Optimal Designing of Variables Sampling Plan for Resubmitted Lots

This article proposes a variables sampling plan that can be applied for sampling inspection of resubmitted lots when the quality characteristic of interest follows the normal distribution. Resubmission of lots for inspection is allowed in some situations where the original inspection results are suspected or when the supplier or producer is allowed to opt for resampling as per the provisions of the contract, etc. The advantages of this proposed variables sampling plan over the existing single sampling variables plan are discussed. Tables are also constructed for the selection of optimal parameters of known and unknown standard deviation variables resampling scheme for specified two points on the operating characteristic curve, namely, the acceptable quality level and the limiting quality level along with the producer and consumer's risks. The optimization problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.     

A flexible sampling scheme for variables inspection with loss consideration

This article develops a variables sampling scheme for resubmitted lots by incorporating the concept of Taguchi loss function. The probability of lot acceptance is derived based on the exact sampling distribution and two-point condition on operating characteristic curve is used to determine the plan parameters that meet both the producer's and consumer's quality and risk requirements. Moreover, the performance of the proposed variables resubmitted sampling plan is investigated and compared with the classical variables single sampling plan. The results indicate that the developed resubmitted sampling plan can provide the same protection with less inspection when the submitted lot is good enough. Tables of the plan parameters under various conditions are provided and the use of the proposed plan is also illustrated with an example.     

Resampling m-Dependent Random Variables with Applications to Forecasting

Resampling methods are proposed to estimate the distributions of sums of m -dependent possibly differently distributed real-valued random variables. The random variables are allowed to have varying mean values. A non parametric resampling method based on the moving blocks bootstrap is proposed for the case in which the mean values are smoothly varying or 'asymptotically equal'. The idea is to resample blocks in pairs. It is also confirmed that a 'circular' block resampling scheme can be used in the case where the mean values are 'asymptotically equal'. A central limit resampling theorem for each of the two cases is proved. The resampling methods have a potential application to time series analysis, to distinguish between two different forecasting models. This is illustrated with an example using Swedish export prices of coated paper products.     

Acceptance sampling by variables when the remainder of rejected lots is inspected

Acceptance sampling plans for inspection by variables, which minimize the mean inspection cost per lot of process average quality (assuming that the remainder of rejected lots is, inspected), were derived under the condition that the probability of accepting a submitted lot of tolerance quality, shall be 0.1. These plans were tabulated for chosen values of the given parameters, and compared with the Dodge-Romig LTPD attribute sampling plans. From the comparison it follows that under the same protection of consumer the LTPD plans for inspection by variables are in many situations more economical than the corresponding Dodge-Romig plans. This result is valid especially for the large lots and for the small values of the tolerance fraction defective.     

Zero acceptance number quick switching system for compliance sampling

The zero acceptance number plan is invariably used for compliance sampling and safety inspection of products. The disadvantage of such a plan is that its discriminating power between good and bad lots is poor. This paper presents a quick switching system that has zero acceptance numbers, with a provision for the resubmission of lots not accepted during normal inspection. The proposed system is found to require a smaller average sample size, and possesses greater discriminating power.     

Developing of a new system of skip-lot reinspection schemes

The skip-lot sampling plans are widely used in industries for quality inspection of products in order to reduce the sampling costs and inspection efforts when products have good quality history. Also, the skip-lot sampling plan concept is sound and useful and it is economically advantageous to use the skip-lot approach in the design of sampling plans. Thus, the skip-lot sampling plans are useful to minimize the cost of the inspection particularly in costly and destructive testing. Hence, a new system of skip-lot sampling plans designated as SkSP-2-R plan is developed in this article by incorporating the idea of resampling procedure in the skip-lot sampling plans of type SkSP-2. A Markov chain formulation and derivation of performance measures for this new plan are presented. The properties and advantages of the SkSP-2-R plan are studied with single sampling plan as the reference plan. The response-to-change characteristics of the SkSP-2-R plan are also investigated, based on the average run length.     

Exact calculation of the Dodge-Romig LTPD single sampling plans for inspection by variables

In this paper we shall deal with the acceptance sampling plans when the remainder of rejected lots is inspected. We shall consider two types of LTPD plans- for inspection by variables and for inspection by variables and attributes (all items from the sample are inspected by variables, remainder of rejected lots is inspected by attributes). We shall report on an algorithm allowing the calculation of these plans when the non-central t distribution is used for the operating characteristic. The calculation is considerably difficult, algorithm for non-central t distribution takes several minutes. For the calculation we shall use an original method.     

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 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.     

The computational aspects of multiple attribute sampling procedures

One method of controlling the quality of incoming lots is through attribute sampling. To simultaneously control several (possibly dependent) attributes, properly chosen single attribute sampling plans can be merged into a multiple attribute sampling plan. The general form of such a plan is given and various alternatives are discussed. The multinomial distribution is used to develop formulae necessary for an analysis of a multiple attribute plan. Due to the lengthy nature of the calculations involved, a computer algorithm is outlined.     

Modified chain sampling plans for lot inspection by variables and attributes

The purpose of acceptance sampling is to develop decision rules to accept or reject production lots based on sample data. When testing is destructive or expensive, dependent sampling procedures cumulate results from several preceding lots. This chaining of past lot results reduces the required size of the samples. A large part of these procedures only chain past lot results when defects are found in the current sample. However, such selective use of past lot results only achieves a limited reduction of sample sizes. In this article, a modified approach for chaining past lot results is proposed that is less selective in its use of quality history and, as a result, requires a smaller sample size than the one required for commonly used dependent sampling procedures, such as multiple dependent sampling plans and chain sampling plans of Dodge. The proposed plans are applicable for inspection by attributes and inspection by variables. Several properties of their operating characteristic-curves are derived, and search procedures are given to select such modified chain sampling plans by using the two-point method.     

Errors in inspection and grading distributional aspects ofscreening and merarchal screening

Continuing the studies of Johnson et al (1980) and Johnson and Kotz (1981), further distributions arising from models of errors in inspection and grading of samples from finite, possibly stratified lots are obtained. Screening, and hierarchal screening forms of inspection are also considered, and the effects of errors on the advantages of these techniques assessed.     

Dodge-Romig AOQL single sampling plans for inspection by variables

Acceptance sampling plans for inspection by variables, which minimize the mean inspection cost per lot of process average quality (assuming that the remainder of rejected lots is inspected), are derived under the condition that the maximum value of the mean fraction defective after sampling inspection, replacing all defective items found by good ones, shall be equal top _L . These plans are tabulated for chosen values of the given parameters, and compared with the Dodge-Romig AOQL attribute sampling plans. From the comparison it follows that under the same protection of consumer the AOQL plans for inspection by variables are in some situations more economical than the corresponding Dodge-Romig plans.     

Optimal acceptance sampling for modules F and F1 of the European Measuring Instruments Directive

ABSTRACT

Acceptance sampling plans offered by ISO 2859-1 are far from optimal under the conditions for statistical verification in modules F and F1 as prescribed by Annex II of the Measuring Instruments Directive (MID) 2014/32/EU, resulting in sample sizes that are larger than necessary. An optimised single-sampling scheme is derived, both for large lots using the binomial distribution and for finite-sized lots using the exact hypergeometric distribution, resulting in smaller sample sizes that are economically more efficient while offering the full statistical protection required by the MID.     

A sampling plan for one-shot systems considering destructive inspection

Abstract

The paper is concerned with an acceptance sampling problem under destructive inspections for one-shot systems. The systems may fail at random times while they are operating (as the systems are considered to be operating when storage begins), and these failures can only be identified by inspection. Thus, n samples are randomly selected from N one-shot systems for periodic destructive inspection. After storage time T, the N systems are replaced if the number of working systems is less than a pre-specified threshold k. The primary purpose of this study is to determine the optimal number of samples n*, extracted from the N for destructive detection and the optimal acceptance number k*, in the sample under the constraint of the system interval availability, to minimize the expected cost rate. Numerical experiments are studied to investigate the effect of the parameters in sampling inspection on the optimal solutions.     

Economic design of quick switching sampling system for resubmitted lots

This paper proposes a quick switching sampling system for the inspection of attributes quality characteristics for resubmitted lots. The optimal parameters for both fraction non conforming items and fraction non conformities of the proposed sampling system are determined using an optimization procedure so that producer’s risk and consumer’s risk are simultaneously satisfied. Tables are also constructed for the selection of parameters for specified AQL and LQL. The advantage of the proposed plan over the existing plan is discussed and illustrate. An economic design of the proposed sampling system is also discussed and shown that the proposed sampling system has minimum total cost and average total inspection compared to other existing sampling plans.     

A generalized framework of sampling inspections by attributes

This paper tries to establish a framework for sampling inspections by attributes based on soft quality standards to pay more attention to some shortcomings in classical modelling concerning the acceptability of inspection lots. As a suggestion, such sampling inspections are described in terms of a statistical test with fuzzy hypothesis and fuzzy data, extending the classical framework of sampling inspections by attributes. Furthermore, the operating characteristics will be explored, and single sampling plans of given strength are investigated.     

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.     

On a problem in two-stage sampling

Beattie 1962 proposed an alternate procedure for monitoring continuous processes which, unlike existing continuous samplingplans under Mil-Std-1235B, does not require periods of 100% inspection. The procedure, which is a composite of two Cumulative (Cusum) procedures, will be analyzed in terms of Cusum average run length (ARL) performance. An algorithm is proposed for generating sample plans based upon specifications on ARL performance in each of the Cusum sampling zones and the overall sampling risks of the procedure. The algorithm is fully described, and implemented using exact expressions for the Cusum ARL. An illustrated example is provided, describing how a continuous sampling maybe selected which matches performances about the AQL for a related plan in ISO 3951.