Degree Type


Date of Award


Degree Name

Doctor of Philosophy



First Advisor

William Q. Meeker, Jr.


With today's high technology, traditional life tests for highly reliable products often result in few or even no failures. This makes it difficult to assess product reliability. For some products, degradation measures taken over time are useful for reliability assessment. By defining product failure in terms of a specified level of degradation, we study the distribution of time to failure for the degradation measures. We develop general statistical methods for using degradation measures to estimate a time-to-failure distribution. These methods employ Monte Carlo simulation to obtain point estimates and confidence intervals for reliability assessment and these can be used with a much more general and practical class of degradation models. An important application for degradation analysis, as an alternate approach in assessing reliability, is in problems where few or even no failures are expected in a life test. It is thus of interest to know how degradation analysis compares with failure time analysis. We make such a comparison, in terms of relative efficiency: the ratio of the asymptotic variances of an estimated p quantile of time-to-failure distribution, by using a simple, but physically reasonable, degradation model. Even for such a simple model, the comparison is impossible to do analytically and we use numerical evaluation. We also look at how the number of inspections, the amount of measurement error, and the quantile of interest affect the asymptotic variance factor of the estimated percentile. We also describe and illustrate the computational and graphical methods for such a degradation analysis, and present the computer programs developed in the S language. We use fatigue crack growth data and a special case of Paris Law as degradation path model to illustrate the methods.



Digital Repository @ Iowa State University,

Copyright Owner

Chi-Hsien Joseph Lu



Proquest ID


File Format


File Size

242 pages