Traditional Life Tests Research Articles

OPTIMAL SELECTION OF THE MOST RELIABLE DESIGN WITH A RECIPROCAL WEIBULL DEGRADATION RATE

ABSTRACT In industries, the manufacturer of a product is usually confronted with the problem of selecting the most reliable design among several competing designs for some parts (or components) at the research and development stage. It is not easy to conduct such a selection work for highly reliable products, since there are few (or even no) failures can be obtained by using traditional life tests or accelerated life tests. In such a case, degradation tests will be effective techniques to assess the products' reliability, if degradation measures relating to reliability can be taken over time. Several experimental elements (e.g., the inspection frequency, the sample size and the termination time) are closely related to the experimental cost and the selection precision of a selection experiment. The main purpose of this paper is to deal with the optimal design problem of selecting the most reliable design with a reciprocal Weibull degradation rate. First, an intuitively appealing selection rule is proposed. Then, under the constraint that the selection precision is not lower than a pre-determined level, the optimal experimental setting (including the sample size, inspection frequency, and the termination time needed by the selection rule for each of competing designs) is determined such that the total experimental cost is minimized. An example is provided to illustrate the proposed method. Finally, we also compare the optimal experimental settings obtained in the present paper with those for a lognormal degradation rate studied in Yu [26].

OPTIMAL CLASSIFICATION OF HIGHLY RELIABLE PRODUCTS WITH A LINEARIZED DEGRADATION MODEL

ABSTRACT In manufacturing a product, some parts (or components) of this product may be purchased from vendors. For the parts (or components), classifying the better and worse designs among several competing designs is helpful for the manufacturer to enhance the product's reliability. It is a great challenge for the manufacturer if these completing designs are highly reliable, since there are few (or even no) failures can be obtained by using traditional life tests or accelerated life tests. In such a case, degradation tests will be effective techniques to assess the products' reliability if degradation measurements relating to reliability can be observed. This paper proposes a systematic approach to the classification problem where the products' degradation paths satisfy a linearized model. An intuitively appealing classification rule is proposed. Then, with respect to the objective of minimizing the total experimental cost, the optimal test plan (including the sample size, inspection frequency, and the termination time needed by the classification rule for each of competing designs) is derived by solving a nonlinear integer programming with a minimum probability of correct classification and a maximum probability of misclassification. Finally, an example is provided to illustrate the proposed method.

A Nonlinear Random-Coefficients Model for Degradation Testing

As an alternative to traditional life testing, degradation tests can be effective in assessing product reliability when measurements of degradation leading to failure can be observed. This article presents a degradation model for highly reliable light displays, such as plasma display panels and vacuum fluorescent displays (VFDs). Standard degradation models fail to capture the burn-in characteristics of VFDs, when emitted light actually increases up to a certain point in time before it decreases (or degrades) continuously. Random coefficients are used to model this phenomenon in a nonlinear way, which allows for a nonmonotonic degradation path. In many situations, the relative efficiency of the lifetime estimate is improved over the standard estimators based on transformed linear models.

Designing an accelerated degradation experiment with a reciprocal Weibull degradation rate

Accelerated degradation tests (ADTs) are usually used to assess the lifetime distribution of highly reliable products which are not likely to fail under the traditional life tests or accelerated life tests. Several factors, such as the inspection frequency, the sample size and the termination time, are closely related to the experimental cost and the estimation precision. Obviously, an inappropriate setting of these decision variables not only wastes the experimental resources, but also reduces the precision of data analysis. Recently, some studies (e.g., Yu (Qual. Reliab. Eng. Internat. 19(3) (2003) 197)) addressed the problem of how to determine the optimal setting of these decision variables for a linearized degradation model, where the degradation rate follows a lognormal distribution. In practical applications, Weibull and lognormal distributions may fit the lifetime data well. However, their predictions may lead to a significant difference. In this paper, we will deal with the optimal design of an ADT where the degradation rate follows a reciprocal Weibull distribution. Under the constraint that the total experimental cost does not exceed a pre-determined budget, the optimal decision variables are solved by minimizing the mean-squared error of the estimated 100 p th percentile of the lifetime distribution of the product at use condition. An example is provided to illustrate the proposed method.

Designing a Degradation Experiment with a Reciprocal Weibull Degradation Rate

Degradation experiments are usually used to assess the lifetime distribution of highly reliable products which are not likely to fail under the traditional life tests or accelerated life tests. Several factors, such as the inspection frequency, the sample size and the termination time, are closely related to the experimental cost and the estimation precision. Obviously, an inappropriate setting of these decision variables not only wastes the experimental resources but also reduces the precision of data analysis. Recently, Yu and Tseng [17] addressed the problem of how to determine the optimal setting of these decision variables for a linearized degradation model where the degradation rate follows a lognormal distribution. In practical applications, Weibull and lognormal distributions may fit the lifetime data quite adequately. However, their predictions may lead to a significant difference. To overcome this difficulty, we first deal with the optimal design of a degradation experiment where the degradation rate follows a reciprocal Weibull distribution. Under the constraint that the total experimental cost does not exceed a pre-determined budget, the optimal decision variables are solved by minimizing the mean squared error of the estimated 100pth percentile of the lifetime distribution of the product. An example is provided to illustrate the proposed method. Finally, we also discuss the effects of using incorrect degradation rates on the optimal test plans.

Optimal selection of the most reliable design whose degradation path satisfies a Wiener process

At the research and development stage of a product, the manufacturer usually faces the problem of selecting the most reliable design among several competing ones for some parts (or components) of the product in order to enhance the product's quality. It is a great challenge for the manufacturer if these completing designs are highly reliable, since there are few (or even no) failures can be obtained by using traditional life tests or accelerated life tests. In such cases, if there exist product characteristics whose degradation over time can be related to reliability, then collecting “degradation data” can provide information about product reliability. This paper proposes a systematic approach to the selection problem where the products' degradation paths satisfy Wiener processes. First, an intuitively appealing selection rule is proposed and, then, the optimal test plan is derived by using the criterion of minimizing the total experimental cost. The sample size, inspection frequency, and termination time needed by the selection rule for each of competing designs are computed by solving a nonlinear integer programming problem with a minimum probability of correct selection. Finally, an example is provided to illustrate the proposed method.

Optimal Classification Of Highly-Reliable Products Whose Degradation Paths Satisfy Wiener Processes

At the research and development stage of a product, the manufacturer usually faces the problem of classifying the better and worse designs among several competing designs for each of these parts (or components). It is a great challenge for the manufacturer if these completing designs are highly reliable, since there are few (or even no) failures that would be obtained by ruing traditional life tests or accelerated life tests. In such cases, if there exist product characteristics whose degradation over time can be related to reliability, then collecting “degradation data” can provide information about product reliability. This paper proposes a systematic approach to the classification problem where the products’ degradation paths satisfy Wiener processes. First, an intuitively appealing classification rule is proposed and, then, the optimal test plan is derived by using the criterion of minimizing the total experimental cost The sample size, inspection frequency, and the termination time needed by the classification rule for each of competing designs are computed by solving a nonlinear integer programming with a minimum probability of correct classification and a maximum probability of misclassification. Finally an example is provided to illustrate the proposed method

Designing an accelerated degradation experiment by optimizing the estimation of the percentile

AbstractDegradation tests are widely used to assess the reliability of highly reliable products which are not likely to fail under traditional life tests or accelerated life tests. However, for some highly reliable products, the degradation may be very slow and hence it is impossible to have a precise assessment within a reasonable amount of testing time. In such cases, an alternative is to use higher stresses to extrapolate the product's reliability at the design stress. This is called an accelerated degradation test (ADT). In conducting an ADT, several decision variables, such s the inspection frequency, sample size and termination time, at each stress level are influential on the experimental efficiency. An inappropriate choice of these decision variables not only wastes experimental resources but also reduces the precision of the estimation of the product's reliability at the use condition. The main purpose of this paper is to deal with the problem of designing an ADT. By using the criterion of minimizing the mean‐squared error of the estimated 100$p$th percentile of the product's lifetime distribution at the use condition subject to the constraint that the total experimental cost does not exceed a predetermined budget, a nonlinear integer programming problem is built to derive the optimal combination of the sample size, inspection frequency and the termination time at each stress level. A numerical example is provided to illustrate the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.

Optimal selection of the most reliable product with degradation data

At the research and development stage of a product, it is a great challenge for the manufacturer to select the most reliable design among several competing product designs which are highly reliable, since few (or even no) failures can be obtained by using traditional life tests or accelerated life tests. In such cases, if there exist product characteristics whose degradation over time can be related to reliability, then collecting degradation data can provide information about product reliability. This paper proposes a systematic approach to the selection problem with degradation data. First, an intuitively appealing selection rule is proposed, and then the optimal test plan is derived by using the criterion of minimizing the total experimental cost. The sample size, inspection frequency, and the termination time needed by the selection rule for each of the competing designs are computed by solving a nonlinear integer programming problem with a minimum probability of correct selection. Finally, an example is provided to illustrate the proposed method.

Designing a degradation experiment

Degradation experiments are widely used to assess the reliability of highly reliable products which are not likely to fail under the traditional life tests. In order to conduct a degradation experiment efficiently, several factors, such as the inspection frequency, the sample size, and the termination time, need to be considered carefully. These factors not only affect the experimental cost, but also affect the precision of the estimate of a product's lifetime. In this paper, we deal with the optimal design of a degradation experiment. Under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal decision variables are solved by minimizing the variance of the estimated 100pth percentile of the lifetime distribution of the product. An example is provided to illustrate the proposed method. Finally, a simulation study is conducted to investigate the robustness of this proposed method. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 689–706, 1999

Accelerated Degradation Tests: Modeling and Analysis

High reliability systems generally require individual system components having extremely high reliability over long periods of time. Short product development times require reliability tests to be conducted with severe time constraints. Frequently few or no failures occur during such tests, even with acceleration. Thus, it is difficult to assess reliability with traditional life tests that record only failure times. For some components, degradation measures can be taken over time. A relationship between component failure and amount of degradation makes it possible to use degradation models and data to make inferences and predictions about a failure-time distribution. This article describes degradation reliability models that correspond to physical-failure mechanisms. We explain the connection between degradation reliability models and failure-time reliability models. Acceleration is modeled by having an acceleration model that describes the effect that temperature (or another accelerating variable) has on...

Accelerated Degradation Tests: Modeling and Analysis

High reliability systems generally require individual system components having extremely high reliability over long periods of time. Short product development times require reliability tests to be conducted with severe time constraints. Frequently few or no failures occur during such tests, even with acceleration. Thus, it is difficult to assess reliability with traditional life tests that record only failure times. For some components, degradation measures can be taken over time. A relationship between component failure and amount of degradation makes it possible to use degradation models and data to make inferences and predictions about a failure-time distribution. This article describes degradation reliability models that correspond to physical-failure mechanisms. We explain the connection between degradation reliability models and failure-time reliability models. Acceleration is modeled by having an acceleration model that describes the effect that temperature (or another accelerating variable) has on the rate of a failure-causing chemical reaction. Approximate maximum likelihood estimation is used to estimate model parameters from the underlying mixed-effects nonlinear regression model. Simulation-based methods are used to compute confidence intervals for quantities of interest (e.g., failure probabilities). Finally we use a numerical example to compare the results of accelerated degradation analysis and traditional accelerated life-test failure-time analysis.

Using Degradation Measures to Estimate a Time-to-Failure Distribution

Some life tests result in few or no failures. In such cases, it is difficult to assess reliability with traditional life tests that record only time to failure. For some devices, it is possible to obtain degradation measurements over time, and these measurements may contain useful information about product reliability. Even with little or no censoring, there may be important practical advantages to analyzing degradation data. If failure is defined in terms of a specified level of degradation, a degradation model defines a particular time-to-failure distribution. Generally it is not possible to obtain a closed-form expression for this distribution. The purpose of this work is to develop statistical methods for using degradation measures to estimate a time-to-failure distribution for a broad class of degradation models. We use a nonlinear mixed-effects model and develop methods based on Monte Carlo simulation to obtain point estimates and confidence intervals for reliability assessment.

Quick Tests for Electromigration: Useful but not without Danger

Traditional electromigration life testing is a time-consuming and often painful process, consuming many expensive samples and weeks of valuable time to collect enough data for a statistically significant conclusion. Annoying, to say the least, this often causes real problems in process development when cycle times of new products can often be measured in months. Therefore, there has been a strong incentive to search for alternatives.