Optimal replacement policy under cumulative damage model and strength degradation with applications

In many real-life scenarios, system failure depends on dynamic stress-strength interference, where strength degrades and stress accumulates concurrently over time. In this paper, we consider the problem of finding an optimal replacement strategy that balances the cost of replacement with the cost of failure and results in the minimum expected cost per unit time under cumulative damage model with strength degradation. In the most general setting, we propose to find optimal choices of three thresholds on operation time, number of arriving shocks and amount of cumulative damage such that replacement of the system due to failure or reaching any of the three thresholds, whichever occurs first, results in the minimum expected cost per unit time. The existing recommendations are applicable only under the assumption of Exponential damage distribution including Poisson arrival of shocks and/or with fixed strength. As theoretical evaluation of the expected cost per unit time turns out to be very complicated, a simulation-based algorithm is proposed to evaluate the expected cost rate and find the optimal replacement strategy. The proposed method is easy to implement having wider domain of application including non-Poisson arrival of shocks and non-Exponential damage distributions. For illustration, the proposed method is applied to real case studies on mailbox and cell-phone battery experiments.

Cost-Sensitive Classification Using Decision Trees, Boosting and MetaCost

This chapter reports results obtained from a series of studies on costsensitive classification using decision trees, boosting algorithms, and MetaCost which is a recently proposed procedure that converts an errorbased algorithm into a cost-sensitive algorithm. The studies give rise to new variants of algorithms designed for cost-sensitive classification, and provide insights into the strength and weaknesses of the algorithms. First, we describe a simple and effective heuristic of converting an error-based decision tree algorithm into a cost-sensitive one via instance weighting. The cost-sensitive version performs better than the error-based version that employs a minimum expected cost criterion during classification. Second, we report results from a study on four variants of cost-sensitive boosting algorithms. We find that boosting can be simplified for costsensitive classification. A new variant which excludes a factor used in ordinary boosting has an advantage of producing smaller trees and different trees for different scenarios; while it performs comparably to ordinary boosting in terms of cost. We find that the minimum expected cost criterion is the major contributor to the improvement of all cost-sensitive adaptations of ordinary boosting. Third, we reveal a limitation of MetaCost. We find that MetaCost retains only part of the performance of the internal classifier on which it relies. This occurs for both boosting and bagging as its internal classifier.

Optimal Network-Level Bridge Maintenance Planning Based on Minimum Expected Cost

The goal of bridge management is to determine and implement the best possible strategy that ensures an adequate level of safety at the lowest possible life-cycle cost. Although this is generally recognized, the integration of life-cycle cost analysis with bridge reliability analysis has been very limited. Moreover, this has been formulated and illustrated only for individual bridges. A framework for optimal network-level bridge maintenance planning based on minimum expected cost is presented. The goal is the minimization of the expected maintenance cost of a bridge stock with maintenance of the lifetime reliability of each bridge above an acceptable (target) level. The approach is illustrated for a stock of realistic highway bridges. Individual bridges in this stock have different ages, and their reliabilities are time dependent. The framework offers a rational basis for optimizing the resource allocation for management of a stock of gradually deteriorating bridges based on balancing life-cycle maintenance cost and lifetime reliability. This has important practical implications in the development of the optimal management strategy for the bridge stock.