Parameters Of Sampling Plan Research Articles

A variable sampling plan based on the coefficient of variation for lots resubmission

This study focuses on the issue of lots resubmission in inspection processes, which often arises when the initial inspection of a lot is suspected, marked as held, or not accepted. To address this problem, a novel variables sampling plan based on the coefficient of variation is proposed. The objective is to determine the sampling plan parameters that minimize the average sample number while satisfying the two-points of operating characteristic curve. Practical considerations are taken into account by providing tabulated values for the inspection sample size and acceptance criteria of the proposed plan. These tables incorporate various combinations of quality levels, considering commonly used producer's risk and consumer's risk. Furthermore, a comparative analysis between the proposed plan and a single sampling plan is conducted to highlight the advantages of the new approach. To illustrate the practical implementation of the proposed plan, an example is presented.

Current sampling plans can introduce high variance in mycotoxin testing results as demonstrated by the online FAO Mycotoxin Sampling Tool

The free-to-use online FAO Mycotoxin Sampling Tool (http://tools.fstools.org/mycotoxins/) provides users an opportunity to easily estimate impacts of adjusting sampling plan parameters on the risk of misclassifying consignments relative to a defined maximum level, as well as the contributions from sampling, sample preparation, and analytical test stages to the total variance of mycotoxin sampling plan designs, without performing resource-intensive sampling and laboratory analyses. The Tool was used to assess variance in the analysis of aflatoxins, deoxynivalenol, fumonisins, and ochratoxin A in maize, wheat, and powdered ginger for various sampling plans, including those specified in the Codex Alimentarius Commission General Standard on Contaminants and Toxins in Food and Feed. Results indicated that the current Codex sampling plans for maize and wheat could result in total measurement error equivalent or greater than 90% of the current and proposed maximum levels for ochratoxin A in wheat and aflatoxins in maize, respectively.

Optimum profit model based on the average outgoing quality limit protection

The optimal setting of process mean is an important issue in operations management and a variable sampling inspection plan is an acceptance sampling technique for quality assurance. In the present study, the newsvendor problem (i.e., the mixed procurement system) is modified by applying a variable sampling inspection plan with specified average outgoing quality limit (AOQL) with maximization of the expected total profit including the manufacturer and the retailer. The optimal retailer’s order quantity and manufacturer’s process mean and the parameters of sampling plan are jointly determined by maximizing the expected total profit. In the model, the single sampling rectifying inspection plan is adopted to determine the quality of lot product and the used cost of customer for product is measured by Taguchi’s quadratic loss function. A numerical example is given and the sensitivity analysis of model parameters are provided for illustration. Based on the results of sensitivity analysis, it may be seen that a higher processing cost per unit generally leads to a lower expected profit. In the meantime, a higher retailer’s selling price always results in a higher expected profit.

Optimum profit model under the single variable sampling plan with consumer’s quality protection

A variables sampling plan is an acceptance sampling technique, where the process/ quality characteristics are measured in a continuous scale, and usually requires a smaller sample size than an attributes sampling plan. In the rectifying sampling plan, 100% inspection is performed to find the defectives in the rejected lot and then to replace those non-conforming items by conforming ones, which is able to provide the assurance of product quality level. In the present study, a newsvendor problem (pure procurement system) with application of a rectifying sampling plan under the constraint of the specified consumer’s risk is formulated to maximize the expected total profit, including both the producer and the retailer. The retailer’s order quantity and producer’s process mean, and the parameters of sampling plan are decision variables in our model and are jointly determined by maximizing the expected total profit. The solution procedure of this model is proposed and a numerical example is given. Based on the sensitivity analysis, it is obvious that producer’s processing cost and retailer’s selling price significantly affect the expected profit. Particularly, a lower processing cost always leads to a larger sample size, a larger order quantity and a higher expected profit. In addition, a lower retailer’s selling price generally results in a lower expected profit.

Consideration of A Priori Information under Serial Production of Nonrepairable Single-Action Items for Optimization of Sampling Plan Parameters

This article deals with estimation of the quality and reliability characteristics of a nonrepairable single-action item sample by a small statistical sample (GOST D 50779.11-2000) applying a priori information. The novelty of the results obtained is set forth in the recommendations for minimization of the size of sample of the nonrepairable single-action products under testing according to the results of analyzing the quantitative information on the parameters tested. Estimates of the quality and reliability of a nonrepairable single-action sample are provided.

Assessing process capability index using sampling plan in the presence of measurement system errors

Measurement system errors impact the collected data used to evaluate the process capability. The work developed in this paper aims at integrating these errors in the calculation of the threshold value of Cpused for making the decision about the process capability $$ \left({C}_{p0}^{\ast}\right) $$ and to propose a procedure that corrects the parameters of the sampling plan used to estimate this capability index. An expression of $$ {C}_{p0}^{\ast } $$ that depends on the gauge repeatability and reproducibility (GR&R), errors type I and type II, the capability index corresponding to the rejectable quality level (CpRQL), and to the acceptable quality level (CpAQL) was developed. The effects of these parameters and their relative interactions on the difference between capability index calculations with and without integrating the measurement system error (ΔCpthreshold) and the corresponding difference in the parts per million of defects ppm (Δppm) were assessed using a response surface design. It was found that the integration of the measurement system error is essential particularly when the difference between CpAQL and CpRQL is small. Concerning the correction of the sampling plan parameters, a procedure was developed to integrate the measurement system error evaluated by the GR&R. This procedure guarantees a common decision concerning the process capability whatever the state of the measurement system is, and this decision would, therefore, depend on the sample quality only.

Acceptance sampling for attributes via hypothesis testing and the hypergeometric distribution

This paper questions some aspects of attribute acceptance sampling in light of the original concepts of hypothesis testing from Neyman and Pearson (NP). Attribute acceptance sampling in industry, as developed by Dodge and Romig (DR), generally follows the international standards of ISO 2859, and similarly the Brazilian standards NBR 5425 to NBR 5427 and the United States Standards ANSI/ASQC Z1.4. The paper evaluates and extends the area of acceptance sampling in two directions. First, by suggesting the use of the hypergeometric distribution to calculate the parameters of sampling plans avoiding the unnecessary use of approximations such as the binomial or Poisson distributions. We show that, under usual conditions, discrepancies can be large. The conclusion is that the hypergeometric distribution, ubiquitously available in commonly used software, is more appropriate than other distributions for acceptance sampling. Second, and more importantly, we elaborate the theory of acceptance sampling in terms of hypothesis testing rigorously following the original concepts of NP. By offering a common theoretical structure, hypothesis testing from NP can produce a better understanding of applications even beyond the usual areas of industry and commerce such as public health and political polling. With the new procedures, both sample size and sample error can be reduced. What is unclear in traditional acceptance sampling is the necessity of linking the acceptable quality limit (AQL) exclusively to the producer and the lot quality percent defective (LTPD) exclusively to the consumer. In reality, the consumer should also be preoccupied with a value of AQL, as should the producer with LTPD. Furthermore, we can also question why type I error is always uniquely associated with the producer as producer risk, and likewise, the same question arises with consumer risk which is necessarily associated with type II error. The resolution of these questions is new to the literature. The article presents R code throughout.

Optimum process mean setting with specified average outgoing quality limit protection for variable single sampling plan

The average outgoing quality limit (AOQL) is a major performance evaluation for assuring the quality of product lot. The process mean setting is an important topic for statistical process control. In this paper, the author applies a variable single sampling inspection plan with the AOQL protection on the consumer for determining the optimal process mean and the parameters of sampling plan. The quality characteristic is considered with one-side lower specification limit and it is normally distributed with known standard deviation and unknown mean. The 100% inspection is adopted when the product lot is rejected. The optimum process mean and parameters of inspection plan are simultaneously determined by maximizing the expected total profit per unit under the specified AOQL value. The numerical example and sensitivity analysis of parameters are provided for illustration.

Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint

This paper considers the problem of integrated production, preventive maintenance and quality control for a stochastic production system subject to both reliability and quality deteriorations. A make-to-stock production strategy is used to provide protection to the serviceable stock against uncertainties. The quality control is performed using a single acceptance sampling plan by attributes. The preventive maintenance strategy consists in carrying out an imperfect maintenance as a part of the setup activity at the beginning of each lot production, while a major maintenance (overhaul) is undertaken once the proportion of defectives in a rejected lot reaches or exceeds a given threshold. The main objective of this study is to jointly optimize the production lot size, the inventory threshold, the sampling plan parameters and the overhaul threshold by minimizing the total incurred cost. To meet customer requirements, the optimization problem is subject to a specified constraint on the average outgoing quality limit (AOQL). A stochastic mathematical model is developed and solved using a simulation-based optimization approach. Numerical examples and thorough sensitivity analyses are provided to illustrate the efficiency of the proposed integrated model. Compared with the 100% inspection policy which is widely used in the literature on integrated production, maintenance and quality control, the results obtained show that an economic design of acceptance sampling in such an integrated context can lead to important cost savings of more than 20%.

Developing a variables repetitive group sampling plan based on process capability index C pk with unknown mean and variance

In this paper, variables repetitive group sampling plans are developed based on the process capability index C pk when the quality characteristic follows a normal distribution with unknown mean and variance. The sampling plan parameters such as the sample size and the acceptance constant are determined to minimize the average sample number. Symmetric and asymmetric cases, in percent defectives due to two specification limits, are dealt with for specified combinations of acceptable quality level and limiting quality level. Tables are provided and examples are given to use proposed plans in practice.

Two-Stage Group Acceptance Sampling Plan for Burr Type X Percentiles

Abstract A two-stage group acceptance sampling plan for the percentile of lifetimes which have the Burr type X distribution is discussed under the time truncated life test. The sampling plan parameters for the two-stage sampling plan are determined such that the producer's risk and consumer's risk are satisfied simultaneously for the given tester size and experiment time. The advantage of the proposed two-stage sampling plan over the single-stage sampling plan is also discussed. Useful tables are given for practical purpose.

Sequential sampling plan using fuzzy SPRT

In this paper we introduce a new sequential sampling plan based on sequential probability ratio test for fuzzy hypotheses testing. In order to deal with uncertainty happened, the triangular fuzzy number TFN is used to express the fuzzy phenomenon of the sampling plan's parameters. In this plan the acceptable quality level AQL and the lot tolerance percent defective LTPD are TFN. For such a plan, we design a decision criterion of acceptance and rejection for every arbitrary λ-cut and a particular table of rejection and acceptance is calculated. This plan is well defined, since, if the parameters are crisp, it changes to a classical plan.

A mathematical model for the joint determination of optimal process and sampling plan parameters

PurposeThe purpose of this paper is to integrate the decisions regarding optimal process mean and the parameters of a sampling plan.Design/methodology/approachA model is developed to determine these parameters. The model maximizes producer expected profit, while protecting the consumer through a constraint on the probability of accepting lots with low incoming quality. The model is presented for two cases. The first one is for non‐destructive testing and the other for destructive testing. An example is presented to demonstrate that the utility of the model and sensitivity analysis on key parameters of the model has been conducted.FindingsThe findings indicated that the optimal parameters for the process and the sampling plan are significantly different from when determined separately. The sensitivity analysis showed that the process parameters are very sensitive to changes in the process variance, moderately sensitive to the limit on incoming quality, and insensitive to the consumer risk and inspection cost.Practical implicationsThe models developed offer an alternative approach for quality managers to address setting process targets, taking into consideration a sampling plan.Originality/valueThe originality of the paper is in the integration of two elements of quality that are usually treated separately in the literature.

Integrated inventory and inspection policies for stochastic demand

In this paper, we develop integrated inventory inspection models with and without replacement of nonconforming items. Inspection policies include no inspection, sampling inspection, and 100% inspection. We consider a buyer who places an order from a supplier when his inventory level drops to a certain point, due to demand which is stochastic in nature. When a lot is received, the buyer uses some type of inspection policy. The fraction nonconforming is assumed to be a random variable following a beta distribution. The order quantity, reorder point and the inspection policy are decision variables. In the inspection policy involving determining sampling plan parameters, constraints on the buyer and manufacturer risks is set in order to obtain a fair plan for both parties. A solution procedure for determining the operating policies for inventory and inspection consisting of order quantity, sample size, and acceptance number is proposed. Numerical examples are presented to conduct a sensitivity analysis for important model parameters and to illustrate important issues about the developed models.

Inspection Error Adjustment in the Design of Single Sampling Attributes Plan

ABSTRACT This article presents an approach for the design of single sampling attributes plans of given strength when inspection errors are present. The design criterion considered is the specification of two points of the Operating Characteristic curve. The design approach also recommends repeated testing of sampled nonconforming units for conformance in order to reduce the adverse effect of the inspection errors. It is shown that realistic sampling plan parameters can be obtained if the inspection error probabilities are taken into account in the design of sampling plans.

Integrated inventory control and inspection policies with deterministic demand

In this paper, we develop integrated inventory inspection models with and without replacement of nonconforming items. Inspection policies include no inspection, sampling inspection, and 100% inspection. We consider a buyer who places an order from a supplier. When a lot is received, the buyer uses some type of inspection policy. The fraction nonconforming is assumed to be a random variable following a beta distribution. Both the order quantity and the inspection policy are decision variables. In the inspection policy involving determining sampling plan parameters, constraints on the buyer and manufacturer risks are set in order to obtain a fair plan for both parties. A solution procedure for determining the operating policies for inventory and inspection consisting of order quantity, sample size, and acceptance number is proposed. Numerical examples are presented to conduct a sensitivity analysis for important model parameters and to illustrate important issues about the developed models.

Minimum Average Fraction Inspected for Combined Continuous Lot by Lot Acceptance Sampling Plan

This article investigates the problem of minimizing the average fraction inspected (AFI) for a combined continuous lot by lot acceptance sampling plan. A solution procedure is developed to find sub-optimal sampling plan parameters that will meet the average outgoing quality limit (AOQL) requirement, while guaranteeing a small AFI when the process average (> AOQL) is known.

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 100 f 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.

OPTIMAL DESIGN OF PLANS FOR ACCEPTANCE SAMPLING BY VARIABLES WITH INVERSE GAUSSIAN DISTRIBUTION

ABSTRACT A vast majority of the literature on the design of sampling plans by variables assumes that the distribution of the quality characteristic variable is normal, and that only its mean varies while its variance is known and remains constant. But, for many processes, the quality variable is nonnormal, and also either one or both of the mean and the variance of the variable can vary randomly. In this paper, an optimal economic approach is developed for design of plans for acceptance sampling by variables having Inverse Gaussian (IG) distributions. The advantage of developing an IG distribution based model is that it can be used for diverse quality variables ranging from highly skewed to almost symmetrical. We assume that the process has two independent assignable causes, one of which shifts the mean of the quality characteristic variable of a product and the other shifts the variance. Since a product quality variable may be affected by any one or both of the assignable causes, three different likely cases of shift (mean shift only, variance shift only, and both mean and variance shift) have been considered in the modeling process. For all of these likely scenarios, mathematical models giving the cost of using a variable acceptance sampling plan are developed. The cost models are optimized in selecting the optimal sampling plan parameters, such as the sample size, and the upper and lower acceptance limits. A large set of numerical example problems is solved for all the cases. Some of these numerical examples are also used in depicting the consequences of: 1) using the assumption that the quality variable is normally distributed when the true distribution is IG, and 2) using sampling plans from the existing standards instead of the optimal plans derived by the methodology developed in this paper. Sensitivities of some of the model input parameters are also studied using the analysis of variance technique. The information obtained on the parameter sensitivities can be used by the model users on prudently allocating resources for estimation of input parameters.

A Note on the Continuous Sampling Plan CSP-V

This note investigates the problem of minimizing the average fraction inspected (AFI) for a CSP – V plan. A solution procedure is developed to find the sampling plan parameters that meet the average outgoing quality limit (AOQL) requirement, while minimizing the AFI when the process average (> AOQL) is known.