the type of decisions and the amount of information available or exploitable by the system. This approach provides a useful categorization and an easy conceptual basis for their theoretical investigation, necessary for the deployment of advanced paging algorithms. Because of its suggested generality, the discussed framework is also laid as reference for further research. As modern networks evolve, more emphasis will be given towards optimization in all aspects of a network system. The schemes presented greatly reduce paging costs and can be used in cooperation with known location update strategies to make part of a real network location management system. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal retrial and timeout strategies for accessing network resources

The notion of timeout (i.e., the maximal time to wait before retrying an action) occurs in many networking contexts. Use of timeouts is encountered especially in large-scale networks, where negative acknowledgments (NACKs) on failures have significantly higher delays than positive acknowledgments (ACKs) and frequently are not employed at all. Selection of a proper timeout involves a tradeoff between waiting too long and loading the network needlessly by waiting too little. The common approach is to set the timeout to a large value, such that, unless the action fails, it is acknowledged within the timeout duration with a high probability. This approach leads to overly long, far from optimal, timeouts. Our quantitative approach has the purpose of computing and studying the optimal timeout strategy. The tradeoff is modeled by introducing a "cost" per unit time (until success) and a "cost" per repeated attempt. The optimal strategy is then defined as one that a selfish user would follow to minimize its expected cost. We discuss various practical interpretations of these costs. We then derive formulas for the optimal timeout values and study some of their fundamental properties. We identify the worthwhile conditions for making parallel attempts from the outset. We also demonstrate a striking property of positive feedback and study the interaction resulting when many users selfishly apply the optimal timeout strategy; we use a noncooperative game model and show that it suffers from an inherent instability problem. Some implications of these results on network design are discussed.