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1.
Belmiro P. M. Duarte José F. O. Granjo 《Journal of Statistical Computation and Simulation》2019,89(17):3313-3329
The design of double acceptance sampling (AS) plans for attributes based on the operating characteristic curve paradigm is usually addressed by enumeration algorithms. These AS plans may be non optimal regarding the sample size to inspect as they were obtained without the requirement that the constraints at the OC curve controlled points are not violated for minimum Average Sample Number (ASN) scenarios. An approach based on mathematical programming is proposed to systematically design double AS plans for attributes, where the characteristics controlled are modelled by binomial or Poisson distributions. Specifically, Mixed Integer Nonlinear Programming (MINLP) formulations are developed and combined with an enumeration algorithm that allows finding ASN minimax optimal plans. A theoretical result is developed with the purpose of assuring the global optimum design is reached by iteration where a convenient solver is used to find local optima. To validate the algorithm, we compare our results with those of tables commonly used for practical purposes, consider different rates of risk, and setups commonly used in Lot Quality Assurance Plans (LQAS) for health monitoring programmes. Finally, we compare AS plans determined for processes described by binomial and Poisson distributions. 相似文献
2.
Lee-Shen Chen Ming-Chung Yang TaChen Liang 《Journal of Statistical Computation and Simulation》2017,87(6):1160-1178
This paper studies the problem of designing a curtailed Bayesian sampling plan (CBSP) with Type-II censored data. We first derive the Bayesian sampling plan (BSP) for exponential distributions based on Type-II censored samples in a general loss function. For the conjugate prior with quadratic loss function, an explicit expression for the Bayes decision function is derived. Using the property of monotonicity of the Bayes decision function, a new Bayesian sampling plan modified by the curtailment procedure, called a CBSP, is proposed. It is shown that the risk of CBSP is less than or equal to that of BSP. Comparisons among some existing BSPs and the proposed CBSP are given. Monte Carlo simulations are conducted, and numerical results indicate that the CBSP outperforms those early existing sampling plans if the time loss is considered in the loss function. 相似文献
3.
《Journal of Statistical Computation and Simulation》2012,82(7):873-882
From the exact distribution of the maximum likelihood estimator of the average lifetime based on progressive hybrid exponential censored sample, we derive an explicit expression for the Bayes risk of a sampling plan when a quadratic loss function is used. The simulated annealing algorithm is then used to determine the optimal sampling plan. Some optimal Bayes solutions under progressive hybrid and ordinary hybrid censoring schemes are presented to illustrate the effectiveness of the proposed method. 相似文献
4.
Min Kim 《Journal of applied statistics》2009,36(1):11-20
Type-I censored reliability acceptance sampling plans (RASPs) are developed for the Weibull lifetime distribution with unknown shape and scale parameters such that the producer and consumer risks are satisfied. It is assumed that the life test is conducted at an accelerated condition for which the acceleration factor (AF) is known, and each item is continuously monitored for failure. Sensitivity analyses are also conducted to assess the effect of the uncertainty in the assumed AF on the actual producer and consumer risks, and a method is developed for constructing RASPs that can accommodate the uncertainty in AF. 相似文献
5.
Gupta and Kundu proposed a new class of weighted exponential distributions using the idea of Azzalini. In this article, we develop an acceptance sampling plan for the weighted exponential distribution under a truncated life test. For various acceptance numbers, consumer’s confidence levels and values of the ratio of the experimental time to the specified mean lifetime, the minimum sample size necessary to ensure a certain mean lifetime are obtained. The operating characteristic function values and the associated producer’s risks are also presented. A numerical example is provided to illustrate the acceptance sampling plan. 相似文献
6.
TaChen LiangLee-Shen Chen Ming-Chung Yang 《Journal of statistical planning and inference》2012,142(2):537-551
This paper considers Bayesian sampling plans for exponential distribution with random censoring. The efficient Bayesian sampling plan for a general loss function is derived. This sampling plan possesses the property that it may make decisions prior to the end of the life test experiment, and its decision function is the same as the Bayes decision function which makes decisions based on data collected at the end of the life test experiment. Compared with the optimal Bayesian sampling plan of Chen et al. (2004), the efficient Bayesian sampling plan has the smaller Bayes risk due to the less duration time of life test experiment. Computations of the efficient Bayes risks for the conjugate prior are given. Numerical comparisons between the proposed efficient Bayesian sampling plan and the optimal Bayesian sampling plan of Chen et al. (2004) under two special decision losses, including the quadratic decision loss, are provided. Numerical results also demonstrate that the performance of the proposed efficient sampling plan is superior to that of the optimal sampling plan by Chen et al. (2004). 相似文献
7.
In this article designing of acceptance sampling plans for the truncated life test is proposed using economic approach by assuming that the lifetime of a product follows Frechet distribution based on median. The optimal sampling plans to meet the consumer’s confidence level with minimum total cost are designed. Efficiency of the proposed plan is also analyzed. 相似文献
8.
TaChen Liang 《Journal of Statistical Computation and Simulation》2013,83(5):922-940
We study variable sampling plans for exponential distributions based on type-I hybrid censored samples. For this problem, two sampling plans based on the non-failure sample proportion and the conditional maximum likelihood estimator are proposed by Chen et al. [J. Chen, W. Chou, H. Wu, and H. Zhou, Designing acceptance sampling schemes for life testing with mixed censoring, Naval Res. Logist. 51 (2004), pp. 597–612] and Lin et al. [C.-T. Lin, Y.-L. Huang, and N. Balakrishnan, Exact Bayesian variable sampling plans for the exponential distribution based on type-I and type-II censored samples, Commun. Statist. Simul. Comput. 37 (2008), pp. 1101–1116], respectively. From the theoretic decision point of view, the preceding two sampling plans are not optimal due to their decision functions not being the Bayes decision functions. In this article, we consider the decision theoretic approach, and the optimal Bayesian sampling plan based on sufficient statistics is derived under a general loss function. Furthermore, for the conjugate prior distribution, the closed-form formula of the Bayes decision rule can be obtained under either the linear or quadratic decision loss. The resulting Bayesian sampling plan has the minimum Bayes risk, and hence it is better than the sampling plans proposed by Chen et al. (2004) and Lin et al. (2008). Numerical comparisons are given and demonstrate that the performance of the proposed Bayesian sampling plan is superior to that of Chen et al. (2004) and Lin et al. (2008). 相似文献
9.
This paper demonstrates the use of maxima nomination sampling (MNS) technique in design and evaluation of single AQL, LTPD, and EQL acceptance sampling plans for attributes. We exploit the effect of sample size and acceptance number on the performance of our proposed MNS plans using operating characteristic (OC) curve. Among other results, we show that MNS acceptance sampling plans with smaller sample size and bigger acceptance number perform better than commonly used acceptance sampling plans for attributes based on simple random sampling (SRS) technique. Indeed, MNS acceptance sampling plans result in OC curves which, compared to their SRS counterparts, are much closer to the ideal OC curve. A computer program is designed which can be used to specify the optimum MNS acceptance sampling plan and to show, visually, how the shape of the OC curve changes when parameters of the acceptance sampling plan vary. Theoretical results and numerical evaluations are given. 相似文献
10.
Acceptance sampling plans for generalized exponential distribution when the lifetime experiment is truncated at a pre-determined time are provided in this article. The tables are provided for the minimum sample size required to ensure a certain median life of the experimental unit when the shape parameter is two. The operating characteristic function values of the sampling plans and the associated producer's risks are also presented. It is shown that the tables presented here can be used if instead of median life, other percentile life is chosen as the criterion or if the shape parameter is not two. Examples are provided for illustrative purposes. 相似文献
11.
12.
Acceptance sampling techniques are used to monitor the accuracy of gas meters. Random samples of meters are taken from homogeneous lots, and two accuracy measurements are recorded for each meter. In the past, the two measurements were averaged, and an acceptance sampling test applied to the sample of averages. In 1987, the plan was modified so that virtually the same test is applied to the two measurements individually. This new procedure is more stringent than the old procedure. In a study of data sampled over three years, the new plan rejects more lots than does the old plan, leading to greatly increased costs to the gas industry and therefore to the consumer. Theoretical reasons are given for why this occurs, and an alternative plan is proposed. 相似文献
13.
In this study, performance of single acceptance sampling plans by attribute is investigated by using the distribution of fraction nonconformance (i.e. lot quality distribution) for a dependent production process. It is the aim of this study to demonstrate that, in order to emphasize consumer risk (i.e. the risk of accepting a bad lot), it is better to evaluate a sampling plan based upon its performance as assessed by the posterior distribution of fractions nonconforming in accepted lots. Similarly, it is the desired posterior distribution that sets the basis for designing a sampling plan. The prior distribution used in this study is derived from a Markovian model of dependence. 相似文献
14.
For the conventional type-II hybrid censoring scheme (HCS) in Childs et al., a Bayesian variable sampling plan among the class of the maximum likelihood estimators was derived by Lin et al. under the loss function, which does not include the cost of experimental time. Instead of taking the conventional type-II hybrid censoring scheme, a persuasive argument leads to taking the modified type-II hybrid censoring scheme (MHCS) if the cost of experimental time is included in the loss function. In this article, we apply the decision-theoretic approach for the concerned acceptance sampling. With the type-II MHCS, based on a sufficient statistics, the optimal Bayesian sampling plan is derived under a general loss function. Furthermore, for the conjugate prior distribution, the closed-form formula of the Bayes decision rule can be obtained under the quadratic decision loss. Numerical study is given to demonstrate the performance of the proposed Bayesian sampling plan. 相似文献
15.
《Journal of Statistical Computation and Simulation》2012,82(8):903-914
This paper considers the design of accelerated life test (ALT) sampling plans under Type I progressive interval censoring with random removals. We assume that the lifetime of products follows a Weibull distribution. Two levels of constant stress higher than the use condition are used. The sample size and the acceptability constant that satisfy given levels of producer's risk and consumer's risk are found. In particular, the optimal stress level and the allocation proportion are obtained by minimizing the generalized asymptotic variance of the maximum likelihood estimators of the model parameters. Furthermore, for validation purposes, a Monte Carlo simulation is conducted to assess the true probability of acceptance for the derived sampling plans. 相似文献
16.
Acceptance sampling, a major division in Statistical quality control, provides a guaranteed confidence on the product quality. Conventionally, when sampling plans are used all bad lots are rejected and good lots are accepted based on the defined conditions. The purpose of designing any sampling plan is to determine a sequence of action to be applied on a series of lots of defined quality and the decisions made on acceptance or rejection of lots sometimes leads to specified risks which may not favor producer and consumer. Thus, the objective of this article is to develop a design methodology of Single sampling plan under the conditions of Intervened Poisson distribution through unity value approach. Further, the efficiency of the proposed plan is assessed over the conventional single sampling plan and it is discussed through the numerical illustration. 相似文献
17.
In this paper, we develop a double acceptance sampling plan for half exponential power distribution when the lifetime experiment is truncated at a prefixed time. The zero and one failure schemes are considered. We obtain the minimum sample sizes of the first and second samples necessary to ensure the specified mean life at the given consumer’s confidence level. The operating characteristic values and the minimum ratios of the mean life to the specified life are also analyzed. Numerical example is provided to illustrate the double acceptance sampling plan. 相似文献
18.
In this paper, we propose a sampling policy considering Bayesian risks. Various definitions of producer's risk and consumer's risk have been made. Bayesian risks for both producer and consumer are proven to give better information to decision-makers than classical definitions of the risks. So considering the Bayesian risk constraints, we seek to find optimal acceptance sampling policy by minimizing total cost, including the cost of rejecting the batch, the cost of inspection, and the cost of defective items detected during the operation. Proper distributions to construct the objective function of the model are specified. In order to demonstrate the application of the proposed model, we illustrate a numerical example. Furthermore, the results of the sensitivity analysis show that lot size, the cost of inspection, and the cost of one defective item are key factors in sampling policies. The acceptable quality level, the lot tolerance proportion defective, and Bayesian risks also affect the sampling policy, but variations of acceptable quality level and producer Bayesian risks, for values more than a specified value, cause no changes in sampling policy. 相似文献
19.
Reliability sampling plans provide an efficient method to determine the acceptability of a product based upon the lifelengths
of some test units. Usually, they depend on the producer and consumer’s quality requirements and do not admit closed form
solutions. Acceptance sampling plans for one- and two-parameter exponential lifetime models, derived by approximating the
operating characteristic curve, are presented in this paper. The accuracy of these approximate plans, which are explicitly
expressible and valid for failure and progressive censoring, is assessed. The approximation proposed in the one-parameter
case is found to be practically exact. Explicit lower and upper bounds on the smallest sample size are given in the two-parameter
case. Some additional advantages are also pointed out. 相似文献
20.
Max Döring 《Journal of Statistical Computation and Simulation》2019,89(16):2997-3034
The aim of this article is to review existing goodness-of-fit tests for the exponential distribution under progressive Type-II censoring and to provide some new ideas and adjustments. In particular, we consider two-parameter exponentially distributed random variables and adapt the proposed test procedures to our scenario if necessary. Then, we compare their power by an extensive simulation study. Furthermore, we propose five new test procedures that provide reasonable alternatives to those already known. 相似文献