Odds ratio-based group sequential analysis for joint binomial and inverse binomial sampling

We consider two treatment comparison in a clinical trial setup where the responses from one treatment are a priori known for a fixed number of individuals and patients are allocated in a groupsequential way for the other treatment using inverse sampling. We consider the odds ratio as the measure of treatment difference at the end of each group, where for the calculation of odds ratios we consider the full data on one treatment, which are a priori known, and the available data on the other treatment up to that point of time. We have calculated the optimal number of index subjects for inverse sampling and examine the effects of different type I and type II error spending functions on group sequential testing in this context. The methodology is illustrated by using a real data set.     

Maximum likelihood estimate following sequential probability ratio tests

We consider Wald's (1947) sequential probability ratio tests for a Brownian motion X(t) with drift ?. Expressions are derived for the distribution and moment generating functions, first and second moments of the maximum likelihood estimate (MLE). Asymptotic behavior of the MLE is also discussed     

Unbalanced and Partial Group Sequential Methods for Normal Responses in Clinical Trials

Abstract

Group sequential methods for a two-treatment clinical trial with normal responses are discussed. First we consider the case where the sample sizes for two treatments are possibly unequal between the treatments due to an unequal randomization. Then we discuss group sequential design in the context of a historical control study, that is, under the partial sequential sampling scheme, in which the samples on one treatment, say control, are available at the outset, and the samples on the other treatment, say experimental, are obtained in the group sequential way. We discuss the cases of known and unknown variance for both unbalanced and partial group sequential setups. All of the procedures are discussed with numerical studies.     

Sequential probability ratio test for the mode of M-Gaussian distribution

Scientific data, as a sequential or a simple random sample, often indicate a unimodal, right-skewed population. For such data, the ubiquitous symmetry assumption and the Gaussian model are inappropriate and in case of high skewness, even corrections using devices such as Box-Cox transformation are inadequate. In such cases, the recently introduced M-Gaussian distribution, which may be described as an R-symmetric Gaussian twin, with its mode as the centrality parameter, can be an appropriate model. In this article, the concept of R-symmetry, the basic properties of the M-Gaussian distribution and some analogies between Gaussian and M-Gaussian distributions are reviewed. Then the sequential probability ratio test (SPRT) for simple a hypothesis about the mode of an M-Gaussian population assuming the dispersion parameter to be known is derived. The average sample number (ASN) and operating characteristic (OC) function are obtained and the robustness properties of the test with respect to the harmonic variance assumption are studied. The results are compared with the existing parallel studies for the mean of the inverse Gaussian (IG) distribution.     

Design of a modified sequential probability ratio test (SPRT) for pipeline leak detection

A classical SPRT likelihood test for sequential independently distributed data is often used in pipeline mass balance leak detection to distinguish between true leaks and false alarms in the minimum time consistent with a user defined error tolerance. However such time series data would not be expected to be independent, especially as it is often moving averaged to remove noise and unwanted transients. In this paper a modified SPRT test is derived using a simple Gaussian Markov process to model a correlated time series. Application of the modified test to correlated time series data is shown to reduce false alarms below that of a classical SPRT.     

A sequential likelihood ratio test for general hypotheses

In statistical inference it is often desired to test a specified funcrion of unkown parameters form an underlying distribution. Sequential procedures utilize information from the already collected observations and allow for a possible eariy termination of experimentation with a concurrent savings in time and cost. In the present work a suitable maximum-likelihood based sequential testing procedure for functions of unknown parameters is developed for independent and identically distributed observations of an underlying distribution of known form. The theoretical Operating Characteristic (OC) and Average Sample Number (ASN) functions are derived for local alternatives by approximating the distribution of the test statistic with linear combinations of the standard Wiener process, Simlriation studies were utilized to investigate the goodness of the asymptotic results in finite samples.     

提高催化裂化柴汽比和汽油辛烷值的工业试验

介绍了乌石化公司炼油厂800kt/a馏分油催化裂化装置提高柴汽比和汽油辛烷值工业试验情况，通过调整操作条件和汽、柴油切割点，使用增产柴油、提高汽油辛烷值的（CC-200D）催化剂，有效提高了装置柴汽比，柴油收率提高7.419个百分点，轻质油收率提高1.395个百分点，产品分布得到改善，稳定汽油研究法辛烷值提高一个单位左右。     

Critical evaluation of approaches for on-line batch process monitoring

Since the introduction of batch process monitoring using component models in 1992, different approaches for statistical batch process monitoring have been suggested in the literature. This is the first evaluation of five proposed approaches so far. The differences and similarities between the approaches are highlighted. The derivation of control charts for these approaches are discussed. A control chart should give a fast and reliable detection of disturbances in the process. These features are evaluated for each approach by means of two performance indices. First, the action signal time for various disturbed batches is tested. Secondly, the probability of a false warning in a control chart is computed. In order to evaluate the five approaches, five different data sets are studied: one simulation of a batch process, three batch processes obtained from industry and one laboratory spectral data set. The obtained results for the performance indices are summarised and discussed. Recommendations helpful for practical use are given.