Auxiliary Information in Reliability and Applications in Computational Probability

Organizer: Paul Kvam, Georgia Tech
Session Chair: Peter Z. G. Qian, University of Wisconsin - Madison


Expert Opinion in Risk and Reliability: Technical Challenges and Recent Developements

Ali Mosleh
Center for Risk and Reliability, Univ. of Maryland College Park

Expert opinion is a major source of information in assessing the risk and reliability of complex, high reliability, high consequence systems. Heavy reliance on expert opinion and engineering judgment in estimating risk/reliability model parameters (e.g., system failure rates, human error probabilities), is in part due to scarcity of statistical data on many events of interest (e.g., system failures) which are rare, or simply unobservable when assessments are made during system design and development. Over the past 30 years the methods for elicitation and use of expert opinion have been improving steadily. This paper provides a brief assessment of the state of the art, identifies current key challenges, and lists some of the proposed solutions. In particular the results of a recent effort on "generic calibration" of expert estimates and correlation between accuracy of experts' estimates and the number of experts elicited will be discussed. The study was based on over 1000 sources and publications that reported use of expert opinion and also provided the actual values of the quantities of interest. The collected experts' estimates was used to develop a generic likelihood function for expert calibration within the Bayesian Framework and to conduct an empirical study on the effect of expert panel size on overall error of estimates.


Warranty Prediction Based on Auxiliary Use-Rate Information

Yili Hong
Department of Statistics, Virginia Tech

Usually the warranty data response used to make predictions of future failures is the number of weeks (or another unit of real time) in service. Use-rate information usually is not available (automobile warranty data are an exception, where both weeks in service and number of miles driven are available for units returned for warranty repair). With new technology, however, sensors and smart chips are being installed in many modern products ranging from computers and printers to automobiles and aircraft engines. Thus the coming generations of Zeld data for many products will provide information on how the product has been used and the environment in which it was used. This paper was motivated by the need to predict warranty returns for a product with multiple failure modes. For this product, cycles-to-failure/use-rate information was available for those units that were connected to the network. We show how to use a cycles-to-failure model to compute predictions and prediction intervals for the number of warranty returns. We also present prediction methods for units not connected to the network. In order to provide insight into the reasons that use-rate models provide better predictions, we also present a comparison of asymptotic variances comparing the cycles-to-failure and time-to-failure models.


Computational Probability Applications

Lawrence Leemis
Dept. of Mathematics, The College of William and Mary

This talk will briefly introduce APPL (A Probability Programming Language) and overview some applications developed by the speaker and collaborators. APPL is a Maple-based language capable of performing standard probability operations (e.g., expected values, products, transformations) on random variables. Applications of APPL will be surveyed in various areas of applied probability.