Designing of multiple deferred state sampling plan for generalized inverted exponential distribution

In this article, we propose a sampling plan called a multiple deferred state sampling plan for sentencing a lot based on the information of current and successive lot samples. Based on this sampling plan, the median life of the product is assured based on a time-truncated life test where the lifetime of the product follows the generalized inverted exponential distribution. The quality of the product is measured by its median life. The optimal parameters of the proposed plan are obtained by using the approach of two points on the operating characteristic curve. Tables are also constructed for determining the optimal parameters with various shape parameters. The implementation of the proposed plan is illustrated with examples. The performance of the proposed plan is compared with the performance of existing sampling plans under the generalized inverted exponential distribution.     

Risk-efficient sequential estimation of multivariate random coefficient autoregressive process

A vector-valued autoregressive time series model is considered. The autoregressive coefficients of the model are random with possible dependencies among them. Estimation of the large number of parameters in such models becomes costly with an increase in dimension. A sequential procedure is proposed that promises a significant gain in the sample size thus reduction in the cost of implementation. The procedure is also risk efficient in the sense that as the cost of sampling becomes negligible the asymptotic predictive risk of the proposed procedure reaches the oracle predictive risk corresponding to the best fixed sample size procedure that assumes the values of the nuisance parameters to be known. Extensive simulation results are presented to illustrate the properties of the proposed procedure in a finite sample.     

Determination of a new sampling system based on exponentially weighted moving average

In this article, a new sampling system based on an exponentially weighted moving average statistic is proposed for the inspection of normally distributed quality characteristics. The proposed sampling system can be applicable for compliance testing. The performance measures of the proposed system are derived and analyzed. Tables are also constructed for determining the optimal parameters of both known and unknown standard deviation cases. An optimization problem is formulated as a nonlinear program in order to construct the tables in which the objective function used is the minimization of the average sample number and the constraints are related to the probability of acceptance at acceptable quality level and limiting quality level under the operating characteristic curve. The efficiency and advantages of the proposed sampling system are discussed over the existing variables sampling plans. Extensive tables are provided for industrial applications. Implementation of the proposed sampling system is discussed with the help of a real-time industrial example.     

Designing of two mixed variable lot-size sampling plans using repetitive sampling and resampling based on the process capability index

In this article, we propose two types mixed variable lot-size sampling plans using the process capability index. The first one is the mixed variable lot-size repetitive sampling plan and the other is the mixed variable lot-size sampling plan for resubmitted lots. The design methodology of the proposed mixed sampling plans for symmetric and asymmetric fraction nonconforming cases is presented. Tables are constructed to determine the optimal parameters for practical applications. The industrial applications of the proposed mixed sampling plans are explained with illustrative examples. Comparison of the proposed sampling plans with other existing sampling plans is also made.     

Determination of multiple dependent state repetitive group sampling plan based on the process capability index

Abstract

In this article, we propose a sampling plan called a multiple dependent state repetitive group sampling plan for variable inspection based on the process capability index C_pk. The proposed sampling plan is applicable for the inspection of normally distributed quality characteristics when both mean and variance are assumed to be unknown. This new plan under variable inspection will be very useful particularly in compliance testing. Tables are also constructed for the determination of optimal parameters for easy selection and implementation of the plan. The optimal parameters can be determined by using the approach of two points on the operating characteristic curve. Symmetric and asymmetric cases based on the fraction nonconforming by the lower and the upper specification limits are also considered. Advantages of the proposed plan are also discussed. It is also shown that the proposed plan outperforms other existing sampling plans under variable inspection.     

Measurements of High Oleic Purity in Peanut Lots Using Rapid,Single Kernel Near-Infrared Reflectance Spectroscopy

High oleic peanuts have improved shelf life vs. conventional peanuts. Purity (percentage of high oleic peanuts within a lot) is critical to ingredient performance and final lot value. Contamination can result from unintentional mix-ups at the breeder/seed level, improper production handling, or due to physiologically immature high oleic kernels. Therefore, industry groups have established unofficial sampling plans to monitor purity. Assuming equivalent measurement performance and simple random sampling, increasing the sample size decreases variance among replicated sample test results and increases the precision of estimated lot purity. A novel instrument (QSorter Explorer by QualySense AG) using near-infrared reflectance spectroscopy was evaluated for high speed (20 kernels per second) high oleic purity measurements. The study objectives were to assess instrument performance in: (1) measuring oleic acid (%) in runner peanuts and (2) estimating the true high oleic purity of artificially mixed peanut lots. Three grades (Jumbo, Medium, and No 1) of US Runner mini-lots each at seven different contamination levels (0, 5, 10, 20, 30, 50, and 100%) were prepared. Oleic acid (%) of individual kernels was measured by scanning replicated samples of 10, 50, 100, and 500 kernels using the QSorter Explorer. The variance associated with each sample size and lot contamination level on returned purity values is discussed in the context of binomial sampling. Overall, the demonstrated measurement performance and capacity of the QSorter Explorer to process much larger sample sizes suggest this instrument can better identify true high oleic peanut lot purity vs. other currently available technologies.     

Minimum risk sequential point estimation of the stress-strength reliability parameter for exponential distribution

Abstract

In this article, using purely and two-stage sequential procedures, the problem of minimum risk point estimation of the reliability parameter (R) under the stress–strength model, in case the loss function is squared error plus sampling cost, is considered when the random stress (X) and the random strength (Y) are independent and both have exponential distributions with different scale parameters. The exact distribution of the total sample size and explicit formulas for the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress–strength model are provided under the two-stage sequential procedure. Using the law of large numbers and Monte Carlo integration, the exact distribution of the stopping rule under the purely sequential procedure is approximated. Moreover, it is shown that both proposed sequential procedures are finite and for special cases the exact distribution of stopping times has a degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally, using a real data set, the procedures are clearly illustrated.     

在线色谱分析及其在石化中的应用问题探讨

目前国内在线色谱仪使用中的最大问题还是在取样和样品预处理上,尤其是高温高压、宽沸程、组成复杂和需特殊处理的样品。因此研究更新采样方法和分析技术,发展适用性强、应用范围宽、高灵敏度、快速、成本低和易于维护的专用／多用在线色谱分析系统,以满足不同工业在线分析的要求和实验室研究的需要,将是在线色谱分析的发展方向之一。     

Normal sequential sampling

Bayesian sequential sampling plans are investigated numerically, for testing the mean of a normal distribution (‘high’ values are acceptable, but 'low' values are not). The variance is known, the prior of the mean is normal, and a linear loss function is used. Various properties of these plans are presented here and compared with results for single and double sampling plans. Robustness of these plans with respect to errors in some of the parameters are investigated as well as methods for reducing the computation for the sequential plans.     

Adaptive two-stage optimal designs for phase II clinical studies that allow early futility stopping

Abstract

Adaptive designs play an important role in contemporary clinical trials to make designs flexible and efficient. In cancer clinical trials, given a relatively small sample size, it is important to obtain as much information as possible during this phase. We propose a new adaptive optimal design that stops for futility only in the first stage as Simon’s two-stage design. The existing adaptive two-stage designs are often allowed to be stopped for futility or efficacy due to computational advantage. It is difficult to search for an optimal design with futility stopping only in the first stage by using efficient search algorithms; for example, the branch-and-bound algorithm. We have to use multiple computational techniques to search for the optimal design. The proposed adaptive design meets the important property of the monotonic property that the second stage sample size is a nonincreasing function of the number of responses from the first stage. In this article, we show that the proposed adaptive design always has a smaller expected sample size than Simon’s optimal design. We recommend it for use in practice as an alternative to the commonly used Simon’s design.     

The choice of sample size: a mixed Bayesian / frequentist approach

Sample size computations are largely based on frequentist or classical methods. In the Bayesian approach the prior information on the unknown parameters is taken into account. In this work we consider a fully Bayesian approach to the sample size determination problem which was introduced by Grundy et al. and developed by Lindley. This approach treats the problem as a decision problem and employs a utility function to find the optimal sample size of a trial. Furthermore, we assume that a regulatory authority, which is deciding on whether or not to grant a licence to a new treatment, uses a frequentist approach. We then find the optimal sample size for the trial by maximising the expected net benefit, which is the expected benefit of subsequent use of the new treatment minus the cost of the trial.     

液位控制系统中混沌运动的最优控制

分析了液位控制系统中的混沌运动,说明了基于局部线性化基础上的最优控制存在的问题,提出在反馈线性化基础上对液位控制系统中的混沌运动进行最优控制.仿真实验表明了该方法的有效性和可行性.     

电镀产品质量的抽样检验- GB/T 12609新版标准的应用

结合GB／T1 2609新版标准的内容,介绍了电镀产品的抽样检验程序、检验的实施以及检验后的处置。对新标准中检验批和批量,缺陷和不合格品类型,批质量水平 的表示。接收质量限,检验水平等指标进行了解释。重点阐述了抽样方案的确定方法和抽样方式的选择。同时,深入讨论了关于孤立批和连续批的理解和应用。     

Construction of an Optimal Sequential Plan for Testing a Treatment for an Adverse Effect

Abstract

Classical sequential procedures that collect a single observation at a time are often found impractical, expensive, and time consuming. Sequentially planned procedures, or simply sequential plans, extend and generalize the concepts of sequential analysis by allowing observations to be collected in groups of variable sizes. After every group, all of the previously collected data are used to determine the next course of action. An optimal (Bayes) sequential plan minimizes the (Bayes) risk function that combines the decision loss, observation (variable) cost, and group (fixed) cost. In general, determining the optimal sequential plan remains an open and challenging problem mainly because it requires risk optimization over a huge and rather unstructured set of all sequential plans. This article demonstrates how to obtain the optimal solution for a particular class of problems that may arise in testing a treatment for a rare but severe adverse effect. This solution is obtained by studying a number of properties of the Bayes sequential plan such as transitivity and monotonicity. This allows one to reduce the search to a small, manageable set of sequential plans within which the optimal plan can be calculated.     

OPTIMAL DESIGN OF MULTIPLE BATCH UNITS WITH FEEDSTOCK/PRODUCT STORAGES

This article derives an analytical solution for determining the optimal size of the multiple batch unit plant with storage units. The total cost to be minimized consists of the setup cost of the batch processing units, the inventory holding cost of feedstock/product storage and the capital cost of the batch and storage units. A novel approach, which is called the PSW(Periodic Square Wave) model, is applied to represent the material flows among the batch and storage units. The PSW model presumes that the material flow between unit and storage is a periodic square shaped wave. The resulting optimal batch size has similar characteristics to the classical economic lot sizing model such as EOQ or EPQ model in the sense that the batch size is determined as the balance between setup and inventory holding cost. However, the influence of inventory holding cost of the PSW model is different from that of EOQ/EPQ model. The EOQ/ EPQ model includes only the product inventory holding cost while the PSW model includes all inventory holding costs around the batch unit.

The PSW model is suitable for analyzing interlinked batch-storage system and is more accurate rather than EOQ/EPQ model. The optimal lot size of the PSW model is much smaller than that of EOQ/EPQ model as shown at an example. This is quite a remarkable result considering that the EOQ/EPQ model has been widely used over the last half century.     

On Optimal Adaptive Prediction of Multivariate Autoregression

Abstract

The problem of asymptotic efficiency of adaptive one-step predictors for a stable multivariate first-order autoregressive process (AR(1)) with unknown parameters is considered. The predictors are based on the truncated estimators of the dynamic matrix parameter. The truncated estimation method is a modification of the truncated sequential estimation method that makes it possible to obtain estimators of ratio-type functionals with a given accuracy by samples of fixed size. The criterion of optimality is based on the loss function, defined as a sum of sample size and squared prediction error's sample mean. The cases of known and unknown variance of the noise model are studied. In the latter case the optimal sample size is a special stopping time. The simulation results are given.     

现代煤化工设计煤质确定方法的探讨

设计煤质数据是现代煤化工项目中重要的设计基础,直接影响到项目能否稳定运行。本文根据神华煤化工项目的建设经验,提出了原料煤设计煤质确定的程序方法。目前煤化工项目常用的煤气化技术包括:干粉气流床气化技术、水煤浆气化技术、固定床碎煤加压气化技术及流化床气化技术。根据不同气化技术对煤质的不同要求,归纳出了在煤化工项目确定设计煤质过程中所需的煤质分析项目。在煤样的采集与分析工作过程中,采集的煤样具有代表性是保证获得典型煤质数据的前提。文中根据项目配套的煤源矿井所处的生产阶段不同,提出了不同的煤样采集方案包括采样地点、煤样类型、采样质量、煤样粒度及采样方式等。同时对后续煤样制备与分析及最终数据校核工作进行了探讨。     

LSSVM过程建模中超参数选取的梯度优化算法

基于结构风险最小的最小二乘支持向量机（least squares support vector machine, LSSVM）为标准支持向量机（SVM）的约简;训练简易;性能良好。其模型精度受超参数影响;常规的网络搜索法很难搜得最佳超参数。在快速留一法的基础上;以全样本留一预测误差平方和最小化为目标;导出基于梯度的最优化算法;用以优选为LSSVM超参数;进而构建G-LSSVM模型。以柠檬酸发酵过程为算例对G-LSSVM进行检验;结果表明G-LSSVM的超参数选取耗时少;模型稳定性良好;且拟合和预报性能都优于标准SVM和神经网络。有望适用于机理不明、高度非线性、小样本的化工过程建模。     

Estimation of the size of a finite population in sequatial sampling:truncatedcombinatiorial numbers

This note considers the problem of unbiased estimation of the size of a finite population, or the number of equiprobable classes in a population, when sequential sampling plans are aplied. Combinatorial numbers, e.g., Stirling numbers of the second kind or Lah numbers, occurring in sampling distributions when the sample size is fixed, have to be adjusted to take into account the stopping rule. This requires the concept of a truncated combinatorial number, and linearly truncated Stirling numbers and Lah numbers are instances discussed here. UMVU estimators of population size are expressible in terms of ratios of such truncated combiantorial numbers.     

Improved sequential and accelerated sequential Procedures for estimating the scale parameter in a aniform distribution

Ghosh and Mukhopadhyay (1975a) and more recently Mukhopadhyay et al.(1983) have consideredsequential minimum risk point estimation of θ in a uniform (0,θ)population.The loss function has been squared error plus linear cost and θ has beencustomarily estimated by the sample maximum.In this paper,we consider instead the best scalarmultiple of the sample aximum as the estimator of θ.The percentage saving in the fictitious optimal fixed sample size as well as the percentage reduction in the corresponding minimum risk ar seen to be about 20.6X when compared with the Mukhopadhyay et al.(1983) cedure.Since thisamount of saving is quite substantial,we set out to develop