Analysis of Reliability Data
Session Chair: Harry Ascher, Harold E. Ascher & AssociatesReliability Data Analysis for Designed Experiments
Laura J. Freeman and G. Geoffrey Vining
Virginia Tech
Abstract: Product reliability is an important characteristic for all manufacturers, engineers and consumers. Industrial statisticians have been planning experiments for years to improve product quality and reliability. However, rarely do experts in the field of reliability have expertise in design of experiments (DOE) and the implications that experimental protocol have on data analysis. Additionally, statisticians who focus on DOE rarely work with reliability data. This talk is an attempt to bridge that divide. We provide a new analysis technique for reliability data from designed experiments. The technique is illustrated on a popular reliability data set. This paper discusses implications of using previous analysis methods versus our new approach to the analysis problem.
A Comparison of Maximum Likelihood and Median Rank Regression for Weibull Estimation
Ulrike Genschel, William Q. Meeker
Iowa State University
Abstract: The Weibull distribution is frequently used in reliability applications. Many different methods of estimating the parameters and important functions of the parameters (e.g. quantiles and failure probabilities) have been suggested. Maximum likelihood and median rank regression methods are most commonly used today. Largely because of conflicting results from different studies that have been conducted to study the properties of these estimators, there are sharp differences of opinion on which method should be used. The purpose of this is to report on the results of our simulation study and to provide insight into the differences between the competing methods and to resolve the differences among the previous studies.
An Application of Reliability Model for Static Fatigue Test
Winson Taam
The Boeing Company
Static fatigue test is a special kind of accelerated life time test. Specimens are subjected to a constant stress over time until failure. It is different from the popular fatigue tests where the stress is cycled over time until failure. Increased stress levels and extreme environmental conditions are typically used to acquire failure data early. In some instances, the specimens fail due to deterioration as the result of being stressed over time. The failure mechanism hence is a function of stress and time of test. Scientists and engineers have examined the rationales for such changes in the specimens, which provided interpretation of parameters used in statistical models. This presentation re-analyzes a well-known study with a special Weibull regression model with piecewise linear relationship.
Reliability Estimation and Confidence Regions from Subsystem and System Tests via Maximum Likelihood
James C. Spall
Johns Hopkins University
This paper considers the problem of estimating reliability for complex systems based on a combination of information from tests on the subsystems and (if available) tests on the full system. A key motivation for this setting comes from the fact that it is often difficult or infeasible to directly evaluate the reliability of complex systems through a large number of full-system tests alone. Such difficulty may arise, for example, when the full system is very costly (or dangerous) to operate and/or when each full-system test requires the destruction of the system itself. Hence, important information about system performance, including reliability, may come from tests on the subsystems entering the full system. Nevertheless, it is also often the case that there are at least a few tests of the full system available; it is obviously desirable to include such information in the overall reliability assessment. This paper develops a rigorous and practical method based on principles of maximum likelihood for estimating the overall system reliability from a combination of full system and subsystem tests. We also discuss the confidence regions and convergence theory for the estimate. Acknowledgments: This work was partially supported by the JHU/APL IRAD program and U.S. Navy Contract N00024-03-D-6606.