Journal of Applied Mathematics
Volume 2013 (2013), Article ID 547209, 13 pages
Research Article

Evaluating the Lifetime Performance Index Based on the Bayesian Estimation for the Rayleigh Lifetime Products with the Upper Record Values

1Department of International Business, Chang Jung Christian University, Tainan 71101, Taiwan
2Department of Applied Mathematics, National Chiayi University, 300 Syuefu Road, Chiayi City 60004, Taiwan
3Department of Information Management, Shih Chien University, Kaohsiung Campus, Kaohsiung 84550, Taiwan

Received 20 October 2012; Accepted 17 December 2012

Academic Editor: Chong Lin

Copyright © 2013 Wen-Chuan Lee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Quality management is very important for many manufacturing industries. Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. Hence, the lifetime performance index is utilized to measure the performance of product, where is the lower specification limit. This study constructs a Bayesian estimator of under a Rayleigh distribution with the upper record values. The Bayesian estimations are based on squared-error loss function, linear exponential loss function, and general entropy loss function, respectively. Further, the Bayesian estimators of are utilized to construct the testing procedure for based on a credible interval in the condition of known . The proposed testing procedure not only can handle nonnormal lifetime data, but also can handle the upper record values. Moreover, the managers can employ the testing procedure to determine whether the lifetime performance of the Rayleigh products adheres to the required level. The hypothesis testing procedure is a quality performance assessment system in enterprise resource planning (ERP).