Life test sampling plans for Weibull distributed lifetimes under accelerated hybrid censoring

Life test sampling plans (LSPs) for the Weibull distribution are usually developed under the assumptions that the shape parameter is known and the life test is conducted at an accelerated condition for which the acceleration factor (AF) is known. However, the sensitivities of a plan to the assumed shape parameter and AF have been rarely investigated. This paper considers the case where the life test is hybrid censored and develops attributes LSPs under the above assumptions. Then, sensitivity analyses are conducted to assess the effects of the uncertainties in the assumed AF and shape parameter on the actual producer and consumer risks. A method is also developed for constructing LSPs that can accommodate these uncertainties.     

Local influence for generalized linear mixed models

The authors describe a method for assessing model inadequacy in maximum likelihood estimation of a generalized linear mixed model. They treat the latent random effects in the model as missing data and develop the influence analysis on the basis of a Q‐function which is associated with the conditional expectation of the complete‐data log‐likelihood function in the EM algorithm. They propose a procedure to detect influential observations in six model perturbation schemes. They also illustrate their methodology in a hypothetical situation and in two real cases.     

Asymptotic properties of the ols and grls estimator for the replicated functional relationship model

For the simple linear functional relationship model with replication, the asymptotic properties of the ordinary (OLS) and grouping least squares (GRLS) estimator of the slope are investi- gated under the assumption of normally distributed errors with unknown covariance matrix. The relative performance of the OLS and GRLS estimator is compared in terms of the asymptotic mean square error, and a set of critical parameters are identified for determining the dominance of one estimator over the other. It is also shown that the GRLS estimator is asymptoticallyequivalent to the maximum likelihood (ML) estimator under the given assumptions.     

Development of life-test sampling plans for exponential distributions based on accelerated life testing

This paper presents a procedure for developing life-test sampling plans for exponential distributions based upon accelerated life testing(ALT). Type II censoring is assumed at each overstress level. The derived test statistic is shown to be a quotient of two independent random variables, each of which is a rational power of a Chi-square random variable. The distribution of the test statistic is characterized by the H-function, which can be numerically evaluated to obtain desired sampling plans.     

Optimal design of accelerated life tests under modified stress loading methods

SUMMARY Most of the previous work on optimal design of accelerated life test (ALT) plans has assumed instantaneous changes in stress levels, which may not be possible or desirable in practice, because of the limited capability of test equipment, possible stress shocks or the presence of undesirable failure modes. We consider the case in which stress levels are changed at a finite rate, and develop two types of ALT plan under the assumptions of exponential lifetimes of test units and type I censoring. One type of plan is the modified step-stress ALT plan, and the other type is the modified constant-stress ALT plan. These two plans are compared in terms of the asymptotic variance of the maximum likelihood estimator of the log mean lifetime for the use condition (i.e. avar\[ln (0)]). Computational results indicate that, for both types of plan, avar\[ln (0)] is not sensitive to the stress-increasing rate R, if R is greater than or equal to 10, say, in the standardized scale. This implies that the proposed stress loading method can be used effectively with little loss in statistical efficiency. In terms of avar\[ln (0)], the modified step-stress ALT generally performs better than the modified constant-stress ALT, unless R or the probability of failure until the censoring time under a certain stress-increasing rate is small. We also compare the progressive-stress ALT plan with the above two modified ALT plans in terms of avar\[ln (0)], using the optimal stress-increasing rate R* determined for the progressivestress ALT plan. We find that the proposed ALTs perform better than the progressivestress ALT for the parameter values considered.     

一种新的快速RSA算法

提出了一种新的快速ＲＳＡ算法。这种算法利用平方剩余和乘同余的对称特性，使ＲＳＡ算法的求模运算量平均减少了约３０％，并通过降低乘数和被乘数的绝对值缩短了乘法时间，从而提高了整个ＲＳＡ算法的速度。     

Development of r,T hybrid sampling plans for exponential lifetime distributions

SUMMARY In the original hybrid reliability acceptance sampling plan RASP developed by Epstein for the exponential lifetime distribution, the sample size n and the number of failures r to be observed are determined given the truncation time T . However, these plans cannot be used when test items are expensive and or limited in number. Therefore, one wishes to have a plan in which n is given. In this paper, we develop hybrid RASPs in which r and T are determined, given n. These plans are tabulated for various combinations of parameter values, so that one may easily determine an appropriate plan.     

Large-sample comparisons of calibration procedures when both measurements are subject to error: the unreplicated case

A predictive functional relationship model is presented for the calibration problem in which the standard as well as the nonstandard measurements are subject to error. For the estimation of the relationship between the two measurements, the ordinary least squares and maximum likelihood estimation methods are considered, while for the prediction of unknown standard measurements we consider direct and inverse approaches. Relative performances of those calibration procedures are compared in terms of the asymptotic mean square error of prediction.