Opportunity-based age replacement with different intensity rates

This article considers an opportunity-based age replacement model with different intensity rates. Most of the articles suppose that opportunities are generated according to a homogeneous Poisson process, where the intensity rate does not change with time. However, social, economical, and physical environments can change the intensity rate. We suppose the intensity rate changes at specific age. The occurrence of opportunities is independent to the failure of a component. Pre ventive replacement is carried out at the first opportunity after ageT. If the component breaks down then it is replaced immediately. We derive the expected cost per unit time for an infinite time horizon. An optimal policy to minimize the expected cost per unit time is derived. Finally, numerical examples are given.     

Nonparametric adaptive opportunity-based age replacement strategies

We consider opportunity-based age replacement (OAR) using nonparametric predictive inference (NPI) for the time to failure of a future unit. Based on n observed failure times, NPI provides lower and upper bounds for the survival function for the time to failure X_n+1 of a future unit which lead to upper and lower cost functions, respectively, for OAR based on the renewal reward theorem. Optimal OAR strategies for unit n+1 follow by minimizing these cost functions. Following this strategy, unit n+1 is correctively replaced upon failure, or preventively replaced upon the first opportunity after the optimal OAR threshold. We study the effect of this replacement information for unit n+1 on the optimal OAR strategy for unit n+2. We illustrate our method with examples and a simulation study. Our method is fully adaptive to available data, providing an alternative to the classical approach where the probability distribution of a unit's time to failure is assumed to be known. We discuss the possible use of our method and compare it with the classical approach, where we conclude that in most situations our adaptive method performs very well, but that counter-intuitive results can occur.     

Optimizing costs of age replacement policies

This paper continues earlier work on the best implementation procedure for an age replacement policy. Under an age replacement policy, a stochastically failing unit is replaced at failure or after being in service for x units of time, whichever comes first. Sequentially estimating φ, the optimal replacement time, produces substantial cost savings. In this paper the rate of convergence of the actual costs to the theoretical optimal cost is studied. For any sequential procedure satisfying some mild measurability conditions, it is shown that with probability one the rate of convergence of the cost can be described based on the rate of convergence of the estimator of φ. Further, a sequential procedure is described whose cost converges to the optimal cost more rapidly than known competing procedures. For this procedure, the rate of convergence of the costs is further described by a result which states that an average actual cost per unit, when suitably standardized, converges in distribution to a normal random variable.     

ε-Forced adaptive policy in age replacement

We consider the problem of minimizing the long-run average cost per unit time in age replacement with an unknown failure distribution. Utilizing the idea of ε-forced choices, which may be thought of as a modification of forced choice circles given by Fox and Rolph (Adaptive policies for Markov renewal programs, Ann. Statist.50 (1973), 334–341), we construct the adaptive policy which has a non-parametrically good property and is Bayes against a Dirichlet process prior.     

Optimal spare ordering policy for preventive replacement under cost effectiveness criterion

This paper presents a spare ordering policy for preventive replacement with age-dependent minimal repair and salvage value consideration. The spare unit for replacement is available only by order and the lead-time for delivering the spare due to regular or expedited ordering follows general distributions. To analyze the ordering policy, the failure process is modelled by a non-homogeneous Poisson process. By introducing the costs due to ordering, repairs, replacements and downtime, as well as the salvage value of an un-failed system, the expected cost effectiveness in the long run are derived as a criterion of optimality. It is shown, under certain conditions, there exists a finite and unique optimum ordering time which maximizes the expected cost effectiveness. Finally, numerical examples are given for illustration.     

Efficiency consideration of generalized age replacement policy

Under the generalized age replacement policy, the system is replaced either at the predetermined age or upon failure if its corresponding repair time exceeds the threshold, whichever comes first. In this paper, we investigate the optimal choice of the pre‐determined preventive replacement age for a nonwarranted system, which minimizes the expected cost rate during the life cycle of the system from the customer's perspective under certain cost structures. Furthermore, we discuss several properties of such a generalized age replacement policy in comparison with the traditional age replacement policy. An efficiency, which represents the fractional time that the system is on, is defined under the proposed generalized age replacement policy and its monotonicity properties are investigated as well. The main objective of this study is to investigate the advantageous features of the generalized age replacement policy over the traditional age replacement policy with regard to the availability of the repairable system. Assuming that the system deteriorates with age, we illustrate our proposed optimal policies numerically and observe the impact of relevant parameters on the optimal preventive replacement age.     

Markov decision processes with a minimum-variance criterion

We consider the optimization of the variance of the sum of costs as well as that of an average expected cost in Markov decision processes with unbounded cost. In case of general state and action space, we find the stationary policy which makes the average variance as small as possible in the class of policies which are ε-optimal in an average expected cost.     

Lost-sales inventory systems with a service level criterion

Competitive retail environments are characterized by service levels and lost sales in case of excess demand. We contribute to research on lost-sales models with a service level criterion in multiple ways. First, we study the optimal replenishment policy for this type of inventory system as well as base-stock policies and (R, s, S) policies. Furthermore, we derive lower and upper bounds on the order-up-to level, and we propose efficient approximation procedures to determine the order-up-to level. The procedures find values of the inventory control variables that are close to the best (R, s, S) policy and comply to the service level restriction for most of the instances, with an average cost increase of 2.3% and 1.2% for the case without and with fixed order costs, respectively.     

Locating an undesirable facility with a minimax criterion

The problem considered in this paper involves the location of an undesirable facility such that the maximum weighted inverse square distance from the facility to n given points is minimized. The region in which the facility is to be located is bounded and contains the n points with which the facility to be located will interact. Applications can include siting an undesirable facility that produces some form of pollutant such as radiation, noise and some gases. Any problem that involves the location of a facility that emits pollutants whose concentrations follow the inverse square law is a candidate for the use of this work. A mathematical programming algorithm is developed for the situation in which the location problem involves a convex polygonal region. An interactive computer graphics approach is described for the case when the location problem involves a general region.     

Adaptive age replacement strategies based on nonparametric predictive inference

We consider an age replacement problem using nonparametric predictive inference (NPI) for the lifetime of a future unit. Based on n observed failure times, NPI provides lower and upper bounds for the survival function for a future lifetime X_n+1, which are lower and upper survival functions in the theory of interval probability, and which lead to upper and lower cost functions, respectively, for age replacement based on the renewal reward theorem. Optimal age replacement times for X_n+1 follow by minimizing these cost functions. Although the renewal reward theorem implicitly assumes that the corresponding optimal strategy will be used for a long period, we study the effect on this strategy when the observed value for X_n+1, which is either an observed failure time or a right-censored observation, becomes available. This is possible due to the fully adaptive nature of our nonparametric approach, and the next optimal strategy will be for X_n+2. We compare the optimal strategies for X_n+1 and X_n+2 both analytically and via simulation studies. Our NPI-based approach is fully adaptive to the data, to which it adds only few structural assumptions. We discuss the possible use of this approach, and indeed the wider importance of the conclusions of this study to situations where one wishes to combine the statistical aspects of estimating a lifetime distribution with the more traditional operational research approach of determining optimal replacement strategies for lifetime distributions that are assumed to be known.     

Quantifying the risk in age and block replacement policies

Preventive maintenance policies have been studied in the literature without considering the risk due to the cost variability. In this paper, we consider the two most popular preventive replacement policies, namely, age and block replacement policies under long-run average cost and expected unit time cost criteria. To quantify the risk in the preventive maintenance policies, we use the long-run variance of the accumulated cost over a time interval. We numerically derive the Risk-sensitive preventive replacement policies and study the impact of the Risk-sensitive optimality criterion on the managerial decisions. We also examine the performance of the expected unit time cost criterion as an alternative to the traditional long-run average cost criterion.     

Control according to a quality criterion with classification errors

Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, PP. 77–83, 1984.     

Periodic review inventory systems with a service level criterion

Full-cost inventory models are mostly studied in the literature, whereas service level constraints are more common to be observed in practical settings. In this paper, we consider periodic review inventory systems with service level restrictions. The control of such inventory systems is limited to (s, S)-type policies in the literature. To the best of our knowledge, we are the first authors to compare such policies with optimal replenishment policies, and illustrate an average cost difference of 0.64%. This justifies the use of these popular (s, S) policies in practice. Furthermore, we propose a new one-dimensional search procedure that is bounded to set the reorder level s and order-up-to level S, whereas the solution space is unbounded and two dimensional. Our heuristic procedure is guaranteed to satisfy the service level constraint and numerical experiments illustrate that it results in an average cost deviation of 1–2% compared with the best (s, S) policy. Consequently, it significantly outperforms all existing procedures from literature, both in service and costs.     

Locating a competitive facility in the plane with a robustness criterion

A new model for locating a competitive facility in the plane in a robust way is presented and embedded in the literature on robustness in facility location. Its mathematical properties are investigated and new sharp bounds for a deterministic method that guarantees the global optimum are derived and evaluated.     

A change point estimation problem related to age replacement policies

The mean time to failure (MTTF) function plays a vital role in the theory of age replacement policies. The point at which the MTTF function changes trend has important implications in the context of cost optimization in such policies. We develop a general methodology for change point estimation in this scenario and also establish the strong consistency of the proposed estimator. We also examine the performance of our estimator by applying it to simulated and real life data sets.     

A stability criterion for a neutral difference equation with delay

A stability criterion for a neutral difference equation with delay is established which extends and improves a result of Ladas et al. [1]. Our derivation is based on Lyapunov's direct method for stability, and avoids the approach employed by Ladas et al. who had considered asymptotic behaviors of oscillatory and nonoscillatory solutions.     

Softness of MALL proof-structures and a correctness criterion with Mix

We show that every MALL proof-structure [9] satisfies the property of softness, originally a categorical notion introduced by Joyal. Furthermore, we show that the notion of hereditary softness precisely captures Girards algebraic restriction of the technical condition on proof-structures. Relying on this characterization, we prove a MALL+Mix sequentialization theorem by a proof-theoretical method, using Girards notion of jump. Our MALL+Mix correctness criterion subsumes the Danos/Fleury-Retoré criterion [6] for MLL+Mix.This work was supported by Grant-in-Aid for Young Scientists of Ministry of Education, Science and Culture of Japan.Mathematics Subject Classification (2000):03F52, 03F07, 03F03Revised version: 9 August 2003