Performance of parameter-estimates in step-stress acceleratedlife-tests with various sample-sizes

摘要

In accelerated life test (ALT) studies, the maximum likelihoodn(ML) method is commonly used in estimating model parameters, and itsnasymptotic variance is the key quantity used in searching for thenoptimum design of ALT plans and in making statistical inferences. Thisnpaper uses simulation techniques to investigate the required sample sizenfor using the large sample Gaussian approximation s-confidence intervalnand the properties of the ML estimators in the finite sample situationnwith different fitting models. Both the likelihood function and itsnsecond derivatives needed for calculating the asymptotic variance arenvery complicated. This paper shows that a sample size of 100 is needednin practice for using large-sample inference procedures. When the modelnis Weibull with a constant shape parameter, fitting exponential modelsncan perform poorly in large-sample cases, and fitting Weibull modelsnwith a regression function of shape parameters can give undesirablenresults in small-sample situations. When small fractions of thenproduct-life distribution are used to establish warranties and servicenpolices, the interests of the producer and consumer should be balancednwith the resources available for conducting life tests. From thenstandpoint of safety, an unrealistically long projected service lifencould harm the consumer. Establishing a short warranty period protectsnthe producer but hurts revenue. An overly generous warranty period couldncost the producer in terms of product replacement. To estimatenlife-distribution parameters well, use more than 100 samples in for LSCInand life-testing plans derived from the asymptotic theory. When thenmodel becomes complicated, as in this paper, monitor the convergence ofnthe parameter estimation algorithm, and do not trust the computernoutputs blindly. In many applications, the likelihood ratio testninverted confidence interval performs better than the usual approximatenconfidence interval in small samples; thus its performance in thenstep-stress ALT studies should be in future research