Optimal Designs of Simple Step-Stress Accelerated Life Tests for Lognormal Lifetime Distributions

1998 ◽  
Vol 05 (04) ◽  
pp. 315-336 ◽  
Author(s):  
Sang Wook Chung ◽  
Do Sun Bai
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Variance ◽  
High Stress ◽  
Optimal Designs ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Design Parameters ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests

This paper considers optimal designs of step-stress accelerated life tests in which each lognormally-distributed test item is first run at low stress, and if it does not fail for a specified time, then it is run at high stress until a predetermined censoring time. It is assumed that a log-linear relation exists between the lognormal location parameter and stress, and that a cumulative exposure model for the effect of changing stress holds. The optimum stress change point minimizes the asymptotic variance of maximum likelihood estimator of a specified percentile at design stress. For selected values of the design parameters, the optimum plans are tabulated. Designs of high-to-low step-stress accelerated life tests (ALTs) in which each item is first run at high stress and then at low stress, and the optimality criterion of minimizing the generalized asymptotic variance of maximum likelihood estimators of model parameters, are also considered. The effects of the incorrect pre-estimates of the design parameters are investigated.

scholarly journals Competing Risks Step-Stress Model with Lagged Effect under Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3206
Author(s):  
Yuan Ma ◽  
Wenhao Gui
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Confidence Intervals ◽  
Competing Risks ◽  
Stress Model ◽  
Gompertz Distribution ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests ◽  
Lag Period

In many survival analysis studies, the failure of a product may be attributed to one of several competing risks. In addition, if survival time is long, researchers can adopt accelerated life tests, causing devices to fail more quickly. One popular type of accelerated life tests is the step-stress test, and in this test, the stress level changes at a predetermined point time. The manner that stress levels change abruptly and increase discontinuously has been studied extensively. This paper considers a more realistic situation where the effect of stress increases cannot be achieved all at once, but with a lag time, and we propose a step-stress model consisting of two independent competing risks with a lag period in which the failure time caused by different risks at different stress levels obey Gompertz distribution, and the range of lag period is predetermined. The unknown parameters are estimated by maximum likelihood estimation and least squares estimation. For comparison, asymptotic confidence intervals and percentile bootstrap confidence intervals are constructed. By using Monte-Carlo simulations, we obtain the means and mean square errors of the maximum likelihood estimates and the least squares estimates, as well as the mean lengths and coverage rates of the two confidence intervals, which show the performance of various methods. Finally, in order to illustrate the model and proposed methods, we analyze a dataset from a solar energy experiment.

scholarly journals Estimation in Step-Stress Accelerated Life Tests for Power Generalized Weibull Distribution with Progressive Censoring

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. M. Mohie EL-Din ◽  
S. E. Abu-Youssef ◽  
Nahed S. A. Ali ◽  
A. M. Abd El-Raheem
Keyword(s):  
Weibull Distribution ◽  
Asymptotic Variance ◽  
Acceleration Factor ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Progressive Censoring ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests

Based on progressive censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows power generalized Weibull distribution. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) are obtained for the distribution parameters and the acceleration factor. In addition, the approximate and bootstrap confidence intervals (CIs) of the estimators are presented. Furthermore, the optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved.

Maximum-Likelihood Estimation of the Parameters with Constraints in Step-Stress Accelerated Life Tests

2011 ◽  
Vol 291-294 ◽  
pp. 2211-2214
Author(s):  
Yu Hong Xing ◽  
Rui Yuan Liu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Test Data ◽  
Likelihood Estimation ◽  
Accelerated Life Test ◽  
Life Test ◽  
Average Lifespan ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests

This paper investigates the maximum likelihood estimation of the average lifespan of products with the constraints, and the estimation of the average lifespan at stress level, which follows the exponential distribution, is derived by transforming the time-censoring step-stress accelerated life test data into the corresponding constant-stress accelerated life test data. The proposed method can overcome the shortcoming of information lose.

OPTIMAL DESIGN OF SIMPLE STEP-STRESS ACCELERATED LIFE TESTS FOR ONE-SHOT DEVICES UNDER EXPONENTIAL DISTRIBUTIONS

2018 ◽  
Vol 33 (1) ◽  
pp. 121-135 ◽  
Author(s):  
Man Ho Ling
Keyword(s):  
Optimal Design ◽  
Asymptotic Variance ◽  
Operating Conditions ◽  
Model Parameters ◽  
Normal Operating ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Decision Variables ◽  
Simple Step ◽  
Life Tests

This paper considers simple step-stress accelerated life tests (SSALTs) for one-shot devices. The one-shot device is an item that cannot be used again after the test, for instance, munitions, rockets, and automobile air-bags. Either left-or right-censored data are collected instead of actual lifetimes of the devices under test. An expectation-maximization algorithm is developed here to find the maximum likelihood estimates of the model parameters based on one-shot device testing data collected from simple SSALTs. Furthermore, the asymptotic variance of the mean lifetime under normal operating conditions is determined under the expectation-maximization framework. On the other hand, the optimal design that minimizes the asymptotic variance of the estimate of the mean lifetime under normal operating conditions in terms of three decision variables, including stress levels, inspection times, and sample allocation is discussed. A procedure then is presented to determine the decision variables when a range of stress levels and the termination time of the test as well as normal operating conditions of the devices are given. The properties of the optimal design and the effects of errors in pre-specified planning values of the model parameters are also investigated. Comprehensive simulation studies show that the procedure is quite reliable for the design of simple SSALTs.

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