Woody, Jonathan R.
Date of Degree
Original embargo terms
Complete embargo for 1 year||forever||12/15/2020
Dissertation - Open Access
Doctor of Philosophy
College of Arts and Sciences
Department of Mathematics and Statistics
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.
Chumnaul, Jularat, "Inferences on the power-law process with applications to repairable systems" (2019). Theses and Dissertations MSU. 2700.