Graduation Year


Document Type




Degree Name

Master of Arts (M.A.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Lu Lu, Ph.D.

Committee Member

Kandethody Ramachandran, Ph.D.

Committee Member

Mingyang Li, Ph.D.


Bayesian Data Analysis, Median Lifetime Prediction, Reliability Analysis, Statistics


ISO (the International Organization for Standardization) 10995:2011 is the inter-national standard providing guidelines for assessing the reliability and service life of optical media, which is designed to be highly reliable and possesses a long lifetime. A well-known challenge of reliability analysis for highly reliable devices is that it is hard to obtain sufficient failure data under their normal use conditions. Accelerated degradation tests (ADTs) are commonly used to quickly obtain physical degradation data under elevated stress conditions, which are then extrapolated to predict reliability under the normal use condition. This standard achieves the estimation of the lifetime of recordable media, such as Magneto-Optical media, via an accelerated degradation test for measuring the error rate of these hard devices under elevated temperature and relative humidity levels. The observed degradation measures are modeled with regression analysis to predict the unobserved failure time, which is then used as ob-served failure time for estimating the lifetime distribution and predict the device quantile/median lifetime. However, the ISO 10995:2011 analysis fails to consider the uncertainty of the predicted failure times, as well as the heterogeneity of the test units, and hence could lead to imprecise and overconfident estimation. This thesis presents a Bayesian method to analyze the ISO degradation data, which (1) provides more accurate quantification of uncertainty through the use of a hierarchical degradation path model, (2) includes random effects to capture the unit-to-unit variation for improving analysis of heterogeneity, and (3) offers more straightforward implementation for estimating reliability and its associated uncertainty based on generalADT data.