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.     

An efficient inspection scheme for variables based on Taguchi capability index

Acceptance sampling has been one of practical tools for quality assurance applications, which provide a general rule to the producer and the consumer for product acceptance determination. It has been shown that variables sampling plans requires less sampling compared with attributes sampling plans. Thus, variables sampling plans become more attractive and desirable especially when the required quality level is very high or the allowable fraction non-conforming is very small. This paper attempts to develop an efficient and economic sampling scheme, variables repetitive group sampling plan, by incorporating the concept of Taguchi loss function. The OC curve of the proposed plan is derived based on the exact sampling distribution and the plan parameters are determined by minimizing the average sample number with two constraints specified by the producer and the consumer. The efficiency of the proposed variables RGS is examined and also compared with the existing variables single sampling plan in terms of the sample size required for inspection. In addition, tables of the plan parameters for various combinations of entry parameters are provided and an example is presented for illustration.     

Bayesian single and double variable sampling plans for the Weibull distribution with censoring

The sampling inspection problem is one of the main research topics in quality control. In this paper, we employ Bayesian decision theory to study single and double variable sampling plans, for the Weibull distribution, with Type II censoring. A general loss function which includes the sampling cost, the time-consuming cost, the salvage value, and the after-sales cost is proposed to determine the Bayes risk and the corresponding optimal sampling plan. Explicit expressions for the Bayes risks for both single and double sampling plans are derived, respectively. Numerical examples are given to illustrate the effectiveness of the proposed method. Comparisons between single and double sampling plans are made, and sensitivity analysis is performed.     

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.     

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.     

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.     

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.     

Improved attribute acceptance sampling plans in the presence of misclassification error

This paper considers an attribute acceptance sampling problem in which inspection errors can occur. Unlike many common situations, the source of the inspection errors is the uncertainty associated with statistical sampling. Consider a lot that consists of N containers, with each container including a large number of units. It is desired to sample some of the containers and inspect a sample of units from these selected containers to determine proper disposition of the entire lot. Results presented in the paper demonstrate significant shortcomings in traditional sampling plans when applied in this context. Alternative sampling plans designed to address the risk of statistical classification error are presented. These plans estimate the rate of classification errors and set plan parameters to reduce the potential impact of such errors. Results are provided comparing traditional plans with the proposed alternatives. Limitations of the new plans are also discussed.     

Cyclic BSEC of block size 3

Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao and Stufken in 1988. In this note, we discuss constructions of these designs having cyclic automorphisms. We use Langford sequences to construct all possible cyclic BSEC (or CBSEC) with block size 3 and λ = 1,2, which establishes the necessary and sufficient conditions for such designs. Some constructions of the balanced sampling plan avoiding adjacent units, a generalization of BSEC, are also given for fixed λ.     

Continuous sampling plans for Markov-dependent production processes under limited inspection capacity

A continuous sampling plan is a set of rules that provide a given Average Outgoing Quality (AOQ), ideally with the minimum of effort (as measured by the Average Fraction Inspected, or AFI). Most such plans are based on the assumption that the quality (either defective or not) of successive production units is uncorrelated. In this paper, we explore the impact of correlation in the production process on the design of a sampling plan when it is not possible to inspect long runs of production unit-by-unit. We shall generalize Dodge's continuous sampling plan on two counts, replacing Level 1 100% inspection by 100f_o% inspection, and considering the production process to be Markov dependent instead of consisting of independent Bernoulli trials. We derive formulae for the AOQ and AFI, and consider how best to choose the sampling plan parameters in the presence of nonzero correlation.     

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．     

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     

Optimal truncated repetitive lot inspection with defect rates

Single and repetitive sampling schemes are conventional methods for evaluating the quality of lots or batches of products. Truncation repetitive sampling plans are introduced in this paper in order to significantly reduce the size of samples drawn from the lot. Under this scheme type, if a decision about the acceptance or rejection of the lots cannot be made in the original inspection, they can be reinspected, at most, a prefixed number of times. The Poisson distribution is assumed for the number of defects found in the samples drawn from the lot. Best truncated repetitive sampling plans are determined by solving integer nonlinear programming problems. A simplified methodology is suggested to obtain the plans with optimal inspection effort and controlled risks by using an iterative procedure. According to the results obtained, optimal truncated plans are shown to be better than the optimal single and repetitive schemes in reducing the average sample number of the inspection. An application to the manufacturing of glass is presented for illustrative purposes.     

Multiple dependent state sampling plans for lot acceptance based on measurement data

This paper proposes a multiple dependent (or deferred) state sampling plan by variables for the inspection of normally distributed quality characteristics. The decision upon the acceptance of the lot is based on the states of the preceding lots (dependent state plan) or on the states of the forthcoming lots (deferred state plan). The lot acceptance probability is derived and the two-point approach to determining the plan parameters is described. The advantages of this new variables plan over conventional sampling plans are discussed. Tables are constructed for the selection of parameters of this plan under the specific values of the producer’s and consumer’s risks, indexed by acceptable quality level and limiting quality level, when the standard deviation is known or unknown.     

A note on optimal foldover four-level factorials

The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the centered L ₂-discrepancy to assess the optimal foldover plans was studied for four-level design. A new analytical expression and a new lower bound of the centered L ₂-discrepancy for fourlevel combined design under a general foldover plan are respectively obtained. A necessary condition for the existence of an optimal foldover plan meeting this lower bound was described. An algorithm for searching the optimal four-level foldover plans is also developed. Illustrative examples are provided, where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient algorithms for searching the optimal four-level foldover plans.     

考虑关联性特征匹配的城市生命线风险应对方案选择方法

针对城市生命线风险应对方案选择问题涉及的特征指标关联性和信息形式多样性,本文提出了一种考虑关联性特征匹配的混合型决策方法。首先,给出实际域、设定域和公共域的定义,并将具有区间数、语言短语等信息形式的风险事件特征指标值和应对方案特征指标值分别映射为实际域和设定域,进而通过两者的面积交织确定公共域;然后,将公理设计方法扩展到混合型决策环境,计算出反映风险事件与应对方案在各个特征指标下匹配程度的信息量,并进行应对方案的初筛;进一步地,采用2-additive Choquet积分算子将特征指标的权重、关联系数和初筛后剩余应对方案的信息量集结为反映风险事件与应对方案综合匹配程度的信息总量,并据此选择最优的应对方案。最后,通过算例分析验证了所提方法的有效性和可行性。研究结果表明,该方法能够为相关监管部门快速响应城市生命线风险、最大程度地降低风险损失和危害提供有效的决策支持。     

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}).     

Capability-based quick switching sampling system for lot disposition

Various acceptance sampling schemes have been developed for quality control and assurance. In this research, two types of variables quick switching sampling (VQSS) system based on the process capability index C_pk are proposed. The VQSS is composed of two single sampling plans, one is under a normal inspection and the other is under a tightened inspection. Requirements for accepting a lot under the tightened inspection are more stringent than under the normal inspection. The concept of the VQSS system is that the sampling mechanism can adjust flexibly based on the quality history of the preceding submitted lots. A minimization model is constructed to solve the plan parameters for each type of the VQSS system under different mixes of quality levels and risk endurance levels, and several tables are prepared for references. In addition, the performance of the two types of VQSS system are compared with the single sampling plan through the operating characteristic (OC) curve and the average sample number (ASN) required for inspection. Finally, a real example from a dielectric layer coating machine is presented to show the practicality of the proposed system.     

一种面向多预案整合的层次网络模型

突发事件发生后,需要启动相应的应急预案来减少突发事件所带来的损失。根据灾害后果的不同,所启动的可能是一个预案,更可能是多个预案。为了使得启动的多个预案能够有效衔接,共同起到一个预案的作用,通过应急响应流程分析,首先,从基础概念出发对应急预案体系各要素的概念进行界定,理清各要素之间的相互关系,构建预案体系概念模型。其次,基于概念模型的要素和结构,采用网络的方法对预案体系进行抽象和分析,提出了预案体系的层次网络模型。最后给出了多预案模型整合流程和建模实例。研究结果表明,该模型不仅可以实现基于预案内容特征的流程的纵向整合,而且可以实现多个预案的横向整合,整合后的预案体系各类要素更完整,元素之间的关系更紧密,有效提高了预案体系的完备性,是实现预案修订以及有效性评估的基础。