Burn-in by environmental shocks for two ordered subpopulations

Burn-in is a widely used engineering method of elimination of defective items before they are shipped to customers or put into field operation. In conventional burn-in procedures, components or systems are subject to a period of simulated operation prior to actual usage. Then those which failed during this period are scrapped and discarded. In this paper, we assume that the population of items is composed of two ordered subpopulations and the elimination of weak items by using environmental shocks is considered. Optimal severity levels of these shocks that minimize the defined expected costs are investigated. Some illustrative examples are discussed.     

Burn-in and the performance quality measures in heterogeneous populations

Burn-in is a widely used engineering method of elimination of defective items before they are shipped to customers or put into field operation. Under the assumption that a population is described by the decreasing or bathtub-shaped failure rate functions, various optimal burn-in problems have been intensively studied in the literature. In this paper, we consider a new model and assume that a population is composed of stochastically ordered subpopulations described by their own performance quality measures. It turns out that this setting can justify burn-in even in situations when it is not justified in the framework of conventional approaches. For instance, it is shown that it can be reasonable to perform burn-in even when the failure rate function that describes the heterogeneous population of items increases and this is one of the main and important findings of our study.     

Optimal burn-in for maximizing reliability of repairable non-series systems

Burn-in is a manufacturing process applied to products to eliminate early failures in the factory before the products reach the customers. Various methods have been proposed for determining an optimal burn-in time of a non-repairable system or a repairable series system, assuming that system burn-in improves all components in the system. In this paper, we establish the trade-off between the component reliabilities during system burn-in and develop an optimal burn-in time for repairable non-series systems to maximize reliability. One impediment to expressing the reliability of a non-series system is in that successive failures during system burn-in cannot be described precisely because a failed component is not detected until the whole system fails. For approximating the successive failures of a non-series system during system burn-in, we considered two types of repair: minimal repair at the time of system failure, and repair at the time of component or connection failure. The two types of repair provide bounds on the optimal system burn-in time of non-series systems.     

Burn-in considering yield loss and reliability gain for integrated circuits

This paper presents burn-in effects on yield loss and reliability gain for a lifetime distribution developed from a negative binomial defect density distribution and a given defect size distribution, after assuming that the rate of defect growth is proportional to the power of the present defect size. While burn-in always results in yield loss, it creates reliability gain only if either defects grow fast or the field operation time is long. Otherwise, burn-in for a short time could result in reliability loss. The optimal burn-in time for maximizing reliability is finite if defects grow linearly in time and is infinite if defects grow nonlinearly in time. The optimal burn-in time for minimizing cost expressed in terms of both yield and reliability increases in the field operation time initially but becomes constant as the field operation time is long enough. It is numerically shown that increasing mean defect density or defect clustering increases the optimal burn-in time.     

Determination of the optimal accelerated burn-in time under Arrhenius–Lognormal distribution assumption

Burn-in has been widely used as an effective procedure for screening out failed electronic products during the early-failure period, before shipment to the customers. Environmental stress such as temperature is increasingly being used to effectively shorten the burn-in time, and this method is usually called an accelerated burn-in test. When different stress levels are chosen for the burn-in operation, the burn-in times must be determined. An Arrhenius–Lognormal distribution can describe the lognormal lifetime of electronic products under different temperature levels. In this paper, the Arrhenius–Lognormal distribution and its mean residual life function are applied to the accelerated burn-in cost model, and a genetic algorithm is used to solve for the optimal burn-in time. We choose a real TFT–LCD module as an example, and determine its optimal accelerated burn-in time. A sensitivity analysis of the TFT–LCD module case shows the effect of model parameters on optimal burn-in time.     

Spatial Autocorrelation for Subdivided Populations with Invariant Migration Schemes

For populations with geographic substructure and selectively neutral genetic data, the short term dynamics is a balance between migration and genetic drift. Before fixation of any allele, the system enters into a quasi equilibrium (QE) state. Hössjer and Ryman (2012) developed a general QE methodology for computing approximations of spatial autocorrelations of allele frequencies between subpopulations, subpopulation differentiation (fixation indexes) and variance effective population sizes. In this paper we treat a class of models with translationally invariant migration and use Fourier transforms for computing these quantities. We show how the QE approach is related to other methods based on conditional kinship coefficients between subpopulations under mutation-migration-drift equilibrium. We also verify that QE autocorrelations of allele frequencies are closely related to the expected value of Moran’s autocorrelation function and treat limits of continuous spatial location (isolation by distance) and an infinite lattice of subpopulations. The theory is illustrated with several examples including island models, circular and torus stepping stone models, von Mises models, hierarchical island models and Gaussian models. It is well known that the fixation index contains information about the effective number of migrants. The spatial autocorrelations are complementary and typically reveal the type of migration (local or global).     

Joint optimization of process improvement investments for supplier–buyer cooperative commerce

This research focuses on supporting the formation of strategic alliances through the concept of cooperative commerce, where suppliers and buyers work together to jointly optimize their business. The general goal of this research is to examine existing cooperative commerce models for obstacles that would hinder their successful implementation into modern industrial applications and to address those shortcomings. Total annual cost equations are formulated to capture the joint total relevant cost of cooperative commerce business relationships. These total joint relevant cost models will include terms that capture the ordering cost, holding cost, and cost of quality, as well as any applicable investment cost for process improvements, consistent with traditional economic order quantity and economic production quantity theory. This research corrects a modelling/computational error found in the literature that led to underestimation of the effectiveness of process improvements in joint economic lot size models by 5–12%. In addition, the models are expanded to accommodate a full range of product quality inspection policies, from 0 to 100% product inspections. Furthermore, the models are modified to account for the cost of scrap generation, as well as the effects of accepting non-conforming product and rejecting conforming product during quality inspections. Once the total cost models are expanded to account for these neglected costs, the joint total relevant cost equations are minimized to find the optimal batch sizes, and the effects of each model extension on the model solution are studied. Results indicate that these extensions have a significant impact on the model results, such as reduced optimal batch sizes and increased optimal fraction conforming product.     

Weak exponential schemes for stochastic differential equations with additive noise

^** Email: cmora{at}ing-mat.udec.cl This paper develops weak exponential schemes for the numericalsolution of stochastic differential equations (SDEs) with additivenoise. In particular, this work provides first and second-ordermethods which use at each iteration the product of the exponentialof the Jacobian of the drift term with a vector. The articlealso addresses the rate of convergence of the new schemes. Moreover,numerical experiments illustrate that the numerical methodsintroduced here are a good alternative to the standard integratorsfor the long time integration of SDEs whose solutions by thecommon explicit schemes exhibit instabilities.     

Optimum Burn-in Time for a Bathtub Shaped Failure Distribution

An important problem in reliability is to define and estimate the optimal burn-in time. For bathtub shaped failure-rate lifetime distributions, the optimal burn-in time is frequently defined as the point where the corresponding mean residual life function achieves its maximum. For this point, we construct an empirical estimator and develop the corresponding statistical inferential theory. Theoretical results are accompanied with simulation studies and applications to real data. Furthermore, we develop a statistical inferential theory for the difference between the minimum point of the corresponding failure rate function and the aforementioned maximum point of the mean residual life function. The difference measures the length of the time interval after the optimal burn-in time during which the failure rate function continues to decrease and thus the burn-in process can be stopped.      

Last time buy decisions for products sold under warranty

Manufacturers supplying products under warranty need a strategy to deal with failures during the warranty period: repair the product or replace it by a new one, depending on e.g. age and/or usage of the failed product. An (implicit) assumption in virtually all models is that new products to replace the failed ones are immediately available at given replacement costs. Because of the short life cycles of many products, manufacturing may be discontinued before the end of the warranty period. At that point in time, the supplier has to decide how many products to put on the shelf to replace failed products under warranty that will be returned from the field (the last time buy decision). This is a trade-off between product availability for replacement and costs of product obsolescence. In this paper, we consider the joint optimization of repair-replacement decisions and the last time buy quantity for products sold under warranty. We develop approximations to estimate the total relevant costs and service levels for this problem, and show that we can easily find near-optimal last time buy quantities using a numerical search. Comparison to discrete event simulation results shows an excellent performance of our methods.     

Two substitutable perishable product disaster inventory systems

A disaster inventory system is considered in which two substitutable items are stored for disaster management. In the event of disaster management, a particular product may become stock-out and the situation warrants that a demand for the particular product during its stock-out period may be substituted with another available similar product in the inventory. From the utility point of view, continuous review inventory models are quite appropriate in disaster inventory management. In this paper, a continuous review two substitutable perishable product disaster inventory model is proposed and analyzed. Since the inventory is maintained for disaster management, an adjustable joint reordering policy for replenishment is adopted. There is no lead time and the replenishment is instantaneous. For this model, some measures of system performance are obtained. The stationary behavior of the model is also considered. Numerical examples are also provided to illustrate the results obtained.     

Scheduling programs with repetitive projects: A comparison of a simulated annealing,a genetic and a pair-wise swap algorithm

We address the problem of scheduling in programs involving the production of multiple units of the same product. Our study was motivated by a construction program for fast naval patrol boats. Other applications of this problem include procurement of multiple copies of aircraft, spacecraft, and weapon systems. In this problem we must decide how many units of the product to assign to each of a number of available crews (individuals, teams, subcontractors, etc.). These types of problems are characterized by two potentially conflicting considerations: 1) the need to complete each unit by its contractual due date, and 2) learning effects. Because of the first consideration, there is a tendency to use multiple crews for simultaneous production, so that meeting due dates is assured. However, the second consideration encourages assigning many units to a single crew so that learning effects are maximized. We study this scheduling problem with two different penalty cost structures and develop models for both versions. The models trade-off the penalty associated with late deliveries and the savings due to learning (and possibly incentive payments for early completion). We discuss different heuristic algorithms — simulated annealing, a genetic algorithm, and a pair-wise swap heuristic — as well as an exhaustive search to determine a baseline for comparisons. Our computational results show that the pair-wise swap algorithm is the most efficient solution procedure for these models.     

Weak Drifts of Infinitely Divisible Distributions and Their Applications

Weak drift of an infinitely divisible distribution μ on ? ^d is defined by analogy with weak mean; properties and applications of weak drift are given. When μ has no Gaussian part, the weak drift of μ equals the minus of the weak mean of the inversion μ′ of μ. Applying the concepts of having weak drift 0 and of having weak drift 0 absolutely, the ranges, the absolute ranges, and the limit of the ranges of iterations are described for some stochastic integral mappings. For Lévy processes, the concepts of weak mean and weak drift are helpful in giving necessary and sufficient conditions for the weak law of large numbers and for the weak version of Shtatland’s theorem on the behavior near t=0; those conditions are obtained from each other through inversion.     

Modelling of an Homogeneous Equilibrium Mixture Model (HEM)

We present here a model for two phase flows which is simpler than the 6-equations models (with two densities, two velocities, two temperatures) but more accurate than the standard mixture models with 4 equations (with two densities, one velocity and one temperature). We are interested in the case when the two-phases have been interacting long enough for the drag force to be small but still not negligible. The so-called Homogeneous Equilibrium Mixture Model (HEM) that we present is dealing with both mixture and relative quantities, allowing in particular to follow both a mixture velocity and a relative velocity. This relative velocity is not tracked by a conservation law but by a closure law (drift relation), whose expression is related to the drag force terms of the two-phase flow. After the derivation of the model, a stability analysis and numerical experiments are presented.     

Stationary distributions for diffusions with inert drift

Consider reflecting Brownian motion in a bounded domain in ${\mathbb R^d}$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential.     

The impact of controllable production rates on the performance of inventory systems: A systematic review of the literature

The lot sizing problem has attracted the attention of researchers for more than a century, and it still belongs to the most relevant decision problems in many manufacturing companies. During the evolution of research on lot sizing, the seminal economic order quantity (EOQ) model proposed by Harris [1913. How many parts to make at once. Factory, the Magazine of Management, 10 (2), 135-136.] has remained the most popular model, despite its limitations. To support lot sizing decisions in practice, researchers have frequently extended Harris’ basic EOQ model to better reflect the characteristics of real production processes. One of these extensions is the consideration of controllable (variable) production rates, which gives production planners more flexibility in managing the build-up and depletion of inventory and in controlling costs.The aim of this paper is to provide a comprehensive and systematic overview of EPQ-type lot sizing models that consider controllable production rates. First, the paper proposes a conceptual framework that captures the characteristics of controllable production rates including the planning horizon (short vs. long term), the number of potential interventions per production run (one vs. multiple), the effect of controllable production rates on the performance of the inventory system (e.g., unit production costs, energy consumption, product quality), and the type of lot sizing model considered (e.g., two-stage models, multi-stage models, multi-item models). Secondly, the paper presents the results of a systematic literature review and evaluates the state-of-research of lot sizing models with controllable production rates. Based on the analysis of the literature, key trends are summarized and promising research opportunities are discussed.     

Regression quantiles for unstable autoregressive models

This paper investigates regression quantiles (RQ) for unstable autoregressive models. The uniform Bahadur representation of the RQ process is obtained. The joint asymptotic distribution of the RQ process is derived in a unified manner for all types of characteristic roots on or outside the unit circle. It involves stochastic integrals in terms of a sequence of independent and identically distributed multivariate Brownian motions with correlated components. The related L-estimator is also discussed. The asymptotic distributions of the RQ and the L-estimator corresponding to the nonstationary componentwise arguments can be transformed into a function of a normal random variable and a sequence of i.i.d. univariate Brownian motions. This is different from the analysis based on the LSE in the literature. As an auxiliary theorem, a weak convergence of a randomly weighted residual empirical process to the stochastic integral of a Kiefer process is established. The results obtained in this paper provide an asymptotic theory for nonstationary time series processes, which can be used to construct robust unit root tests.     

The tail empirical process of regularly varying functions of geometrically ergodic Markov chains

We consider a stationary regularly varying time series which can be expressed as a function of a geometrically ergodic Markov chain. We obtain practical conditions for the weak convergence of the tail array sums and feasible estimators of cluster statistics. These conditions include the so-called geometric drift or Foster–Lyapunov condition and can be easily checked for most usual time series models with a Markovian structure. We illustrate these conditions on several models and statistical applications. A counterexample is given to show a different limiting behavior when the geometric drift condition is not fulfilled.     

General analysis of l-out-of-2: f system exposed to cumulative damage processes

This paper presents models in l-out-of-2:F system. In Model 1, one unit is exposed to cumulative damage process and the other unit lias a constant failure rate. In Model 2, the two units are exposed to cumulative damage processes. They have exponential thresholds and exponential inter-damage times. Introducing a repair facility which repairs ail the damages one by one after the system-failure, this paper treats the joint Laplace transforms of the up and the down times. Marginal down time distributions .are calculated when there exists a repair facility for every damage.     

Normal form construction for nearly-integrable systems with dissipation

We consider a dissipative vector field which is represented by a nearly-integrable Hamiltonian flow to which a dissipative contribution is added. The vector field depends upon two parameters, namely the perturbing and dissipative parameters, and by a drift term. We study an ?-dimensional, time-dependent vector field, which is motivated by mathematical models in Celestial Mechanics. Assuming to start with non-resonant initial conditions, we provide the construction of the normal form up to an arbitrary order. To construct the normal form, a suitable choice of the drift parameter must be performed. The normal form allows also to provide an explicit expression of the frequency associated to the normalized coordinates. We also give an example in which we construct explicitly the normal form, we make a comparison with a numerical integration, and we determine the parameter values and the time interval of validity of the normal form.