Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Sepehrifar, Mohammad

Committee Member

Qian, Chuanxi

Committee Member

Woody, Jonathan R.

Committee Member

Zhou, Qian

Committee Member

Wu, Tung-Lung

Date of Degree

12-13-2019

Original embargo terms

Worldwide

Document Type

Dissertation - Open Access

Major

Mathematical Science

Degree Name

Doctor of Philosophy

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

System testing is very time-consuming and costly, especially for complex high-cost and high-reliability systems. For this reason, the number of failures needed for the developmental phase of system testing should be relatively small in general. To assess the reliability growth of a repairable system, the generalized confidence interval and the modified signed log-likelihood ratio test for the scale parameter of the power-law process are studied concerning incomplete failure data. Specifically, some recorded failure times in the early developmental phase of system testing cannot be observed; this circumstance is essential to establish a warranty period or determine a maintenance phase for repairable systems. For the proposed generalized confidence interval, we have found that this method is not biased estimates which can be seen from the coverage probabilities obtained from this method being close to the nominal level 0.95 for all levels of γ and β. When the performance of the proposed method and the existing method are compared and validated regarding average widths, the simulation results show that the proposed method is superior to another method due to shorter average widths when the predetermined number of failures is small. For the proposed modified signed log-likelihood ratio test, we have found that this test performs well in controlling type I errors for complete failure data, and it has desirable powers for all parameters configurations even for the small number of failures. For incomplete failure data, the proposed modified signed log-likelihood ratio test is preferable to the signed log-likelihood ratio test in most situations in terms of controlling type I errors. Moreover, the proposed test also performs well when the missing ratio is up to 30% and n > 10. In terms of empirical powers, the proposed modified signed log-likelihood ratio test is superior to another test for most situations. In conclusion, it is quite clear that the proposed methods, the generalized confidence interval, and the modified signed log-likelihood ratio test, are practically useful to save business costs and time during the developmental phase of system testing since the only small number of failures is required to test systems, and it yields precise results.

URI

https://hdl.handle.net/11668/16457

Comments

generalized confidence interval||power-law process||signed log-likelihood ratio test||substitution method||system reliability||third-order approximation

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