Stability Estimation for Markov Control Processes with Discounted Cost

This article explores controllable Borel spaces, stationary, homogeneous Markov processes, discrete time with infinite horizon, with bounded cost functions and using the expected total discounted cost criterion. The problem of the estimation of stability for this type of process is set. The central objective is to obtain a bounded stability index expressed in terms of the Lévy-Prokhorov metric;likewise, sufficient conditions are provided for the existence of such inequalities.

Optimization of post-warranty sequential inspection for second-hand products

This paper considers an optimal sequential inspection schedule for a second-hand product after that the free nonrenewable warranty is expired. The length of warranty is prespecified and during the warranty period, the product is minimally repaired by the dealer when it fails. Following the expiration of the non-renewing warranty, the product is inspected and upgraded sequentially a fixed number of times at the expenses of the customer.At each inspection, the failure rate of the product is reduced proportionally so that the product is upgraded. The product is assumed to deteriorate as it ages and the replacement of the product occurs when a fixed number of inspections are rendered. In addition,the intervals between two successive inspections are assumed to decrease monotonically. The main objective of this paper is to determine the optimal improvement level to upgrade the product at each inspection so that the expected maintenance cost during the life cycle of the product is minimized from the perspective of the customer. Under the given cost structures, we derive an explicit formula to obtain the expected maintenance cost incurred during the life cycle of the product and discuss the method to find the optimal level of the improvement analytically in case the failure times follow the Weibull distribution. Numerical results are analyzed to observe the impact of relevant parameters on the optimal solution.

Improving Software Quality Prediction by Noise Filtering Techniques

Accuracy of machine learners is affected by quality of the data the learners are induced on. In this paper, quality of the training dataset is improved by removing instances detected as noisy by the Partitioning Filter. The fit dataset is first split into subsets, and different base learners are induced on each of these splits. The predictions are combined in such a way that an instance is identified as noisy if it is misclassified by a certain number of base learners. Two versions of the Partitioning Filter are used： Multiple-Partitioning Filter and Iterative-Partitioning Filter. The number of instances removed by the filters is tuned by the voting scheme of the filter and the number of iterations. The primary aim of this study is to compare the predictive performances of the final models built on the filtered and the un-filtered training datasets. A case study of software measurement data of a high assurance software project is performed. It is shown that predictive performances of models built on the filtered fit datasets and evaluated on a noisy test dataset are generally better than those built on the noisy （un-filtered） fit dataset. However, predictive performance based on certain aggressive filters is affected by presence of noise in the evaluation dataset.

Optimal Age Replacement Policy with Replacement Occurrence While the Warranty is in Effect

This study considers an age replacement policy(ARP) for a repairable product with an increasing failure rate with and without a product warranty. As for the warranty policy to consider in association with such an age replacement policy, we adapt a renewable minimal repair-replacement warrant(MRRW) policy with 2D factors of failure time of the product and its corresponding repair time. The expected cost rate during the life cycle of the product is utilized as a criterion to find the optimal policies for both with and without the product warranty. We determine the optimal replacement age that minimizes the objective function which evaluates the expected cost rate during the product cycle and investigate the impact of several factors on the optimal replacement age. The main objective of this study lies on the generalization of the classical age replacement policy to the situation where a renewable warranty depending on 2D factors is in effect. We present some interesting observations regarding the effect of relevant factors based on numerical analysis.

Optimal periodic replacement policy for a warranted product subject to multi modes failure process

A complex product subjects to multiple failure modes such as minor and catastrophic failure with some probability.This paper investigates the effects of minor failure and catastrophic failure on the periodic replacement policy for a complex product supported by a warranty period.Cost models are developed and the expected optimal replacement policies are developed analytically such that long run expected life-cycle cost rate is minimized.Structural properties of the optimal replacement policies are derived for a product which fails with multiple failure modes and the failure rate is an increasing function of time.Finally,a numerical experiment is performed to show the important features of our study.

Optimal Energy Reserve Scheduling in Integrated Electricity and Gas Systems Considering Reliability Requirements

With the growing interdependence between the electricity system and the natural gas system,the operation uncertainties in either subsystem,such as wind fluctuations or component failures,could have a magnified impact on the reliability of the whole system due to energy interactions.A joint reserve scheduling model considering the cross-sectorial impacts of operation uncertainties is essential but still insufficient to guarantee the reliable operation of the integrated electricity and natural gas system(IEGS).Therefore,this paper proposes a day-ahead security-constrained unit commitment(SCUC)model for the IEGS to schedule the operation and reserve simultaneously considering reliability requirements.Firstly,the multi-state models for generating units and gas wells are established.Based on the multi-state models,the expected unserved energy cost(EUEC)and the expected wind curtailment cost(EWC)criteria are proposed based on probabilistic methods considering wind fluctuation and random failures of components in IEGS.Furthermore,the EUEC and EWC criteria are incorporated into the day-ahead SCUC model,which is nonconvex and mathematically reformulated into a solvable mixed-integer second-order cone programming(MISOCP)problem.The proposed model is validated using an IEEE 30-bus system and Belgium 20-node natural gas system.Numerical results demonstrate that the proposed model can effectively schedule the energy reserve to guarantee the reliable operation of the IEGS considering the multiple uncertainties in different subsystems and the cross-sectorial failure propagation.