Asia-Pacific Journal of Operational Research

This paper addresses statistical estimation problems of the optimal repair-cost limits minimizing the long-run average costs per unit time in discrete seting. Two discrete repair-cost limit replacement models with/without imperfect repair are considered. We derive the optimal repair-cost limits analytically and develop the statistical non-parametric procedures to estimate them from the complete sample of repair cost. Then the discrete total time on test (DTTT) concept is introduced and applied to propose the resulting estimators. Numerical experiments through Monte Carlo simulation are provided to show their asymptotic convergence properties as the number of repair-cost data increases. A comprehensive bibliography in this research topic is also provided.

Traditional economic manufacturing quantity (EMQ) model addressed the perfect production for product. However, there possibly exists the defective product in the production process. In this paper, we present a modified EMQ model with shortage based on considering the product revenue and the inventory cost. The economic production run length, the maximum shortage level, and the optimal warranty period are simultaneously determined for obtaining the maximum expected total profit per year. The numerical example and the sensitivity analysis are further provided for illustration.

We propose the performance evaluation method for the multi-task system with software reliability growth process. The software fault-detection phenomenon in the dynamic environment is described by the Markovian software reliability model with imperfect debugging. We assume that the cumulative number of tasks arriving at the system follows the homogeneous Poisson process. Then we can formulate the distribution of the number of tasks whose processes can be complete within a prespecified processing time limit with the infinite-server queueing model. From the model, several quantities for software performance measurement considering the real-time property can be derived and given as the functions of time and the number of debuggings. Finally, we present several numerical examples of the quantities to analyze the relationship between the software reliability characteristics and the system performance measurement.

This investigation elucidates the feasibility of monitoring a process for which observational data are largely autocorrelated. Special causes typically affect not only the process mean but also the process variance. The EWMA control chart has recently been developed and adopted to detect small shifts in the process mean and/or variance. This work extends the EWMA control chart, called the generally weighted moving average (GWMA) control chart, to monitor a process in which the observations can be regarded as a first-order autoregressive process with a random error. The EWMA and GWMA control charts of residuals used to monitor process variability and to monitor simultaneously the process mean and variance are considered to evaluate how average run lengths (ARLs) differ in each case.

From the literature, it is known that preventive maintenance (PM) can reduce the deterioration of system or equipment to a younger level. Researchers usually develop optimal PM policies based on the assumption that the PM can reduce system's age or failure rate. However, the PM actions, such as cleaning, adjustment, alignment, and lubrication work, may not always reduce system's age or failure rate. Instead, it may only reduce the degradation rate of the system to a certain level. In addition, most of the existing optimal PM policies are developed by minimizing the expected cost rate only. Yet, as demonstrated in this paper, the system will have very low reliability at the time of preventive replacement if the reliability limit is not considered.

Hence, this paper is to develop an optimal periodic PM model by minimizing the expected cost rate per unit time with the consideration of reliability limit for repairable systems with degradation rate reduction after each PM. The improvement factor method is used to measure the reduction effect of the degradation rate. The algorithm for searching the optimal solutions for this PM model is developed. Examples are also presented with discussions of parameter sensitivity and special cases.

In this paper, the manufacturing lead time in a production system with maintenance period, non-renewal BMAP (Batch Markovian Arrival process) input and bilevel threshold control is analyzed. The factorization principle is used to derive the distribution of the manufacturing lead time and the mean value. A numerical example is provided to see the effect of the non-renewal input on the system performance.

This paper deals with the analysis of uncertain parameters in the (S - 1, S) inventory control policy. In order to determine the number of spare parts under the policy, parameters in a probability model for the number of failures during a replenishment lead time should be interpreted first. In case of the negative binomial distributed failures, the presented interpretation facilitates the incorporation of experts' opinions into the estimation of uncertain parameters. Determination of parameters via their interpretation is useful for deciding a service level in the area of reliability-based inventory control.

This paper presents a combined framework of Multi-Objective Generic Algorithm (MOGA) and Monte Carlo Simulation (MCS) in order to improve backbone topology by leveraging the Virtual Link (VL) system in an hierarchical Link-State (LS) routing domain. Given that the sound backbone topology structure has a great impact on the overall routing performance in a hierarchical LS domain, the importance of this research is evident. The proposed decision model is to find an optimal configuration of VLs that properly meets two-pronged engineering goals in installing and maintaining VLs: i.e., operational costs and network reliability. The experiment results clearly indicates that it is essential to the effective operations of hierarchical LS routing domain to consider not only engineering aspects but also specific benefits from systematical layout of VLs, thereby presenting the validity of the decision model and MOGA with MCS.

An analytical model is developed for accelerated performance degradation tests. The performance degradations of products at a specified exposure time are assumed to follow a normal distribution. It is assumed that the relationship between the location parameter of normal distribution and the exposure time is a linear function of the exposure time that the slope coefficient of the linear relationship has an Arrhenius dependence on temperature, and that the scale parameter of the normal distribution is constant and independent of temperature or exposure time. The method of maximum likelihood estimation is used to estimate the parameters involved. The likelihood function for the accelerated performance degradation data is derived. The approximated variance-covariance matrix is also derived for calculating approximated confidence intervals of maximum likelihood estimates. Finally we use two real examples for estimating the failure-time distribution, technically defined as the time when performance degrades below a specified level.