Diagnosis Aids in Multivariate Multiple Linear Regression Profiles Monitoring

Diagnosis aids in addition to detecting the out-of-control state is an important issue in multivariate multiple linear regression profiles monitoring; because a large number of parameters and profiles in this structure are involved. In this paper, we specifically concentrate on identification of profile(s) and parameter(s) which have changed during the process in multivariate multiple linear regression profiles structure in Phase II. We demonstrate the effectiveness of our proposed approaches through Monte Carlo simulations and a real case study in terms of accuracy percent.     

Robust Small Sample Inference for Generalised Estimating Equations: An Application of the Anova‐type Test

Asymptotically, the Wald‐type test for generalised estimating equations (GEE) models can control the type I error rate at the nominal level. However in small sample studies, it may lead to inflated type I error rates. Even with currently available small sample corrections for the GEE Wald‐type test, the type I error rate inflation is still serious when the tested contrast is multidimensional. This paper extends the ANOVA‐type test for heteroscedastic factorial designs to GEE and shows that the proposed ANOVA‐type test can also control the type I error rate at the nominal level in small sample studies while still maintaining robustness with respect to mis‐specification of the working correlation matrix. Differences of inference between the Wald‐type test and the proposed test are observed in a two‐way repeated measures ANOVA model for a diet‐induced obesity study and a two‐way repeated measures logistic regression for a collagen‐induced arthritis study. Simulation studies confirm that the proposed test has better control of the type I error rate than the Wald‐type test in small sample repeated measures models. Additional simulation studies further show that the proposed test can even achieve larger power than the Wald‐type test in some cases of the large sample repeated measures ANOVA models that were investigated.     

Exact Non-parametric Confidence Intervals for Quantiles with Progressive Type-II Censoring

It is shown how various exact non-parametric inferences based on order statistics in one or two random samples can be generalized to situations with progressive type-II censoring, which is a kind of evolutionary right censoring. Ordinary type-II right censoring is a special case of such progressive censoring. These inferences include confidence intervals for a given parent quantile, prediction intervals for a given order statistic of a future sample, and related two-sample inferences based on exceedance probabilities. The proposed inferences are valid for any parent distribution with continuous distribution function. The key result is that each observable uncensored order statistic that becomes available with progressive type-II censoring can be represented as a mixture with known weights of underlying ordinary order statistics. The importance of this mixture representation lies in that various properties of such observable order statistics can be deduced immediately from well-known properties of ordinary order statistics.     

Likelihood Based Inference in Non-linear Regression Models Using the p* and R* Approach

We develop second order asymptotic results for likelihood-based inference in Gaussian non-linear regression models. We provide an approximation to the conditional density of the maximum likelihood estimator given an approximate ancillary statistic (the affine ancillary). From this approximation, we derive a statistic to test an hypothesis on one component of the parameter. This test statistic is an adjustment of the signed log-likelihood ratio statistic. The distributional approximations (for the maximum likelihood estimator and for the test statistic) are of second order in large deviation regions.     

可靠性质量管理現状

本文通过从不同渠道来的调查资料,综述了目前我国可靠性质量管理的现状。其内容用数表、数学模型、统计计算结果和经济效益等进行了论证,对概括了解当前我国可靠性质量管理和产品质量状况、正确认识质量管理形势、寻找对策提供了依据。尤其重要的一点,使质量和效益挂钩,综述了一些有吸引力的设想模型,可供读者深入研究探讨。文中最后论述的几个问题,是当前我国有关方面应重点考虑、首先解决的问题。