A FUZZY ACCEPTANCE SAMPLING PLANS BASED ON NEGATIVE BINOMIAL DISTRIBUTION

In this dissertation an on-line interactive system for generating and analyzing various acceptance sampling plans is presented. This real-time sampling plan system utilizes a series of algorithms to perform the necessary functions for generating information pertinent to single, double, and multiple sampling plans. These algorithms along with other special programming considerations allow for fast generation of the following information relative to single, double, and multiple sampling plans: (1) the operating characteristic (OC) curve, (2) the average outgoing quality (AOQ) curve, (3) the average sample number (ASN) curve, (4) the average total inspection (ATI) curve, (5) multiple plots per graph, (6) the sample size(s), (7) the acceptance number(s), (8) the rejection number(s), (9) the average outgoing quality number (AOQL), (10) the lot size, (11) the lot quality (p' 95' p' 50' p' 10), and (12) the alpha and bet&adot value&sdot for a specified AQL and LPTD. This information for single, double, and multiple sampling plans can be generated by using either the Poisson, binomial, or hypergeometric distribution. Two procedures are available to the user for generating information pertinent to a particular sampling plan. The first procedure enables the user to generate single, double, and multiple sampling plans given the acceptance quality level (AQL) and the lot tolerance percent defective (LTPD). This procedure allows for the generation of two types of sampling plans: one plan minimizes consumers' risk and the other plan minimizes producers' risk. The second procedure permits the user to specify the sample size(s), the acceptance number(s), the rejection numbers (in case of multiple sampling plans), the lot size, and the percent defective used to scale the x-axis. The system is designed for use by a person with various backgrounds in programming or statistical quality control. Several examples of its use are given to illustrate one or more important points. The sampling plan system was found to be an acceptable means of generating and analyzing various sampling plans on a real-time basis.

ABSTRACTAn acceptance sampling plan (ASP) is a commonly used tool in quality assurance that allows business partners to make decisions about lot disposition. To enhance the efficiency and applicability of inspection, various ASPs have been constructed to meet different circumstances in practical applications. One of these ASPs is the skip‐lot sampling plan (SkSP), which reduces inspection time and cost for a series of product lots from a supplier with excellent quality records. Based on the structure of the SkSP, we propose an improved variables SkSP that uses a repetitive group sampling (RGS) plan based on the most commonly used capability index Cpk as the reference plan, designated as Cpk‐based SkSP‐RGS. This plan is optimized using a model that ensures the operating characteristic function meets a two‐point condition and minimizes the average sample number (ASN). Additionally, two main performance measures of sampling plans, ASN and discriminatory power, are investigated. The results reveal the superiority of the proposed plan over conventional Cpk‐based sampling plans. Lastly, a case study from the liquid crystal module industry is demonstrated using the proposed plan to show its applicability and practicality.

Monte Carlo operating characteristic (OC) and average sample number (ASN) functions were compared with Wald's OC and ASN equations for sequential sampling plans based on Wald's sequential probability ratio test (SPRT) using the binomial, negative binomial, normal, and Poisson distributions. This comparison showed that the errors inherent in Wald's equations as a result of "overshooting" the decision boundaries of the SPRT can be large. Relative errors increased for the OC and ASN equations as the difference between the null (θ0)) and alternative (θ1) test parameter values increased. Relative errors also increased for the ASN equation as the probabilities of type I (α) and type II (β) errors increased. For discrete distributions, the relative errors also increased as θ0 increased with θ1/θ0 fixed. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN. For the values of θ0, θ1, α, and β used in many sequential sampling plans in forestry, Wald's equations may not be adequate. For those cases where the errors in Wald's equations are important compared with the other errors associated with the sampling plan, two alternative Monte Carlo OC and ASN functions are proposed.

Multiple sampling plan (MSP) is a generalization of single and double sampling plans that enhances the efficiency by reducing the number of sample items needed for inspection. However, the operating characteristic function of MSP is relatively complicated to derive because the inspection at each stage is dependent on others, i.e., the lot judgment on the current lot not only depends on its inspected result but also considers the results of the previous stages. Therefore, in this study, we propose a stage-independent MSP (SIMSP) and integrate it with a loss-based capability index. SIMSP can be regarded as a relaxed form of the traditional MSP, assuming independence in inspections at each stage. SIMSP’s parameters are solved for a cost-efficient purpose under an optimization model that aims to minimize the average sample number (ASN), adhering to constraints aligned with predefined quality and acceptable risk levels. The results indicate that SIMSP can not only perform better discriminatory power but also require fewer ASN for making lot disposition. Besides, SIMSP’s performance is evaluated, analyzed, and contrasted with the traditional sampling plan under various settings. In addition, an example is presented using the developed graphical user interface to illustrate the real-world application of SIMSP.

Five acceptance sampling plans in which the flow of items produced by a continuous process is regarded as a flow of groups of items are considered in terms of the amount of inspection and the average outgoing quality. Some general results and nomograms to aid in the choice of a plan are given.

Fuzzy acceptance sampling plans for inspection of geospatial data with ambiguity in quality characteristics

An instantaneous replenishment model under the effect of a sampling policy for defective items

Sequential sampling plans based on the negative binomial distribution were developed for egg mass density of spruce budworm, Choristoneura fumiferana (Clemens), in Michigan's Upper Peninsula. Plans developed were modifications of Wald's sequential probability ratio test (SPRT) based on Monte Carlo simulation. Parameters of the negative binomial distribution were estimated by the maximum likelihood method. Sampling models developed classify egg mass populations into low and high categories using the number of egg masses on whole branch samples of balsam fir, Abies balsamifera (L.) Voss. Plans are presented for three pairs of population density hypotheses to give forest pest managers the flexibility to select a plan that best meets management objectives. Monte Carlo estimates indicated that Wald's average sample number (ASN) and operating characteristic (OC) equations underestimated the actual ASN values, and the actual alpha and beta error probabilities were smaller than the values prescribed by Wald's equations. Errors were sufficiently large to have serious economic implications during implementation of plans developed from Wald's approximate procedure. The sequential plans developed by modifying the decision boundaries of Wald's SPRT using the Monte Carlo procedure had error probabilities, OC functions, and ASN values that were approximately equal to those desired.

This chapter addresses the issue of quality assurance for the incoming materials and the role of purchasing in preventing quality problems to crop up. Communicating specifications unambiguously and completely at the time of placing orders and choosing a vendor who has the requisite process capability to supply quality as per those specifications are the preventive strategies in quality assurance of incoming materials. Design of an optimal inspection policy to get the requisite quality protection against defectives being accepted as good with the minimum inspection cost should be the objective of incoming materials quality assurance program. Acceptance sampling plans, OC curve, AQL, and LTPD are described. In double sampling plans, the decision to accept or reject the lot can be taken after the first sample if the lot quality is very good or very bad, respectively. However, in doubtful cases, a second sample is taken, and based on combined inspection outcomes of the two samples, a decision to either accept or reject the lot is taken.KeywordsQuality assuranceVendorProcess capabilitySpecificationsOptimal inspection policySampling plansOC curveAQLLTPDDouble sampling

To stay competitive in today’s global market, manufacturers must ensure products released to consumers, meet international regulations and standards and this can only be done by putting in place sampling plans to guarantee the release of quality lots of products into the market. Hence, the objective of this paper is to design a variables sampling plan for the released of packed yam flour in view of international regulations on the net content of packaged goods. Probability plots, operating characteristic curves, the average outgoing quality (AOQ), average outgoing quality limit (AOQL) and average total inspection (ATI) were useful measures to evaluate the fitness of the sampling plan using the Minitab 2021 statistical software package. The packing process net weight, was found to be normally distributed with a p-value of 0.075 and a process standard deviation of 2.16. A comparative analysis on sample size, sampling plan measures, such as the AOQ, AOQL, and ATI and in view of best practice, were decisive in selecting a sampling plan with a sample size of 31 packs per lot as the most economic plan for lot sentencing. A practical demonstration on this sampling plan usage was also showcased. This sampling plan elevates and improves the net content of the packed product released into the market in view of international regulatory laws.

The concept of acceptance sampling plans ensures the quality of products and materials used in highway construction. These acceptance sampling plans require the testing of each and every individual lot of products for the highway construction and materials. This approach of sampling is applicable and appropriate if the supplier or contractor is unreliable. If the contractor is consistent and reliable, then instead of inspecting each and every lot of products, skip-lot sampling system can be utilized where only a fraction of the lots are inspected after assuring the quality and after a certain number of conforming lots is obtained. Skip-lot sampling plan can be used for reducing the amount of inspection on product that has an excellent quality history. Thus, skip-lot sampling plans are designed to reduce inspection costs. Moreover, skip-lot concept is sound and useful and it is economically advantageous in the design of sampling plans. Hence, this paper presents an improved system of skip-lot sampling plans designated as SkSP-V plan for the application of highway construction and materials. Advantages of this plan over the existing skip-lot plan and AASHTO’s lot-by-lot sampling plan are also discussed. The efficiency of this new plan is also investigated.

Acceptance sampling is a statistical quality control technique whereby the final decision to accept or reject a lot is based on the outcome from the inspection of its sample. A recent development in acceptance sampling includes the group chain acceptance sampling plan (GChSP) to rectify the problems with the single acceptance sampling plans (SSP) and chain acceptance sampling plans (ChSP). To date, the GChSP has been developed using two different approaches: minimizing the consumer’s risk (CR) and balancing both the CR and producer’s risk (PR) via minimum angle method. For both approaches, the GChSP has been developed by applying exponential distribution to the sampling plans. However, previous researchers only developed GChSP using these approaches without comparing their performance. Therefore, this article compares the performance of the GChSP using both approaches but considering the CR only. Both the GChSPs are developed via the same phases: (i) identifying the design parameters, (ii) developing operating procedures, (iii) deriving the probability of lot acceptance, (iv) deriving the probability of zero or one defective, (v) selecting lifetime distribution and (vi) measuring performance. The results reveal two interesting findings. The first finding shows that at the lower value of a, the minimum angle method has better protection for the consumer. The second finding shows that when the value of a increases, both approaches actually protect the consumer at the same level.

Acceptance sampling is one of the imperative methods used in statistical quality control through judgement a lot concerning its quality of 100% inspection and no inspection. Acceptance sampling plan is able to minimise the inspection cost and sampling error. It is a technique that deals with accepting or not the lot to be found on sampling inspection that delivers the quality of products manufactured by industries. This paper portrays designing procedure and development of skip-lot sampling plan of type SkSP-T with special type double sampling plan (STDSP) as reference plan which is designated as SkSTDSP-T. Operating characteristics and performance measures are derived, evaluated and tables involving incoming and outgoing quality levels are constructed for SkSTDSP-T plan. Tables are simulated by changing various parametric values of SkSP-T and STDSP plan. Table values are calculated, operating characteristic curve is drawn by using R (programming) language. Additionally, the efficiency of the proposed plan is discussed.

Acceptance sampling plan is a product control technique, which plays a vital role in industries to inspect the quality of the raw materials processing at various stages of manufacturing and finished products at the specified quality levels. Various methods are used for monitoring and maintaining the quality of the products and services. Using acceptance sampling techniques, the quality of the products and services are decided, whether to accept or reject the finished product. In this situation the interest is to keep away from wrong selections, which is accepting the product of bad quality and rejecting the product of good quality. Accordingly, the usual objective in these cases is to use the overall risk of a wrong decision as optimization criteria. This situation is called as Minimum Risks Sampling Plan. In this paper, Hurdle Poisson distribution has been used to select the parameters of Repetitive Group Sampling Attribute Plan involving minimum sum of producer’s and consumer’s risks for specified Acceptable Quality Level and Limiting Quality Level.

From quality and reliability perspectives, acceptance sampling plans play a significant role in manufacturing and industries in order to minimize the defect in the process. It is essential that the final product received by the customers, either external or internal, to be defect-free. In this regard, this paper presents the special case of acceptance sampling plan referred to as quick switching sampling (QSS) plan in the context of failure censoring reliability tests by considering the information from lifetime performance index (LPI). Unlike the common process capability indexes, LPI is usually appropriate for processes with non-negative quality characteristics. It is assumed that the lifetime of items follows Weibull distribution. Derivations of the operating characteristic curves are developed and a mathematical model is presented which determines the optimal parameters of the QSS plan. In order to see the effectiveness of proposed QSS, a real example is presented. In addition, different sensitivity analyses are conducted which the results indicate that proposed QSS plan can significantly decrease the costs of the life testing and sampling in comparison with a single sampling plan.