A double acceptance sampling plan for generalized log-logistic distributions with known shape parameters

A double acceptance sampling plan for the truncated life test is developed assuming that the lifetime of a product follows a generalized log-logistic distribution with known shape parameters. The zero and one failure scheme is mainly considered, where the lot is accepted if no failures are observed from the first sample and it is rejected if two or more failures occur. When there is one failure from the first sample, the second sample is drawn and tested for the same duration as the first sample. The minimum sample sizes of the first and second samples are determined to ensure that the true median life is longer than the given life at the specified consumer’s confidence level. The operating characteristics are analyzed according to various ratios of the true median life to the specified life. The minimum such ratios are also obtained so as to lower the producer’s risk at the specified level. The results are explained with examples.     

Assessment of acceptance sampling plans using posterior distribution for a dependent process

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.     

Optimal design of variable acceptance sampling plans for mixture distribution

ABSTRACT

The paper investigates the design of single and sequential variable acceptance sampling plans for a mixture distribution. Mixture distributions are seen in many practical problems such as life testing experiments of electronic components and clinical trials. The sampling plans for this kind of situations are not well addressed in the literature. We first propose a single sampling plan for a distribution which is a mixture of two exponential distributions. An optimization problem which minimizes the total cost of testing at given producer's and consumer's risks is solved to obtain the plan parameters. Two different sequential sampling plans are also defined and plan parameters are obtained by solving corresponding optimization problems. Finally, a case study, a simulation study and a sensitivity analysis are presented to illustrate our sampling plans.     

Optimal Bayesian sampling plans for exponential distributions based on hybrid censored samples

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).     

Reliability acceptance sampling plans for the Weibull distribution under accelerated Type-I censoring

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.     

Small-sample performance of a modified least-failures sampling procedure for bernoulli subset selection

We describe two sequential sampling procedures for Bernoulli subset selection which were shown to exhibit desirable behavior for large-sample problems. These procedures have identical performance characteristics in terms of the number of observations taken from any one of the populations under investigation, but one of the procedures employs one-at-a-time sampling while theother allows observations to be taken in blocks during early stages of experimentation. In this paper, a simulation study of their behavior for small-sample cases (n > 25) reveals that they canresult in a savings (sometimes substantial) in the expected total number of observations requiredto terminate the experiment as compared to single-stage procedures. Hence they may be quite usefulto a practitioner for screening purposes when sampling is limited.     

Repetitive group sampling plan based on the process capability index for the lot acceptance problem

An acceptance sampling plan is a method used to make a decision about acceptance or rejection of a product, based on adherence to a standard. Meanwhile, process capability indices (PCIs) have been applied in different manufacturing industries as capability measures based on specified criteria which include process departure from a target, process consistency, process yield and process loss. In this paper, a repetitive group sampling (RGS) plan based on PCI is introduced for variables’ inspection. First, the optimal parameters of the developed RGS plan are obtained considering constraints related to the risk of consumers and producers and also a double sampling plan, a multiple dependent state sampling plan and a sampling plan for resubmitted lots have been designed. Finally, after the development of variable sampling plans based on the Bayesian and exact approach, a comparison study has been performed between the developed RGS plan and other types of sampling plans and the results are elaborated.     

Double acceptance sampling plan based on truncated life tests for half exponential power distribution

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.     

Double and group acceptance sampling plan for truncated life test based on inverse log-logistic distribution

This paper introduces a double and group acceptance sampling plans based on time truncated lifetimes when the lifetime of an item follows the inverse log-logistic (ILL) distribution with known shape parameter. The operating characteristic function and average sample number (ASN) values of the double acceptance sampling inspection plan are provided. The values of the minimum number of groups and operating characteristic function for various quality levels are obtained for a group acceptance sampling inspection plan. A comparative study between single acceptance sampling inspection plan and double acceptance sampling inspection plan is carried out in terms of sample size. One simulated example and four real-life examples are discussed to show the applicability of the proposed double and group acceptance sampling inspection plans for ILL distributed quality parameters.     

Estimating the total number of distinct species using quadrat sampling and under-dependence structure

To estimate the total number of distinct species in a given region, Bayesian methods along with quadrat sampling procedures have been used by several authors. A key underlying assumption relies on the independence among the species. In this note, we analyse these estimates allowing a generalized binomial dependence between species.     

Analysis of reliability characteristics in the acceptance sampling tests

Until now, various acceptance reliability sampling plans have been developed based on different life tests of items. However, the statistical effect of the acceptance sampling tests on the reliability characteristic of the lots accepted in the test has not been appropriately addressed. In this paper, we deal with an acceptance reliability sampling plan under a ‘general framework’ and discuss the corresponding statistical effect of the acceptance sampling tests. The lifetime of the population before the acceptance test and that of population ‘conditional on the acceptance’ in the sampling test are stochastically compared. The improvement of reliability characteristics of the population conditional on the acceptance in the sampling test is precisely analyzed.     

Optimal designing of skip-lot sampling plan of type SkSP-2 with group acceptance sampling plan as reference plan under Burr-type XII distribution

In this paper, skip-lot sampling plan of type SkSP-2 with group acceptance sampling plans is proposed when the lifetime of the product follows the Burr-type XII distributions. The optimal parameters of the proposed plan are determined when two points on operating characteristics curve namely acceptable quality level and limiting quality level and the number of testers are specified. We also considered the Burr-type XII distribution to find the plan parameters. Several tables are given for practical use. We compare the results of proposed plan with the existing plans. Results are explained using real-world examples.     

On designing an acceptance sampling plan for the Pareto lifetime model

In this paper, the design of reliability sampling plans for the Pareto lifetime model under progressive Type-II right censoring is considered. Sampling plans are derived using the decision theoretic approach with a suitable loss or cost function that consists of sampling cost, rejection cost, and acceptance cost. The decision rule is based on the estimated reliability function. Plans are constructed within the Bayesian context using the natural conjugate prior. Simulations for evaluating the Bayes risk are carried out and the optimal sampling plans are reported for various sample sizes, observed number of failures and removal probabilities.     

A new policy for designing acceptance sampling plan based on Bayesian inference in the presence of inspection errors

The purpose of this article is to present a new policy for designing an acceptance sampling plan based on the minimum proportion of the lot that should be inspected in the presence of inspection errors. It is assumed that inspection is not perfect and every defective item cannot be detected with complete certainty. The Bayesian method is used for obtaining the probability distribution function of the number of defective items in the lot. To design this model, two constraints of producer risk and consumer risk are considered during the inspection process by using two specified points on operating characteristic curve. In order to illustrate the application of the proposed model, an example is presented. In addition, a sensitivity analysis is performed to analyze the model performance under different scenarios of process parameters and the results are elaborated. Finally, the efficiency of the proposed model is compared with the sampling method of Spencer and Kevan de Lopez (2017) at the same conditions.     

A procedure for selection of a gamma-Poisson single sampling plan by attributes

Design and evaluation of sampling plans by attributes and by variables are important aspects in the area of acceptance sampling research. Various procedures for the selection of conventional single sampling by attributes have been developed and are available in the literature. This paper presents a design methodology and tables for the selection of parameters of single sampling plans for specified requirements (strengths) under the conditions of a gamma prior and Poisson sampling distribution. The relative efficiency of gamma-Poisson single sampling plans over conventional plans is discussed through empirical illustrations.     

On some properties of variable size simple random sampling and a limit theorem

This paper introduces a sampling plan for finite populations herein called “variable size simple random sampling” and compares properties of estimators based on it with results from the usual fixed size simple random sampling without replacement. Necessary and sufficient conditions (in the spirit of Hajek (1960)) for the limiting distribution of the sample total (or sample mean) to be normal are given.     

A fast algorithm for sampling from the posterior of a von Mises distribution

Motivated by molecular biology, there has been an upsurge of research activities in directional statistics in general and its Bayesian aspect in particular. The central distribution for the circular case is von Mises distribution which has two parameters (mean and concentration) akin to the univariate normal distribution. However, there has been a challenge to sample efficiently from the posterior distribution of the concentration parameter. We describe a novel, highly efficient algorithm to sample from the posterior distribution and fill this long-standing gap.     

Triple sampling procedure for estimating the scale parameters of pareto distributions

This paper sheds light on the large sample performance of the three stage sam- pling procedure, as it pertains to estimating the scale parameter(s) of the Pareto distribution(s). This group sampling procedure merges the efficiency of the purely sequential procedure of Anscombe (1953) and Chow and Robbins (1965) with substan-tial savings in the number of sampling operations, as noted by Hall (1981). Both its simplicity and its economical features provide visible advantages over the one-by-one sampling as an alternative. In this paper we develop some asymptotic properties for the final stage sample size of the triple stage sampling originated by Hall (1981). These results are used to study both the point and the interval estimation problems for the scale parameters of the Pareto distributions. Since our results are asymptotic in nature, a simulation study is given to discuss the moderate sample size peformance of the proposed procedures.     

Entropy estimation and goodness-of-fit tests for the inverse Gaussian and Laplace distributions using paired ranked set sampling

ABSTRACT

In this paper, Vasicek [A test for normality based on sample entropy. J R Stat Soc Ser B. 1976;38:54–59] entropy estimator is modified using paired ranked set sampling (PRSS) method. Also, two goodness-of-fit tests using PRSS are suggested for the inverse Gaussian and Laplace distributions. The new suggested entropy estimator and goodness-of-fit tests using PRSS are compared with their counterparts using simple random sampling (SRS) via Monte Carlo simulations. The critical values of the suggested tests are obtained, and the powers of the tests based on several alternatives hypotheses using SRS and PRSS are calculated. It turns out that the proposed PRSS entropy estimator is more efficient than the SRS counterpart in terms of root mean square error. Also, the proposed PRSS goodness-of-fit tests have higher powers than their counterparts using SRS for all alternative considered in this study.     

Optimal design of the variable sampling size and sampling interval variable dimension T2 control chart for monitoring the mean vector of a multivariate normal process

This paper develops the algorithm for the optimization designs of the adaptive T² Control Chart for Monitoring the Mean Vector of a Multivariate Normal Process. It includes the variable sample size, variable sampling interval and variable dimensional chart. The VDT² control chart performs well for moderate and large shifts in the mean vector. However, its performance for small shifts is poor. To improve the chart's performance in detecting such shifts, we propose the application of the variable sample size and sampling interval technique to the VDT² control chart, resulting in the VSSIVDT² control chart.