Estimation and Design of Sampling Plans for Monitoring Dependent Production Processes

We consider the problem of designing single and the double sampling plans for monitoring dependent production processes. Based on simulated samples from the process, Nelson proposed a new approach of estimating the characteristics of single sampling plans and, using these estimates, designing optimal plans. In this paper, we extend his approach to the design of optimal double sampling plans. We first propose a simple methodology for obtaining the unbiased estimators of various characteristics of single and double sampling plans. This is achieved by defining the various characteristics of sampling plans as explicit random variables. Some of the important properties of the double sampling plans are established. Using these results, an efficient algorithm is developed to obtain optimal double sampling plans. A comparison with a crude search shows that our algorithm leads to about 90% savings, on the average, in computational timings. The procedure is also explained through a suitable example for the ARMA(1,1) model. It is observed, for instance, that an optimal double sampling plan leads to about 23% reduction in average sample number, compared to an optimal single sampling plan. Tables for choosing the optimal plans for certain auto regressive moving average processes at some practically useful values of acceptable quality level and rejectable quality level are also presented.     

一般寿命分布和定时截尾的Bayes变量抽样方案

林（1994）研究了指数分布和定时截尾的变量抽样方案．本文将讨论一般寿命分布和定时截尾的一次抽样方案．在多项式损失函数的假设下,我们讨论了Weibull分布、双参数指数分布和-分布三种情形,并着重讨论Weibull分布的情形．本文还提出了一个可用于近似地确定最优抽样方案的有报算法,并且进行了灵敏度分析,还同林较早的模型（1990,1994）做了比较．     

Compressed limit sampling inspection plans for food safety

The design of attribute sampling inspection plans based on compressed or narrow limits for food safety applications is covered. Artificially compressed limits allow a significant reduction in the number of analytical tests to be carried out while maintaining the risks at predefined levels. The design of optimal sampling plans is discussed for two given points on the operating characteristic curve and especially for the zero acceptance number case. Compressed limit plans matching the attribute plans of the International Commission on Microbiological Specifications for Foods are also given. The case of unknown batch standard deviation is also discussed. Three‐class attribute plans with optimal positions for given microbiological limit M and good manufacturing practices limit m are derived. The proposed plans are illustrated through examples. R software codes to obtain sampling plans are also given. Copyright © 2016 John Wiley & Sons, Ltd.     

A new system of skip‐lot sampling plans having a provision for reducing normal inspection

The skip‐lot sampling program can be used for reducing the amount of inspection on a product that has excellent quality history. Thus skip‐lot sampling plans are designed to reduce inspection costs. Moreover, the skip‐lot concept is sound and useful and is economically advantageous to use in the design of sampling plans. Hence, a new system of skip‐lot sampling plans designated as the SkSP‐V plan is developed in this paper. The proposed plan requires a return to normal inspection whenever a lot is rejected during sampling inspection, but has a provision for a reduced normal inspection upon demonstration of superior product quality. A Markov chain formulation and derivation of performance measures for this new plan are presented. The properties of SkSP‐V plan are studied with single sampling plan as the reference plan. Advantages of this new plan are also discussed. Finally, certain cost models are given for the economic design of the SkSP‐V plan. Copyright © 2010 John Wiley & Sons, Ltd.     

记数抽样检查方案设计与分析软件研制

利用VisualC++6.0Windows开发设计了抽样方案分析与设计软件。软件集成多种功能于一窗口,直观性强,操作方便,计算速度快,不仅可对现行抽样方案检索与分析,而且还可对一次、二次、五次和序贯抽样方案进行设计与分析,并作计算机模拟,可供抽样检查和抽样方案设计人员使用。     

A Unified Approach for Modeling and Designing Attribute Sampling Plans for Monitoring Dependent Production Processes

In this paper, we consider a probabilistic model to represent some general dependent production processes and present a unified approach for designing attribute sampling plans for monitoring the ongoing production process. This model includes the classical iid model, independent model, Markov-dependent model and previous-sum dependent model, to mention a few. Some important properties of this model are established. We derive the recurrence relations for the probability distribution of the sum of n consecutive characteristics observed from the process. Using these recurrence relations, we present efficient algorithms for designing optimal single and double sampling plans for attributes, for monitoring the ongoing production process. Our algorithmic approach, which uses effectively the recurrence relations, yields a direct and an exact method, unlike many approximate methods adopted in the literature. Several interesting examples concerning specific models are discussed and a few tables for some special cases are also presented. It is demonstrated that the optimal double sampling plans lead to about 42% reduction in average sample number over the single sampling plans for process monitoring. AMS 2000 Subject Classifications: Primary 62P30; Secondary 62E15, 65C60     

随机截尾试验变量抽样接收方案的贝叶斯决策

本运用Bayes决策理论研究指数分布和随机截尾试验的抽样接收方案的一般模型,我们证明了最优Bayes法则具有单调性,并对二个特殊的决策损失函数给出了最优Bayes法则和Bayes风险的具体表达式。     

链型抽样方案综述(Ⅰ)

本文讨论了链型抽样方案（ｎ,ｉ）及其操作特性函数,并介绍了选取方案的方法。为制定链型抽样方案的检验标准及在实际中使用链型抽样方案提供理论依据     

定时截尾下指数分布产品可靠性抽样检验方案

本文给出了制订定时截尾下指数分布产品可靠性抽样检验方案的统计方法.检验统计量是平均寿命倒数的极大似然估计.提出了一种选择截尾时间的方法.利用分布分位数的Cornish-Fisher展开近似地确定了样本量和接收常数.模拟结果表明,本文给出的方法是可行的.     

Multiple states repetitive group sampling plans with process loss consideration

We propose a multiple state repetitive group sampling plan by considering the process loss. The optimal plan parameters of the proposed plan are selected such that producer’s risk and consumer’s risk are satisfied simultaneously by minimizing the average sample number. The advantages of the proposed plan over the existing sampling plans are given. Extensive tables are provided for practical applications of the proposed plan. Two real world examples are given for the illustration purpose.     

A Kind of the ASN' Extreme Value forMeasuring Double Sampling Plan

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Optional sampling of submartingales with scanned index sets

The implication of Doob's optional sampling theorem in general fails to hold for submartingales with partially ordered index sets. Under an additional assumption on the index set (scanning property) we prove optional sampling theorems which are general enough to cover all previous results and, moreover, can be applied for continuous time sampling plans.     

用于连续抽样方案的两类更优的中止规则

本文提出并讨论了适用于各类连续抽样方案的两参数中止规则 [N ,c]和 [R ,d]。作为应用 ,以MIL STD 12 35B中公布的CSP V方案为例 ,计算并给出了相应的中止参数 ,还将 [N ,c],[R ,d]与已有的两类规则 [S],[R]进行了特性比较。结果表明 ,[N ,c]和 [R ,d]均具有更优的统计特性     

Bayesian variable sampling plan for the weibull distribution with type I censoring

In this article, we study a model of a single variable sampling plan with Type I censoring. Assume that the quality of an item in a batch is measured by a random variable which follows a Weibull distributionW (λ,m), with scale parameter λ and shape parameterm having a gamma-discrete prior distribution or σ=1/λ andm having an inverse gamma-uniform prior distribution. The decision function is based on the Kaplan-Meier estimator. Then, the explicit expressions of the Bayes risk are derived. In addition, an algorithm is suggested so that an optimal sampling plan can be determined approximately after a finite number of searching steps.     

指数-威布尔分布下基于期望总成本最小的寿命试验抽样方案

对于寿命遵从指数-威布尔分布的产品,在生产商提供优质保修服务的前提下,采用生产商在产品抽验过程中与产品接收后所承担的总成本期望最小的准则,制定寿命试验的最优抽样方案.通过实例,证实指数-威布尔分布适宜作为当前产品的寿命分布,并验证了这种抽样方案的合理性.     

计数集团检查的抽查特征函数

本文给出计数型集团检查一次、二次抽样方案的抽查特征函数及其算法, 并且通过与近似算法的比较和计算机抽样检查模拟, 验证了该方法的正确性, 并对该抽查特征函数性质和应用作了初步讨论.     

Bayesian Sampling Plans for Exponential Distribution Based on Type I Censoring Data

We study variable sampling plans for the exponential distribution based on type I censoring data. Using a suitable loss function, a Bayesian variable sampling plan (n _B , t _B , _B ) is derived. For certain prior distributions and loss functions, the numerical values of the Bayesian sampling plans and the associated minimum Bayes risks are tabulated. In terms of Bayes risks, comparisons between the proposed Bayesian sampling plans (n _B , t _B , _B ) and the Bayesian variable sampling plans (n ₀, t ₀, ^L _{T 0}) of Lam (1994, Ann. Statist., 22, 696–711) have been made. The numerical results indicate that under the same conditions, the proposed Bayesian sampling plan is superior to that of Lam in the sense that the Bayes risk of (n _B , t _B , _B ) is less than that of (n ₀, t ₀, ^L _{T 0}).     

An Empirical Comparison of Methods for Computing Bayes Factors in Generalized Linear Mixed Models

Generalized linear mixed models (GLMM) are used in situations where a number of characteristics (covariates) affect a nonnormal response variable and the responses are correlated due to the existence of clusters or groups. For example, the responses in biological applications may be correlated due to common genetic factors or environmental factors. The clustering or grouping is addressed by introducing cluster effects to the model; the associated parameters are often treated as random effects parameters. In many applications, the magnitude of the variance components corresponding to one or more of the sets of random effects parameters are of interest, especially the point null hypothesis that one or more of the variance components is zero. A Bayesian approach to test the hypothesis is to use Bayes factors comparing the models with and without the random effects in question—this work reviews a number of approaches for estimating the Bayes factor. We perform a comparative study of the different approaches to compute Bayes factors for GLMMs by applying them to two different datasets. The first example employs a probit regression model with a single variance component to data from a natural selection study on turtles. The second example uses a disease mapping model from epidemiology, a Poisson regression model with two variance components. Bridge sampling and a recent improvement known as warp bridge sampling, importance sampling, and Chib's marginal likelihood calculation are all found to be effective. The relative advantages of the different approaches are discussed.     

Design of accelerated life test sampling plans with a nonconstant shape parameter

Accelerated life test sampling plans (ALTSPs) provide information quickly on the lifetime distribution of products by testing them at higher-than-usual stress level to induce early failures and reduce the testing efforts. In the traditional design of ALTSPs for Weibull distribution, it is assumed that the shape parameter remains constant over all stress levels. This paper extends the existing design of ALTSPs to Weibull distribution with a nonconstant shape parameter and presents two types of ALTSPs; time-censored and failure-censored. Optimum ALTSPs which satisfy the producer’s and consumer’s risk requirements and minimize the asymptotic variance of the test statistic for deciding the lot acceptability are obtained. The properties of the proposed ALTSPs and the effects of errors in pre-estimate of the design parameters are also investigated.