Wald-Wolfowitz Type Sampling Plans for Continuous Production

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.

This paper suggests a novel method for acceptance sampling that integrates fuzzy logic with the negative binomial distribution. In quality control and reliability assessment, acceptance sampling plans play a crucial role in decision-making under uncertainty. Traditional sampling plans often rely on precise information and fixed parameters, which may not reflect real-world vagueness and imprecision. This paper introduces a Fuzzy Acceptance Sampling Plan (FASP) based on the Negative Binomial Distribution (NBD), providing a more flexible and realistic framework for dealing with over-dispersed count data and uncertainty in quality inspection. By incorporating fuzzy set theory, key parameters such as the acceptance number, lot quality, and inspection risks are modeled as fuzzy numbers. The plan allows for soft decision boundaries, enhancing the responsiveness to varying production conditions. Analytical expressions for the operating characteristic (OC) function, the average sample number (ASN) and average outgoing quality (AOQ) are derived in the fuzzy environment using membership functions. Numerical examples illustrate the application and advantages of the proposed plan over classical approaches, particularly in handling uncertain or imprecise inspection data. The proposed FASP-NBD model is especially useful in industries where defective items occur in clusters, and precise parameter estimation is difficult.

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.

A sampling system, MIL-STD-105D, used in quality control consists of three sampling plans with different acceptance probabilities used in turn for lot inspection. The decision to switch plan is based on the history of the lot acceptance records and a set of stopping rules. We derive the performance measure, average outgoing quality (AOQ), of this sampling system from a renewal process in which AOQ is expressed in terms of the moments of the stopping times. The renewal approach is simpler than that of the Markov chain generally used in computing AOQ for an infinite sequence of lots; it also provides a formula for AOQ for a finite sequence of lots.

A CSP-C continuous sampling plan is a new single-level continuous sampling procedure developed by Govindaraju & Kandasamy (2000) by incorporating the concept of acceptance number to the CSP-1 plan for the application of continuous production processes. In this new plan, the sampling inspection phase is characterized by a maximum allowable number of non-conforming units, c, and a constant sampling rate, f. Govindaraju & Kandasamy ( 000) derived the performance measures such as average outgoing quality (AOQ), average fraction inspected (AFI) etc, of the CSP-C plan using a Markov chain model for long run production processes. Yang (1983) has observed that the AOQ and AFI, being long run average measures, are not satisfactory measures of performance for short run production processes. Hence, formulas are derived in this paper, using the renewal theory approach enabling one to compute AOQ and AFI for both long run and short run production processes. Numerical illustrations are also given. By simulation, the accuracy of the short run measures is studied.

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.

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

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.

The concept of the quality loss derived by Taguchi has been accepted as the evaluation measure of quality instead of the traditional attribute property such as the proportion of non-conforming items. Since the variable single sampling plan having the desired operating characteristics indexed by the quality loss was proposed in 1997, various kinds of sampling plans indexed by the quality loss have been considered. Among them, there are two kinds of rectifying variable single sampling (RVSS) plans indexed by the quality loss. In the RVSS plans, two inspection schemes called the acceptance quality loss limit (AQLL) scheme and the permissible average outgoing surplus quality loss limit (PAOSQLL) scheme have been formulated. Note that the concepts of the AQLL and PAOSQLL schemes in the RVSS plans indexed by the quality loss are equivalent to those of the lot tolerance percent defective (LTPD) and the average outgoing quality limit (AOQL) schemes in the traditional rectifying attribute single sampling plans, respectively. On the other hand, in the sampling plan having the desired operating characteristics, an attribute repetitive group sampling plan was proposed for the purpose of reducing the average sampling number in the inspection. Recently, by applying the repetitive group sampling to the rectifying variable sampling plan for the AQLL scheme, the rectifying variable repetitive group sampling (RVRGS) plan for the AQLL scheme has been considered for the purpose of reducing the average total inspection (ATI). However, the RVRGS plan for the PAOSQLL scheme has not been investigated yet. Accordingly, the RVRGS plan for the PAOSQLL scheme must be investigated to complete the RVRGS plans indexed by the quality loss. In this article, the RVRGS plan for the PAOSQLL scheme is addressed. Then, the design procedure in the RVRGS plan for the PAOSQLL scheme is proposed for the purpose of reducing ATI. Through some numerical investigations, the effectiveness to reduce ATI by the RVRGS plan for the PAOSQLL scheme is confirmed.

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.

In this article, a modified continuous sampling of type II is provided for finite production runs. The suggested sampling plan revises the continuous sampling plan-2 of Yang (1983). The proposed plan places no predetermined limit on the number of items to be inspected until the second defect is detected when in partial inspection mode. A similar derivation to that of Yang is used to find an approximation to the average outgoing quality of the modified continuous sampling plan-2 in finite production runs. Some tables are provided to aid in the selection of the clearance number and sampling fraction when the production run length and an average outgoing quality limit are given. Copyright © 2002 John Wiley & Sons, Ltd.

\n Quality assurance is an integrated part of any calibration facility. The calibration\n facility as well as its customers are interested in the facility production outgoing\n quality. In most calibration labs the inspection of calibrated items is performed\n according to a suitable sampling inspection policy. Some of these policies are very good\n in assuring the quality of the calibration services they offer, but do not provide a clear\n assessment of the outgoing quality of the entire production of the facility. This paper\n has developed two methods of calculating the average outgoing quality (AOQ) of a\n calibration lab that uses a multistage sampling inspection policy. The policy structure is\n presented first along with the exact procedure of how to perform it by the inspectors and\n the methods to calculate the AOQ. The two methods differ from each another in the type of\n data required to calculate the AOQ. The first method requires the technicians’ production,\n the number of items subject to inspections and the number of failing items found. The\n second method requires only the number of technicians at each level of the multistage\n inspection policy. The verifications of the performances of two methods are accomplished\n by building a simulation model on an Excel worksheet. The model simulates the calibration\n facility with the right parameters, and then compares the two methods with the actual AOQ.\n The paper further discusses the advantages and disadvantages of each method in a broader\n context of quality assurance. \n

Time to failure due to fatigue is one of the common quality characteristics in material engineering applications. In this article, acceptance sampling plans are developed for the Birnbaum–Saunders distribution percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer's risk. The operating characteristic values (and curves) of the sampling plans as well as the producer's risk are presented. The R package named spbsq is developed to implement the developed sampling plans. Two examples with real data sets are also given as illustration.

Acceptance sampling plans are a cross-functional quality control instrument for benchmarking compliant standards of incoming as well as outgoing lots. The multiple dependent state (MDS) plan has been proposed and proven to advantage the conventional single sampling plan (SSP). However, the MDS plan presents a contradictory situation: Its performance depreciates as the number of previously considered lots increases. This outcome implies that the greater the number of cumulative lot-sentencing results one intends to include is, the greater the sample size is required for inspection, where a loosened criterion for quality acceptance levels, unfavorably, is introduced as well. Therefore, we proposed a modified MDS plan that depends on the loss-based capability index to accommodate an adjustable mechanism, namely, the adjustable multiple dependent state (AMDS) sampling plan. The AMDS plan allows encompassing not only a greater number of preceding lots in the lot disposition decision but also reducing the sample size required for the inspection and raising the lot-sentencing quality standards to stimulate the supplier attaining with persistently reliable submissions for a long-term supplier-consumer relationship. In comparison to the plans’ performance, our proposed AMDS plans demonstrate superior cost-effectiveness, discriminatory powers, and average run lengths than those of the SSP and MDS sampling plans. Furthermore, we tabulated the plan parameters under numerous conditions and delivered a real industry case to demonstrate its applicability.

<abstract> <p>This paper addresses neutrosophic statistics that will be used to design a double- acceptance sampling plan. We will design the sampling plans when the lifetime of the product follows the neutrosophic Weibull distribution. The plan parameters of the proposed double sampling plan will be determined using nonlinear optimization at various indeterminacy values and parameters. The productivity of the double sampling plan using neutrosophic statistics over the sampling plan under classical statistics will be given. The presentation of the proposed double sampling plan will be given with the help of industrial data.</p> </abstract>