All opportunity-triggered replacement policy for multiple-unitsystems

A model is presented for a system which consists of n i.i.d units. Hazard rates of these units are increasing in time. A unit is replaced at failure or when the age of a unit exceeds T, whichever occurs first. When a unit is replaced, all the operating units with their age in the interval (T-w,T) are replaced. Both failure replacement and active replacement create the opportunities to replace other units preventively. This policy allows joint replacements and avoids the disadvantages resulting from replacement of new units, down time, and unrealistic assumptions for distributions of unit life. An algorithm is developed to compute the steady-state cost rate. Optimal T&W are obtained to minimize the mean total replacement cost rate. Application and analysis of results are illustrated through a numerical example     

A maintenance policy for repairable systems based on opportunisticfailure-rate tolerance

An opportunistic hazard rate replacement policy for a repairable system with several types of units is presented. A unit is repaired at failure when the hazard rate falls in (0, L-u). A unit is replaced at failure when the hazard rate falls in (L-u , L). An operating unit is replaced when its hazard rate reaches L. When a unit is replaced because its hazard rate reaches L, all operating units with their hazard rates falling in (L-u, L) are replaced. The long-run mean cost rate as a function of L and u is derived. Optimal L and u are obtained to minimize the total maintenance cost rate. Application and analysis of results are demonstrated through a numerical example. The maintenance model is designed for a system with multitype units. Each type has its own increasing hazard rate. Units are repaired or replaced depending on their hazard rate at a failure or active replacement of another unit. The repair interval, replacement limit, and replacement tolerance are determined to yield the optimal total maintenance cost rate     

Cost-benefit analysis of a single server three-unit redundant system with inspection, delayed replacement and two types of repair

This paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement at the time of failure of the active unit and a cold standby (stock) unit which can be replaced after a random amount of time. The type of the failure of operative or warm standby unit is detected by inspection only. The service facility plays the triple role of replacement, inspection and repair of a unit. Failure time distributions of operative and warm standby units are negative exponential whereas the distributions of replacement time, inspection time and repair times are arbitrary. The system has been studied by using regenerative points.     

Hazard-rate tolerance method for an opportunistic-replacementpolicy

A model for a system with several types of units is presented. A unit is replaced at failure or when its hazard (failure) rate exceeds limit L, whichever occurs first. When a unit is replaced because its hazard rates reaches L, all the operating units with their hazard rate falling in the interval (L-u, L) are replaced. This policy allows joint replacements and avoids the disadvantages resulting from the replacement of new units, down time, and unrealistic assumptions for distributions of unit life. The long-run cost rate is derived. Optimal L and u are obtained to minimize the average total replacement cost rate. Application and analysis of results are demonstrated through a numerical example     

Preventive Replacement of a 1-Unit System with a Wearout State

This paper is concerned with a 1-unit system with 3 types of states: usual, wearout, and failure; the hazard rate is constant in the usual state and is monotonically increasing and unbounded in the wearout state. In order to deal with this system in detail, we introduce two models: model 1 in which the period of normal operation is fixed and model 2 in which it is a random variable with a negative exponential distribution function. The models have different preventive replacement policies based on both age and state. Moreover we give the conditions under which these policies are effective.     

Time-shifted rayleigh density for wearout failures

A time-shifted Rayleigh density model is proposed for wearout failures in reliability theory. Reliability, failure rate and MTTF in the wearout period are calculated. The model predicts a linearly increasing failure rate due to wearout after the useful life.     

(τ, k) block replacement policy with idle count

The authors propose a new block replacement policy for a group of nominally identical units. Each unit is individually replaced on failure during a specified time interval. Beyond the failure replacement interval, failed units are left idle until a specified number of failures occur, then a block replacement is performed. The average cost rate for this two-phase block replacement policy is derived and analyzed. The policy yields lower cost rate than two block replacement policies published previously. Numerical examples demonstrate the results     

Maintenance strategies following the expiration of warranty

The authors study two types of replacement policies, following the expiration of warranty, for a unit with an IFR failure-time distribution: (1) the user applies minimal repair for a fixed length of time and replaces the unit by a new one at the end of this period; and (2) the unit is replaced by the user at first failure following the minimal repair period. In addition to stationary strategies that minimize the long-run mean cost to the user, the authors also consider nonstationary strategies that arise following the expiration of a nonrenewing warranty. Following renewing warranties, they prove that the cost rate function is pseudo-convex under a fixed maintenance period policy. The same result holds under nonrenewing repair warranties, and nonrenewing replacement warranties when the optimal maintenance period of each cycle is determined as a function of the age of the item in use at the end of the warranty period     

Abrupt breakdown in dielectric/metal gate stacks: a potential reliability limitation?

In downscaled poly-Si gate MOSFET devices reliability margin is gained by progressive wearout. When the poly-Si gate is replaced with a metal gate, the slow wearout phase observed in ultrathin SiON and HfSiON dielectrics with poly-Si gate disappears, and with it, the reliability margin. We demonstrate for several combinations of dielectric and gate materials that the large abrupt current increase (/spl Delta/I) as compared to poly-Si is not likely due to process issues, but is an intrinsic property of the dielectric/metal gate stack. The occurrence of large /spl Delta/I is a potential limitation for the reliability of metal gate devices.     

On the decision to replace a unit early or late—A graphical solution

In this note we consider an age replacement problem studied by T. Nakagawa (Microelectron. Reliab. 19, 265–267), where a unit cannot be replaced exactly at the optimum replacement time. A graphical procedure for the determination whether the unit should be replaced early or late is suggested.     

Analysis of a repairable redundant system with delayed replacement

The paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement at the time of failure of the active unit and a cold standby (stock) unit which can be replaced after a random amount of time. Failure time distributions of operative and standby units are exponential whereas all repair times follow arbitrary distributions. The system has been studied in detail by applying the results from the theory of semi-Markov process and mean-time-to-system-failure, steady-state availability, expected number of visits to a state, second moment of time in an up-state and expected profit of the system have been obtained.     

An age replacement policy with minimal repair and general random repair cost

An age replacement policy is introduced which incorporates minimal repair, replacement, and general random repair costs. If an operating unit fails at age y<T, it is either replaced by a new unit with probability p(y) at a cost c₀, or it undergoes minimal repair with probability q(y) = 1−p(y). Otherwise, a unit is replaced when it fails for the first time after age T. The cost of the i-th minimal repair of an unit at age y depends on the random part C(y) and the deterministic part c_i(y). The aim of the paper is to find the optimal T which minimizes the long run expected cost per unit time of the policy. Various special cases are considered.     

An optimal inspection policy for a storage system with high reliability

A system such as missiles and spare parts of aircrafts has to perform a normal operation at any time when it is used. However, a system is in storage for a long time from the transportation to the usage and its reliability goes down with time. Such a system should be inspected and maintained at periodic times to hold a higher reliability than a prespecified value q. This paper suggests a periodic inspection of a storage system with two kinds of units where unit 1 is inspected and maintained at each inspection, however, unit 2 is not done. The system is replaced at detection of failure or at time when the reliability is below q. The total expected cost until replacement is derived and an optimal inspection time which minimizes it is discussed. Numerical examples are given when failure time distributions are exponential and Weibull ones.     

Replacement policies for a cumulative damage model with minimalrepair at failure

The authors apply periodic replacement with minimal repair at failure to cumulative damage models: a unit is replaced at time T , at shock N, or at damage Z and undergoes minimal repair between replacements. The mean cost-rate is obtained, and each optimal T*, N*, and Z* to minimize the cost-rate is discussed. A numerical example is given for an exponential case     

Implications of accelerated self-healing as a key design knob for cross-layer resilience

In this paper we propose a cross-layer accelerated self-healing (CLASH) system which “repairs” its wearout issues in a physical sense through accelerated and active recovery, by which wearout can be reversed while actively applying several accelerated self-healing techniques, such as high temperature and negative voltages. Different from previous solutions of coping with wearout issues (e.g. BTI) by “tolerating”, “slowing down” or “compensating”, which still leave the irreversible (permanent) wearout component unchecked, the proposed solution is able to fully avoid the irreversible wearout through periodic rejuvenation, and this is inspired by the explored frequency dependent behaviors of wearout and (accelerated and active) recovery based on measurements on FPGAs. We demonstrate a case where the chip can always be brought back to the fresh status by employing a pattern of 31-h regular operation (under room temperature and nominal voltage) followed by a 1-h accelerated self-healing (under high temperature and negative voltage). The proposed system integrates the notions of accelerated self-healing across multiple layers of the system stack. At the circuit level, a negative voltage generator and heating elements are designed and implemented; at the architecture level, the core can be allocated in a way such that the dark silicon or redundant resources can be healed by active elements; at the system level, right balance of stress and accelerated/active recovery can be employed by the system scheduler to fully mitigate the wearout; various wearout sensors act as the media between different layers. Overall, these techniques work together to guarantee that the whole system performs for more of the time at higher levels of performance and power efficiency by fully taking advantage of the extra opportunities enabled by the accelerated self-healing.     

Failure mechanism models for cyclic fatigue

This work illustrates design situations where mechanical fatigue under cyclic loading, of one or more components, can compromise system performance. In this failure mechanism, damage accumulates with each load cycle, thereby causing a physical wearout failure mechanism. Phenomenological continuum length-scale models, based on micromechanical considerations, are presented to predict the onset (or initiation) of fatigue cracking in ductile materials. Fatigue crack propagation is modeled with continuum fracture mechanics principles. The number of load cycles required to cause failure is predicted based on these models. Approaches for modeling creep fatigue interactions are briefly discussed. Analytic physics-of-failure method and examples are presented for designing against wearout failure due to cyclic fatigue. These models can be implemented in an engineering design environment. The associated stress analysis requires numerical finite element techniques in many cases. The associated material property characterization techniques have matured since the 1950s and are specified in engineering handbooks     

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 replacement of an item subject to cumulative damage under periodic inspections

An item undergoes cumulative damage through use. The item fails randomly but the failure rate depends on the accumulated damage. The item is preventively replaced if it survives a certain damage limit at periodic inspections; on failure, it is replaced immediately. The optimal damage limit for preventive replacement which minimizes the long-run expected cost rate is derived. It is unique if an item has increasing damage-dependent failure rate. Numerical example for a stationary gamma process with Weibull distributed failure is given.     

Failure mechanism models for electromigration

This tutorial illustrates situations where electromigration (a wearout failure mechanism) in electronic devices can degrade performance. Electromigration and its relation to microstructure is discussed. Temperature considerations are treated. A practical model for electromigration and two application examples of it are given. Qualitative design procedures for avoiding solid-state electromigration failure are briefly discussed