BIAS CALCULATIONS FOR ADAPTIVE URN DESIGNS

A clinical trial model is considered in which two treatments with immediate binary responses are to be compared. An adaptive urn design is used to assign patients to the treatments. The bias and variance of the maximum likelihood estimators of the probabilities of success are derived by differentiating the fundamental identity of sequential analysis. By embedding the design in a continuous-time process, probability generating functions are then calculated to obtain approximations for the bias and variance. Simulation is used to assess the accuracy of the approximations. It is shown that the bias cannot be ignored, and that the adaptive rules which are subcritical in nature have the most mathematically tractable bias and are the least variable. Methods for correcting for the bias are also addressed.     

Study of Optimal Adaptive Rule in Testing Composite Hypothesis

Abstract

In this article on sequential adaptive testing, we have studied the optimal allocation between two populations for testing a composite hypothesis involving the parameters, with the goal of decreasing allocation of one of the treatments to the order of the logarithm of the sample size while decreasing the probability of incorrect selection to zero. We have proved the result for large sample sizes both mathematically and by simulation studies.     

On an Inequality That Implies the Lower Bound Formula for the Probability of Correct Selection in the Levin-Robbins-Leu Family of Sequential Binomial Subset Selection Procedures

Abstract

We study a key inequality that implies the lower bound formula for the probability of correct selection and other selection-related events of interest in the Levin-Robbins-Leu family of sequential binomial subset selection procedures. We present a strategy for the proof of the key inequality, and a mostly complete general proof is given. The strategy provides an entirely complete and rigorous proof of the inequality for as many as seven competing populations using computer-assisted symbolic manipulation.     

Study of probability integration method parameter inversion by the genetic algorithm

In order to obtain accurate probability integration method(PIM) parameters for surface movement of multi-panel mining, a genetic algorithm(GA) was used to optimize the parameters. As the measured surface movement is affected by more than one mining panel, traditional PIM parameter inversion model is difficult to ensure the reliability of the results due to the complexity of rock movement. With crossover,mutation and selection operators, GA can perform a global optimization search and has high computation efficiency. Compared with the pattern search algorithm, the fitness function can avoid falling into local minima traps. GA reduces the risk of local minima traps which improves the accuracy and reliability with the mutation mechanism. Application at Xuehu colliery shows that GA can be used to inverse the PIM parameters for multi-panel surface movement observation, and reliable results can be obtained. The research provides a new way for back-analysis of PIM parameters for mining subsidence under complex conditions.     

CDP／PA6桔瓣型复合纤维纺丝工艺

研究了阳离子染料可染PET与PA6复合纤维纺丝工艺,讨论了两组分复合比、纺丝温度、卷绕工艺等对复合纤维的生产过程及产品品质的影响。发现二者的复合比为80／20、纺丝温度为278℃及266℃、卷绕速度为3150m／min时,纺丝顺利,产品品质较好。     

Detectability of corrosion damage with circumferential guided waves in reflection and transmission

There is an increasing interest in high frequency short range guided waves to screen or monitor for corrosion. This contrasts with long range guided waves (LRGWs) which screen pipes for large patches of corrosion and have been successfully used in corrosion management for the past twenty years. The fundamental setup described in this paper uses circumferential guided waves, which are excited at a single location on a pipe and travel around the pipe wall and are detected at the same location. The study uses a finite element model assisted method to evaluate the detection capability of two short range circumferential guided wave setups which use both the reflected and transmitted signals. The setups themselves consist of either an axial array of transducers, for monitoring, or a single transducer which axially scans a pipe. Both setups have an array or scan pitch between either adjacent transducers or measurements. The detection capability of the fundamental Lamb wave modes (A0 and S0) in both reflection and transmission have been compared, as well as a hybrid shear horizontal wave setup, which uses the SH0 mode in reflection and the SH1 mode in transmission. A sensitivity analysis was conducted using two separate methods to determine the probability of detection (POD) for either the reflection or transmission signals. Both methods determine a POD for a specific defect, noise level, and array or scan pitch. Probability images are produced which map the POD for a range of defect sizes. For the parameters investigated in this study, it was found that in transmission large diameter defects have a higher detectability, whereas deep, narrow diameter defects are more detectable in reflection. A generalised overview of the sensitivity of short range guided waves is presented by combining both the reflection and transmission PODs. The data fused sensitivity of the S0 and SH hybrid modes are given as 0.6% and 0.75% cross sectional area (CSA) respectively, allowing for the comparison with LRGWs. The A0 mode was excluded from the POD analysis because it was much less sensitive than the other two modes.     

油气管道腐蚀安全评估与维修优化模型

综合考虑管道服役期内检测及维修活动的影响以及检测数据、管材特性、工作载荷和腐蚀增长率等不确定性因素,将概率论引入油气管道的腐蚀评估,提出了一种油气管道腐蚀评估和维修优化模型;该模型可用来优化管道的检测周期及维修准则,使其满足目标可靠度要求;针对管道维修后失效概率需要重新确定的问题,提出了一种近似方法,运用Monte Carlo模拟并验证了其准确性;实例表明,该模型用于油气管道腐蚀评估和维修优化是可行的,易于工程应用.     

基于概率熵判据的大坝位移预警概型比较

基于数理统计原理,依据概率分布采用小概率估计方法拟定大坝位移预警指标是实现大坝安全监控的常用手段.借助系统可靠度分析方法,选取能够良好刻画系统服役性态的威布尔(Weibull)分布(三参数及二参数)、伽玛(Gamma)分布和对数正态(Log-normal)分布,针对大坝典型坝段位移监测序列,分别建立其概率分布模型,实现对分布参数的求解,再以最大熵原理为判据,选取能最客观描述大坝服役性态的分布,结合大坝失事概率,完成概率分布模型比较研究和位移预警值估计工作.实例表明:相较于其他分布,三参数Weibull分布能最客观描述典型坝段服役性态,故利用其对坝段位移预警值进行估计更加可靠.     

Modelling the combined effects of salt,sorbic acid and nisin on the probability of growth of Clostridium sporogenes in a controlled environment (nutrient broth)

The safe preservation of new generation foods (high moisture, low salt, high pH and shelf stable under ambient conditions) is microbiologically challenging. The growth of Clostridium botulinum in low acid foods is a hazard for consumers. In this study the combined effect of salt (sodium chloride) (0–4% w/v), potassium sorbate (0–4% w/v) and nisin (0–300 ppm) at two different pHs (5.5 and 7) on the probability of growth of Clostridium sporogenes spores, as a non-toxigenic surrogate of C. botulinum, was evaluated in nutrient broth. Nutrient broth was used as it can easily and accurately be adjusted and controlled in terms of composition, and allows more rapid growth than is observed in food. The aims of this study were to develop probability of growth models in which the logit is expressed as a function of the concentrations of the selected preservatives. The developed models fit the data adequately. The c-values models were close to 1, indicating good predictive power. This indicates the performance of models would be satisfactory. The results of this study indicated that salt, potassium sorbate and nisin had significant inhibitory effects on the growth of C. sporogenes in high moisture (>95%) and high pH conditions (pH > 4.5). Combinations of the selected preservatives were more effective than any of them individually. The inhibitory effects of all three preservatives in the current study were pH dependent. Less stringent combinations of preservative concentrations were required experimentally to stop growth at pH 5.5 compared with pH 7.     

基于横波速度差异的裂缝分布识别方法——以准噶尔盆地火山岩地层为应用实例

在火成岩等裂缝和微裂缝发育地层的钻井过程中,井壁掉块甚至井壁坍塌引起的卡钻事故时有发生,严重影响了钻井安全和施工进度,要解决上述问题,需要在钻前了解地层的裂缝分布情况,进而设计合理的井身结构并采用有针对性的钻井工艺。为此,在详细分析声波速度与岩石力学特征参数关系的基础上,给出了以声波测井数据为依据的裂缝概率分布的定量计算方法,并且通过分析井径对声波时差影响的机理,提出了井径对声波时差影响的校正方法,进而建立了基于声波测井数据的裂缝识别模型。将该模型应用于准噶尔盆地2口深探井,应用效果表明:1裂缝识别结果与井径分布情况吻合较好,从而反映出该方法能够较准确地对裂缝进行识别;2井径变化对于声波时差会产生较大的影响,在数据处理过程中必须进行校正;3该方法利用常规的声波测井数据进行裂缝识别,也为一些仅有常规测井资料的老井进行裂缝识别提供了一条新的途径。