Progressively interval-censored life test with acceptance sampling

[[abstract]]Considering the producer and consumer risks, the paper develops acceptance sampling procedures under the progressively interval-censored test with intermittent inspections for the exponential lifetime model. The proposed approach allows removing surviving items during the life test such that some extreme lifetimes can be sought, or the test facilities can be freed up for other tests. A reduction in testing effort and administrative convenience can be achieved by employing the proposed approach. One example is introduced for illustration.[[conferencetype]]國際[[conferencedate]]20080618~20080620[[conferencelocation]]Dalian, Chin

Parameter Estimation of the Burr Type XII Distribution with a Progressively Interval-Censored Scheme Using Genetic Algorithm

[[abstract]]Burr type XII distribution (BXIID) has been widely used to model lifetime data sets. The flexibility of the BXIID is established due to its two shape parameters. To save test time and cost, the BXIID parameters can be inferred by using the maximum likelihood estimation method based on a date set with incomplete lifetime information. But the maximum likelihood estimates (MLEs) of BXIID parameters could have a big bias and mean squared error (MSE) if the sample size is small or the MLEs are evaluated with improper initial parameters. In this study, a progressively interval-censored (PIC) scheme is used to implement the life test, and the Genetic Algorithm (GA) is applied to reduce the bias and MSEs of the MLEs of the BXIID parameters. An extensive Monte Carlo simulation was conducted to evaluate the estimation performance of the typical maximum likelihood estimation method (TMLEM) and GA. Simulation results show that the GA is competitive with the TMLEM in terms of resulting in a smaller bias and MSE in parameter estimation.[[notice]]補正完

Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions

[[abstract]]A composite dynamic system (CDS) is composed of multiple components. Each component failure can equally induce higher loading on the surviving components and, hence, enhances the hazard rate of each surviving component. The applications of CDS and the reliability evaluation of CDS has earned more attention in the recent two decades. Because the lifetime quality of components could be inconsistent, the lifetimes of components in the CDS is considered to follow heterogeneous baseline Gompertz distributions in this study. A power-trend hazard rate function is used in order to characterize the hazard rate of the CDS. In order to overcome the difficulty of obtaining reliable estimates of the parameters in the CDS model, the Bayesian estimation method utilizing a hybrid Gibbs sampling and Metropolis-Hasting algorithm to implement the Markov chain Monte Carlo approach is proposed for obtaining the Bayes estimators of the CDS parameters. An intensive simulation study is carried out to evaluate the performance of the proposed estimation method. The simulation results show that the proposed estimation method is reliable in providing reliability evaluation information for the CDS. An example regarding the service system of small electric carts is used for illustration.[[notice]]補正完

Parameter estimation for the composite dynamic systems based on sequential order statistics from Burr type XII mixture distribution

[[abstract]]Considering the impact of the heterogeneous conditions of the mixture baseline distribution on the parameter estimation of a composite dynamical system (CDS), we propose an approach to infer the model parameters and baseline survival function of CDS using the maximum likelihood estimation and Bayesian estimation methods. The power-trend hazard rate function and Burr type XII mixture distribution as the baseline distribution are used to characterize the changes of the residual lifetime distribution of surviving components. The Markov chain Monte Carlo approach via using a new Metropolis–Hastings within the Gibbs sampling algorithm is proposed to overcome the computation complexity when obtaining the Bayes estimates of model parameters. A numerical example is generated from the proposed CDS to analyze the proposed procedure. Monte Carlo simulations are conducted to investigate the performance of the proposed methods, and results show that the proposed Bayesian estimation method outperforms the maximum likelihood estimation method to obtain reliable estimates of the model parameters and baseline survival function in terms of the bias and mean square error[[notice]]補正完

Bayesian sampling plans with interval censoring

This paper employs Bayesian approach to establish acceptance sampling plans for life tests with interval censoring. Assume that interval data have a multinomial distribution, and the interval probabilities are random and vary from lot to lot according to a conjugate prior of Dirichlet distribution. A Bayes risk is defined with a suitable loss function and a predictive distribution. Optimal Bayesian sampling plans are determined by minimizing the Bayes risk per lot. An example is used and some optimal Bayesian sampling plans with three equally-spaced intervals are tabulated for illustration. Sensitivity analysis are conducted to evaluate the influence of the parameter of prior distribution, the cost per sampled item and the cost per used unit time on the proposed Bayesian sampling plans

On monitoring of multiple non-linear profiles

Most state-of-the-art profile monitoring methods involve studies of one profile. However, a process may contain several sensors or probes that generate multiple profiles over time. Quality characteristics presented in multiple profiles may be related multiple aspects of product or process quality. Existing charting methods for simultaneous monitoring of each multiple profile may result in high false alarm rates. Or worse, they cannot correctly detect potential relationship changes among profiles. In this study, we propose two approaches to detect process shifts in multiple non-linear profiles. A simulation study was conducted to evaluate the performance of the proposed approaches in terms of average run length under different process shift scenarios. Pros and cons of the proposed methods are discussed. A guideline for choosing the proposed methods is introduced. In addition, a hybrid method combining the salient points of both approaches is explored. Finally, a real-world data-set from a vulcanisation process is used to demonstrate the implementation of the proposed methods

Optimal maintenance time for imperfect maintenance actions on repairable product

[[abstract]]This paper develops a maintenance strategy for repairable products that combines imperfect maintenance actions at pre-scheduled times and minimal repair actions for failures. Under a power law process of failures, an expected total cost is developed that involves the sum of the total cost of imperfect preventive maintenances and the expected total cost of minimal repairs. Moreover, a searching procedure is provided to determine the optimal maintenance schedule within a finite time span of warranty. When the parameters of the power law process are unknown, the accuracy of the estimated maintenance schedule is evaluated based on data through an asymptotic upper bound for the difference of the true expected total cost and its estimate. The proposed method is applied to an example regarding the maintenance of power transformers and the performance of the proposed method is investigated through a numerical study. Numerical results show that the proposed maintenance strategy could save cost whether an imperfect maintenance action or the perfect maintenance action is implemented.[[journaltype]]國外[[incitationindex]]SCI[[booktype]]紙本[[countrycodes]]GB

Statistical Process Control for Monitoring a Diffusion Process

[[abstract]]This study presents a new statistical process control (SPC) procedure for a process together with degradation and diffusion effects. One of such examples is the initial cool-down process of high-pressure hose production. The air temperature readings during the initial cool-down process often exhibit a non-increasing trend with a diffusion effect in that profiles generated from cycle to cycle deviates from each other more over time. A new charting procedure using the Wiener diffusion model is developed in this article. A real data set, generated from the cool-down process of high-pressure hose production, is used to demonstrate the application of proposed method.[[journaltype]]國外[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]JP

A DESIGN OF OPTIMUM SCREENING PROCEDURE USING SURROGATE VARIABLE

[[abstract]]In this article, a new profit function based on a surrogate variable of its performance variable is provided to develop an optimum screening procedure for manufacturing. The optimum screening procedure helps producers set up the mean level of manufacturing and the screening limits of a surrogate variable to reach a maximum expected profit per unit. The proposed method is useful when the products in the manufacturing process are classified into different grades and sold in two alternate markets. A cement-packing example is used to illustrate the proposed method, and a numerical study is conducted to evaluate the effects of cost components and distribution parameters on the expected profit per unit. The proposed screening procedure provides a significant improvement over existing methods in term of higher expected profit per unit.[[notice]]補正完畢[[journaltype]]國外[[booktype]]紙本[[countrycodes]]SG