Optimal continuous-wear limit replacement under periodicinspections

An item breaks down when it wears continuously beyond a certain threshold. The item is preventively replaced as the wear at periodic inspections exceeds a certain wear limit; on failure, it is replaced immediately. The optimal wear limit for preventive replacement that minimizes the long-run total average-cost rate is derived. A numerical example demonstrates its computability     

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.     

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     

Optimal replacement policies for systems with multiple standbycomponents

The authors consider two new preventive replacement policies for a multiple-component cold-standby system. The failure rate of the component in operation is constant. The system is inspected at random points over time to determine whether it is to be replaced. The replacement decision is based on the number of failed components at the time of inspection. There are two replacement options if the complete system fails during operation: (i) replace the system if an inspection reveals that it has failed (system failure is not self-announcing), and (ii) replace the system the instant it fails (system failure is self-announcing). There is a threshold value on the number of failed components (at the time of inspection) which minimizes the mean total cost. The authors develop a simple efficient procedure to find the optimal threshold value. They compare the cost of operating a system that is inspected at random points in time, with the cost of operating a system that is monitored continuously through an attached monitoring device, and discuss cost tradeoffs     

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     

Load-capacity interference and the bathtub curve

Load-capacity (stress-strength) interference theory is used to derive a heuristic failure rate for an item subjected to repetitive loading which is Poisson distributed in time. Numerical calculations are performed using Gaussian distributions in load and capacity. Infant mortality, constant failure rate (Poisson failures), and aging are shown to be associated with capacity variability, load variability, and capacity deterioration, respectively. Bathtub-shaped failure rate curves are obtained when all three failure types are present. Changes in load or capacity distribution parameters often strongly affect the quantitative behavior of the failure-rate curves, but they do not affect the qualitative behavior of the bathtub curve. Neither is it likely that the qualitative behavior will be affected by the use of nonGaussian distributions. The numerical results, however, indicate that infant mortality and wear-out failures interact strongly with load variability. Thus bathtub curves arising from this model cannot be represented as simple superpositions of independent contributions from the three failure types. Only if the three failure types arise from independent failure mechanisms or in different components is it legitimate simply to sum the failure rate contributions     

Estimation in a random censoring model with incomplete information:exponential lifetime distribution

Analysis of methods and simulation results for estimating the exponential mean lifetime in a random-censoring model with incomplete information are presented. The instant of an item's failure is observed if it occurs before a randomly chosen inspection time and the failure is signaled. Otherwise, the experiment is terminated at the instant of inspection during which the true state of the item is discovered. The maximum-likelihood method (MLM) is used to obtain point and interval estimates for item mean lifetime, for the exponential model. It is demonstrated, using Monte Carlo simulation, that the MLM provides positively biased estimates for the mean lifetime and that the large-sample approximation to the log-likelihood ratio produces accurate confidence intervals. The quality of the estimates is slightly influenced by the value of the probability of failure to signal. Properties of the Fisher information in the censored sample are investigated theoretically and numerically     

Material failure mechanisms and damage models

This work introduces a tutorial series on material failure mechanisms and damage models to familiarize nonspecialists with the fundamentals of failure mechanisms in engineering assemblies. Since failure is a complicated concept, four simple conceptual models for failure are discussed: stress-strength, damage-endurance, challenge-response, and tolerance-requirement. The specific failure mechanisms depend on material or structural defects, damage induced during manufacture and assembly, and on conditions during storage and field use. Conditions that affect the state of an item are broadly termed stresses (loads), e.g., mechanical stress and strain, electrical current and voltage, temperature, humidity, chemical environment, and radiation. The effects of stresses are influenced by geometry, constitutive and damage properties of the materials, manufacturing parameters, and the application environment     

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∗.     

Cost-benefit analysis of one-server two-unit replacement system with imperfect switch

This paper deals with the cost-benefit analysis of a one-server two-unit system with imperfect switch where the unit, if available, is preferred to the standby. The repair time of an item (unit/standby/switch is arbitrarily distributed while failure rate of an item is constant. Initially, the unit is switched on (switch is working at t = 0). The repair of the switch is given preference after the current repair of the unit or standby is over. Explicit expressions for the expected up-time due to the unit, expected up-time due to the standby; expected busy period of the server due to the unit, due to the standby and that due to the switch are obtained to carry out the cost-benefit analysis.     

Reliability of Two Items in Sequence with Sensing and Switching

This paper discusses a mathematical model of a redundant device consisting of an active item, a standby item, and a failure-sensing switch. It is assumed that the failure rate of the standby item is less than that of the active item and that there is no repair. The results obtained for the reliability of the device represent several improvements over known results.     

Bayes credibility estimation of an exponential parameter for randomcensoring and incomplete information

A Bayes interval estimation for an exponential parameter Θ in a model of random censoring with incomplete information is investigated. The instant of item failure is observed if it occurs before a randomly chosen inspection time and the failure was signaled; otherwise, the experiment is terminated at the instant of inspection. An explicit expression for the posterior PDF (probability distribution function) of the parameter is derived, and a normal approximation to it based on Taylor expansion near the maximum likelihood estimate is suggested. The results of an extension simulation showed that the reparametrization Θ₁=log Θ appreciably increases the accuracy of the normal approximation. Highly accurate highest posterior density intervals for Θ₁ are derived in a closed form for a normal prior for Θ₁ or, equivalently, for the lognormal prior on Θ     

Open & Short Circuit Reliability of Systems of Identical Items

The paper is about reliability and risk analysis of systems of s-identical, s-independent items in terms of their probabilities of failure in open and short circuit. It is importantly assumed that the system is operational while at least one (or as a special case, more) operational item is connected physically to the input and output of the system either directly or through other good or shorted items and there is no overall system short-circuit. Two or more items so connected, whether in physical series or parallel or any combination have the same effect as a single item, and such redundancy does not alter the item failure probabilities. The probabilities could be those arising from identical, s-independent distributions (iid) over a fixed period with fixed starting conditions or alternatively probabilities of failure upon switching on. The work applies therefore to systems of adjustable or self-adjusting items such as amplifiers, rheostats, or fluid control valves, but not, for example, to systems of fixed resistors if the output values of voltage and current are important. Methods are developed for finding the most reliable physical arrangements of 2, 3, 4, items given the item failure probabilities. These display symmetry arising from the equivalence of the reliability block diagrams for items in physical series failing short and items in physical parallel failing open and vice versa. Three or four items are often sufficient to meet reliability requirements.     

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     

Replacement Policies for a Unit with Random and Wearout Failures

This paper considers three replacement models with random and wearout failures; a) the unit is replaced at failure, b) the unit undergoes minimal repair at failure, and c) the unit is replaced at failure only in a wearout failure period. Optimum replacement policies which minimize the s-expected cost rate for each model are discussed.     

Plasma-charging damage in ultra-thin gate oxide

The impact of plasma-charging damage on ultra-thin gate oxide is discussed. The argument for plasma-charging damage becoming less important is examined. Without considering the area and failure rate scaling effect, one mode of charging damage does become less important while other modes continue to be a serious problem. After scaling is properly accounted for, all charging damage remains a serious problem. The problem is more serious for thinner gate oxides because its life time becomes a limiting factor in device scaling. No one has yet made proper measurement for charging damage in the ultra-thin gate oxide regime. Stress-induced leakage current with properly designed tester may be used for ultra-thin gate-oxide damage measurement if one has the required sensitivity in the measurement. However, one must take care to use stress to reveal the latent defects that are hidden by annealing.     

Optimal number of major failures before replacement

When the repair cost of a failed system is random, it is no longer meaningful to expend more than the replacement cost on a catastrophic failure. This paper presents a mathematical model that uses two cost limits to combine and extend the replacement models based on minor-failure number[8] and constant repair cost limit[5] for general time-to-failure distributions. When the failed system requires repair, it is first inspected and the repair cost is estimated. Minimal repair is only then undertaken if the estimated cost is less than the minor repair-cost limit; or if the estimated cost is less than the replacement cost and the predetermined major-failure number is not reached. An example with a Weibull time-to-failure distribution and a negative exponential distribution of estimated repair cost is given to illustrate the computational results.     

Hazard Versus Renewal Rate of Electronic Items

Two different indexes, the hazard rate and the renewal rate, which are implied by conventional uses of the bathtub-shaped curve, are often noted in reliability. The hazard rate is applicable for a single failure time of each item, such as that of a nonrepairable part; the renewal rate is applicable for multiple failure times of each item, such as those of repairable equipment. Occasionally, remarks are made in the literature concerning the mathematical models for the bathtub-shaped hazard rate but not for the renewal rate. Furthermore, bathtub-shaped hazard and renewal curves as conventionally used are each based on certain assumptions concerning failure time distributions. Little data have been recorded for electronic parts and equipment which would substantiate the widespread use of the conventional implications of the bathtub-shaped hazard and renewal rates. The validity of the assumptions concerning the underlying distributions of failure times affects the accuracy of the results of reliability analyses, such as prediction, data analysis, formal assurance tests, operational planning, and maintenance planning. A study of the applications-oriented literature suggests that the distinction between the hazard rate and the renewal rate, as well as some associated implications, are not generally appreciated. Thus the existing situation is apt to lead engineers astray as well as others with application interests. Basic concepts and definitions are emphasized and extensions and implications are sketched. References are selected and noted for those interested in further pursuit.     

关联规则快速聚焦算法研究与实现

提出了一种实用的快速聚焦关联规则更新算法。在需要反复调整最小支持度的情况下,如何充分利用以往挖掘过程中的信息,避免多次扫描数据集;在如何有针对性的产生候选项集,从而减少候选集的规模;在如何提高候选项集的支持事务计数的效率等方面进行了研究,给出了算法的具体实现。通过分析,本算法是可行的。     

Coupling damage and reliability modeling for creep and fatigue of solder joint

Solder joint often plays a crucial role in the normal operation of electronic equipment due to its unique material properties and harsh working condition, making it very important to carry out the accurate reliability analysis of solder joint. The low-cycle fatigue due to temperature cycling and the creep brought by continuous high temperature are two dominant failure modes of the solder joint. Current modeling methods for these two mechanisms mainly focus on failure process of each mechanism separately, with little consideration of the coupling relationship in the material properties. This paper introduces a coupling damage model considering both low-cycle fatigue and creep. The coupling relationship between these two failure mechanisms is investigated with the effects of creep strain rate on the ductility and the effects of damage on mechanical properties of solder joint. The analysis of the former mechanism concerns the fatigue parameter of Coffin-Manson model, while the latter one focuses on the applied stress increasing with the accumulation of damage. Further, considering that creep degradation rate would increase once the cumulative damage reaches a trigger threshold, a generalized cumulative damage model is developed. Based on this assumption, a reliability model for solder joint considering the uncertainty of model parameters is then proposed. Finally, a case study of a lead-free solder joint is given to validate this method.