Wayne Nelson

Theory and applications of hazard plotting for censored failure data

This paper presents theory and applications of a simple graphical method, called hazard plotting, for the analysis of multiply censored life data consisting of failure times of failed units intermixed with running times on unfailed units. Applications of the method are given for multiply censored data on service life of equipment, for strength data on an item with different failure modes, and for biological data multiply censored on both sides from paired comparisons. Theory for the hazard plotting method, which is based on the hazard function of a distribution, is developed from the properties of order statistics from Type II multiply censored samples.

Accelerated Life Testing - Step-Stress Models and Data Analyses

This paper presents statistical models and methods for analyzing accelerated life-test data from step-stress tests. Maximum likelihood methods provide estimates of the parameters of such models, the life distribution under constant stress, and other information. While the methods are applied to the Weibull distribution and inverse power law, they apply to many other accelerated life test models. These methods are illustrated with step-stress data on time to breakdown of an electrical insulation.

Hazard Plotting for Incomplete Failure Data

Incomplete failure data consisting of times to failure on failed units and differing running times or unfailed units are called multiply censored. Data on units operating in the field, for example, are usually multiply censored. Presented in this paper ..

Optimum Simple Step-Stress Plans for Accelerated Life Testing

This paper presents optimum plans for simple (two stresses) step-stress tests where all units are run to failure. Such plans minimize the asymptotic variance of the maximum likelihood estimator (MLE) of the mean life at a design stress. The life-test model consists of: 1) an exponential life distribution with 2) a mean that is a log-linear function of stress, and 3) a cumulative exposure model for the effect of changing stress. Two types of simple step-stress tests are considered: 1) a time-step test and 2) a failure-step test. A time-step test runs a specified time at the first stress, whereas, a failure-step test runs until a specified proportion of units fail at the first stress. New results include: 1) the optimum time at the first stress for time-step test and 2) the optimum proportion failing at the low stress for a failure-step test, and 3) the asymptotic variance of these optimum tests. Both the optimum time-step and failure-step tests have the same asymptotic variance as the corresponding optimum constant-stress test. Thus step-stress tests yield the same amount of information as constant-stress tests.

Theory for Optimum Accelerated Censored Life Tests for Weibull and Extreme Value Distributions

This paper presents maximum likelihood theory for large-sample optimum accelerated life test plans. The plans are used to estimate a simple linear relationship between (transformed) stress and product life, which has a Weibull or smallest extreme value distribution. Censored data are to be analyzed before all test units fail. The plans show that all test units need not run to failure and that more units should be tested at low test stresses than at high ones. The plans are illustrated with a voltage-accelerated life test of an electrical insulating fluid.

Graphical Analysis of System Repair Data

(This paper was presented at the Journal of Quality Technology Session at the 31st Annual Fall Technical Conference of the Chemical and Process Industries Division of the American Society for Quality Control and the Section on Physical and Engineering S..

Theory for Optimum Censored Accelerated Life Tests for Normal and Lognormal Life Distributions

This paper presents optimum accelerated life test plans for estimating a simple linear relationship between a stress and the median of product life which has a s-normal or lognormal distribution when the data are analyzed before all test units fail. Also, plans with equal numbers of test units at equally spaced test stresses are compared with the optimum plans. The plans are illustrated with a temperature-accelerated life test of electrical insulation.

Graphical Analysis of Accelerated Life Test Data with the Inverse Power Law Model

In this paper, graphical methods are presented for analyzing accelerated life test data with the inverse power law model, when all test units are run to failure. The inverse power law model is described, and graphical methods for estimating its parameters from such complete data are given. These methods are illustrated with accelerated test data on time to breakdown of an insulating fluid. While the methods are presented with the inverse power law model, they can be used for analyzing many other accelerated life test situations. These methods are presented so that they can be used by individuals with a limited statistical background.

Weibull Analysis of Reliability Data with Few or No Failures

This expository paper presents estimates and confidence limits for Weibull percentiles and reliabilities when the Weibull shape parameter β is assumed to have a known value. The methods are particu...

Optimum Accelerated Life-Tests for the Weibull and Extreme Value Distributions

This paper presents charts for optimum accelerated life-test plans for estimating a simple linear relationship between an accelerating stress and product life, which has a Weibull or smallest extreme value distribution, when the data are to be analyzed before all tests units fail. The plans show that one need not run all test units to failure and that more units ought to be tested at low test stresses than at high ones. The plans are illustrated with a voltage-accelerated life test of an electrical insulating fluid.