Estimating Component Failure Rates From Combined Component and Systems Data: Exponentially Distributed Component Lifetimes

The situation in which test results are available on systems consisting of some of k independent but nonidentical components in series is studied. The underlying distribution of the lifetime of the component is assumed to be an exponential. The method of maximum likelihood is used to obtain estimates, a chi squared approximation is used to approximate the mean and variance of the maximum likelihood estimate, and a method for reducing its bias is presented.     

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

This expository paper presents theory for optimum plans for accelerated life tests for estimating a simple linear relationship between a stress and product life, which has a normal or lognormal distribution, when the data are to be analyzed before all test units fail. Standard plans with equal numbers of test units at equally spaced test stresses are presented and are compared with the optimum plans. While the optimllm plans may not always be robust enough in practice, they indicate that more test units should be run at low stress than at high stress. The plans are illustrated with a temperatllre-accelersted life test of an electrical insulation analyzed with the Arrhenius model.     

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.     

Field Reliability Prediction in Consumer Electronics Using Warranty Data

In innovative fast product development processes, such as consumer electronics, it is necessary to check as quickly as possible, using field data, whether the product reliability is at the right level. In consumer electronics, some major companies use the Warranty Call Rate (WCR) for this purpose. This paper discusses extensively the theoretical and practical drawbacks of the WCR. Subsequently, it is demonstrated, using a Weibull failure distribution, that only a few months after product launch, say three months, the warranty data offer the opportunity to estimate the parameters of the failure distribution. Of course, this requires that the warranty data are available in the quality department. Unfortunately, for some companies the field feedback information process from the repair centres to the quality department causes a delay of several months. These companies have to speed up their field feedback information process before they can fully take advantage of the proposed estimation procedure. Copyright © 2006 John Wiley & Sons, Ltd.     

Accelerated Life Testing for a Class of Linear Hazard Rate Type Distributions

Accelerated life testing for distributions with hazard rate functions of the form r(t) = Ag(t) + Bh(t) are considered. Let V ₁, …, V _k be stress levels larger than V ₀—the stress level under normal conditions [V ₀ > 0]—and let a(v) be a nondecreasing function on (0, ∞). We discuss a generalization of the common accelerated models (the power rule model and the Arrhenius model) by assuming that the hazard rate under the stress level V, is of the form (a(V _t )) ^P (Ag(t) + Bh(t)). The maximum likelihood estimators of A, B and P for complete and censored samples are studied. The estimation procedure reduces to a solution of one equation with one unknown parameter. The estimation procedure under the assumption of aging is also described. The asymptotic variance-covariance matrix is given.