Average Sample Number Research Articles

A new omnibus SPRT chart for monitoring process mean and variability based on the average number of observations to signal

The recent development of the omnibus sequential probability ratio test (OSPRT) chart marks a significant contribution to the advancement of joint monitoring schemes. As the OSPRT chart is a variable-sample-size control chart, practitioners often wish to understand its inspection efficiency, i.e. the number of observations it samples before producing a signal. In this article, we propose two enhanced optimization designs for the OSPRT chart based on the average number of observations of signal (ANOS) and expected value of the ANOS (EANOS) metrics under deterministic and unknown shift sizes, respectively. The ANOS metric is central to our design as it perfectly combines both the average run length (ARL) and the average sample number. A comparative analysis reveals that the OSPRT chart outperforms four benchmarking control charts in terms of the ANOS and EANOS metrics. Finally, an implementation of the OSPRT chart is presented with a ball shear test dataset.

Spatial distribution and fixed-precision sequential sampling plans for Popillia japonica (Coleoptera: Scarabaeidae) adults in primocane raspberry: influence of foliar insecticides.

The Japanese beetle, Popillia japonica Newman (Coleoptera: Scarabaeidae), an invasive species from northern Japan, was first detected in Minnesota in 1968. According to fruit growers and the Minnesota Department of Agriculture, population size and feeding damage has been an increasing concern since 2010. Based on trap-catch data, populations have recently exceeded 4,000 beetles/trap/week during July-August near raspberry fields, and can increase by an order of magnitude within 7-10 days. The primary goals of this study were to assess the spatial distribution of P. japonica adults in raspberry, and to develop and validate a practical fixed-precision sequential sampling plan for grower use. Taylor's Power Law (TPL) regression was used to characterize the beetle's spatial pattern in research plots and commercial fields, either with or without insecticide applications. We then used Green's plan to develop an enumerative sequential sampling plan to estimate P. japonica density in primocane raspberry. Beetle population data were collected at two locations in southern Minnesota, including the Rosemount Research and Outreach Center, and a commercial field near Forest Lake. The TPL results, via slope comparisons, indicated no significant differences in P. japonica spatial pattern between insecticide treated plots versus untreated plots, or among 4 different insecticides (P>0.05). Utilizing all spatial pattern data, we characterized the distribution of P. japonica beetles to be highly aggregated in raspberry, with TPL slopes ranging from b = 1.38 to 1.55; all slopes were found to be >1.0. Although the slopes were not significantly different, we accounted for variability in spatial pattern by using 33 independent data sets, and the Resampling for Validation of Sampling Plans (RVSP) model to validate a sampling plan with a final average precision level of 0.25 (SEM/mean), recommended for integrated pest management (IPM) purposes. The final sampling plan required an average sample number of only 15, 1-m-row samples, while providing high relative net precision (RNP), and thus a cost-effective, efficient sample plan for growers.

On the ARL of Cusum in Multinomial Models

There is no known closed form expression for the average sample number, also known as average run length, of a multivariate cusum procedure N = min{M1, M2, · · · , Mm} for m ≥ 3, where Mi are univariate cusum procedures. The problem is generally considered to be hopelessly complicated for any model. In this paper, for the multinomial model we show, however, that there is a rather simple closed form expression for the ARL of N with an elementary proof. A bit surprisingly, we further show that the ARL of N is related to the ARLs of Mi the same way as the capacitance of a series network of capacitors is related to the capacitances of its own components.

Beta Distribution Function for Cooperative Spectrum Sensing against Byzantine Attack in Cognitive Wireless Sensor Networks

In order to explore more spectrum resources to support sensors and their related applications, cognitive wireless sensor networks (CWSNs) have emerged to identify available channels being underutilized by the primary user (PU). To improve the detection accuracy of the PU signal, cooperative spectrum sensing (CSS) among sensor paradigms is proposed to make a global decision about the PU status for CWSNs. However, CSS is susceptible to Byzantine attacks from malicious sensor nodes due to its open nature, resulting in wastage of spectrum resources or causing harmful interference to PUs. To suppress the negative impact of Byzantine attacks, this paper proposes a beta distribution function (BDF) for CSS among multiple sensors, which includes a sequential process, beta reputation model, and weight evaluation. Based on the sequential probability ratio test (SPRT), we integrate the proposed beta reputation model into SPRT, while improving and reducing the positive and negative impacts of reliable and unreliable sensor nodes on the global decision, respectively. The numerical simulation results demonstrate that, compared to SPRT and weighted sequential probability ratio test (WSPRT), the proposed BDF has outstanding effects in terms of the error probability and average number of samples under various attack ratios and probabilities.

Integrating capability index and generalized rule-switching mechanism for enhanced quick-switch sampling systems

Variables Quick-Switch Sampling Systems (VQSSs) that involve both normal and tightened inspections for lot dispositions have attracted significant attention and discussion. However, existing VQSS models exhibit limitations, particularly in their rule-switching mechanism. Practitioners may encounter situations where multiple rounds of tightened inspection are necessary to ensure submission quality when suspicions of process degradation arise. Current VQSS models do not effectively address this need. To overcome this limitation, we present VQSSG by integrating a VQSS with a generalized rule-switching mechanism and the widely used capability index Cpk. VQSSG offers practitioners the flexibility to specify the number of successive lot acceptances under tightened inspection before transitioning to normal inspection. Our research includes the derivation of operating characteristics and average sample number functions for VQSSG, based on the Cpk index. Through in-depth investigations, we construct nonlinear optimisation models to determine the optimal system design and identify distinct types and settings for VQSSG, highlighting its strengths and weaknesses. Additionally, we provide managerial insights and recommendations for the effective implementation and application of VQSSG. To validate the practicality of this system, an industrial case study is presented. This paper significantly enhances the efficiency and adaptability of sampling systems by introducing VQSSG. The findings and managerial suggestions contribute to a deeper understanding of potential real-world applications, thereby enhancing quality control and decision-making processes.

Designing acceptance sampling plans for polynomial profiles using EWMA statistics based on process yield index

Inspection of raw materials, semi-finished products or final products is an important part of a quality assurance system. Acceptance sampling is a procedure used to decide either to accept or reject suppliers’ submitted lots in accordance with a specific standard. In this manuscript, designing acceptance sampling plans for lots with polynomial profile as quality characteristic is considered. To use previous lot information on deciding for accept or reject the available lot, exponentially weighted moving average (EWMA) statistic based on process yield index (Spk ) of polynomial profiles with two-sided specification limits is applied. For this purpose, three acceptance sampling plans of repetitive group sampling (RGS), resubmitted and also combined RGS-resubmitted plans are developed in this paper. The Parameters of the proposed plans are determined using non-linear optimization model. Performance of the proposed acceptance sampling plans are compared using numerical methods and Monte-Carlo simulations. Simulation results emphasize that the proposed combined sampling plan mostly requires less average sampling number (ASN) and consequently leads to decreasing inspection time and costs. The application of the proposed combined plan is also demonstrated using a real case.

Establishment and evaluation of Voting algorithm-based internal quality control (ViQC), a patient-based real-time quality control

BackgroundPatient-Based Real-Time Quality Control (PBRTQC) has emerged as a supplementary programme to traditional internal quality control (iQC) mechanisms. Despite its growing popularity, practical applications in clinical settings reveal several challenges. The primary objective of this research is to introduce and develop an Artificial Intelligence (AI)-based method, named Voting algorithm based iQC (ViQC), designed to enhance the precision and reliability of existing PBRTQC systems. MethodsIn this study, we conducted a retrospective analysis of 111,925 inpatient serum glucose test results from Nanjing Drum Tower Hospital, Nanjing, China, to provide an unbiased data set. The Voting iQC (ViQC) algorithm, established by the principles of the Voting algorithm, was then developed. Its analytical performance was evaluated through the calculation of random errors (RE). Subsequently, its clinical efficacy was assessed by comparison with five statistical algorithms: Moving Average (MA), Exponentially Weighted Moving Average (EWMA), Moving Median (movMed, MM), Moving Quartile (MQ), and Moving Standard Deviation (MovSD). ResultsThe ViQC model incorporates a variety of machine learning models, including logistic regression, Bayesian methods, K-Nearest Neighbor, decision trees, random forests, and gradient boosting decision trees, to establish a robust predictive framework. This model consistently maintains a false positive rate below 0.002 across all six evaluated error factors, showcasing exceptional precision. Notably, its performance further excels with an error factor of 3.0, where the false positive rate drops below 0.001, and achieves an accuracy rate as high as 0.965 at an error factor of 2.0. The classification effectiveness of ViQC model is evaluated by an area under the curve (AUC) exceeding 0.97 for all error factors. In comparison to five conventional PBRTQC statistical methods, ViQC significantly enhances error detection efficiency, maximum reducing the trimmed average number of patient samples required for detecting errors from 724 to 168, thereby affirming its superior error detection capability. ConclusionThe new established PBRTQC using artificial intelligence yielded satisfactory performance compared to the traditional PBBTQC in real world setting.

Developing Machine Learning-based Control Charts for Monitoring Different GLM-type Profiles With Different Link Functions

ABSTRACT In certain situations, the quality of a process is determined by dependent variables in relation to independent variables, often modeled through a regression framework referred to as a profile. The practice of monitoring and preserving this relationship is known as profile monitoring. In this paper, we propose an innovative approach that uses different machine-learning (ML) techniques for constructing control charts and monitoring generalized linear model (GLM) profiles with three different GLM-type response distributions of Binomial, Poisson, and Gamma, and by examining different link functions for each response distribution. Through our simulation study, we undertake a comparative analysis of different training methods. We measure the charts’ performance using the average run length, which signifies the average number of samples taken before observing a data point that exceeds the predefined control limits. The result shows that the selection of ML control charts is contingent on the response distribution and link function, and depends on the shift sizes in the process and the utilized training method. To illustrate the practical application of the proposed ML control charts, we present two real-world cases as examples: a drug–response study and a volcano-eruption study, to demonstrate how each ML chart can be implemented in practice.

Developing a stage-independent multiple sampling plan with loss-based capability index for lot disposition

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.

Determination and economic design of repetitive group sampling plan under two parameter Lindley distribution

ABSTRACT A designing procedure of repetitive group sampling plan for assuring mean life under a two-parameter Lindley distribution is proposed, and the optimization model is developed for finding the optimal plan parameters such that the demands of both supplier and buyer are satisfied simultaneously. A real-time data set of ball bearings is used to explain the application of the proposed plan. A comparison between the proposed plan and the single sampling plan is done to reveal the better performance of the proposed plan based on operating characteristic function and average sample number. Applying the proposed plan to provide lifetime assurance reduces the inspection effort and related costs. We discuss the design of the proposed plan with an economic aspect. In addition, the sensitivity of the optimal sampling plans concerning the failure probability and cost parameters is analyzed. Finally, it is evident from the study that the proposed plan will be preferable to a single sampling plan for providing quality assurance with a minimum cost of the inspection.

Optimal designing of skip-lot sampling plan with a provision for reducing the normal inspection using the Taguchi process capability index

A product with a strong track record of quality might have less inspection according to the skip-lot sampling plan. As a result, skip-lot sampling plans are created to cut down the inspection cost with desired protection. The skip-lot sampling method is also reliable, practical, and favorable from an economic standpoint. As a result, this work develops the SkSP-V plan, a novel system of skip-lot sampling plan, based on the Taguchi process capability index. The proposed plan stipulates that any lot is rejected during sampling inspection, normal inspection must resume, however, it also allows for a reduced level of normal inspection in the event that higher product quality is demonstrated. The exact sampling distribution of the estimated Taguchi capability index is used to derive the operating characteristic function of the proposed plan. An optimization model is employed to establish the optimal plan parameters, guaranteeing adherence to the specified quality levels and risk criteria. The performance measures such as probability of acceptance and average sample number of the proposed plan are examined and compared with existing plans. This article also includes real-world example to effectively demonstrate the practical implementation of the proposed SkSP-V plan based on the Taguchi process capability index.

A Perspective of the Epidemiology of Rabies in South Africa, 1998-2019.

Despite the implementation of various control strategies aimed at eliminating canine-mediated rabies, the disease is still endemic in up to 150 countries across the world. Rabies remains endemic to South Africa, with various reservoir species (both wildlife species and domestic dogs) capable of maintaining rabies infection, and the epidemiology of the disease is yet to be adequately defined. As such, this study used surveillance data collected between 1998 and 2019 from the two diagnostic laboratories in the country for a statistical space-time analysis to determine regions where significant disease clusters could occur. In addition, the robustness of surveillance activities across the country was evaluated through the mathematical evaluation and visualization of testing rates based on the average number of samples tested per species group. In our study, various significant disease clusters were detected for domestic animals, wildlife and livestock. The significant disease clusters for domestic animals and livestock were primarily restricted to eastern South Africa, while the significant disease clusters in wildlife species were detected across northern and western South Africa. Furthermore, the testing rates identified districts from various provinces where surveillance activities could be considered inadequate, consequently influencing the geographical range of the observed clusters. These results could be used to direct intervention campaigns towards high-risk areas, while also allocating the required resources to improve surveillance in the surrounding areas where surveillance was deemed inadequate.

A cost-effective skip-lot sampling scheme using loss-based capability index for product acceptance determination

Acceptance sampling plans are essential for quality control and assurance, empowering businesses to make well-informed decisions regarding lot disposition. Among these plans, the skip-lot sampling plan (SkSP) stands out as a cost-effective strategy for suppliers with consistently excellent product quality. In this article, we present an enhanced version of the SkSP, termed Cpm-based SkSP-RGSP, which incorporates a repetitive group sampling plan (RGSP) using the Taguchi capability index Cpm as its reference plan. We develop an optimization model to ensure that the proposed plan meets a two-point condition in its operating characteristic function and effectively minimizes the average sample number (ASN). Through investigations of two critical performance measures, ASN and discriminatory power, we demonstrate the superiority of our plan over conventional sampling approaches. Detailed plan parameters, including required sample size and lot sentencing criteria, are provided to assist examiners in practical implementation. Additionally, we showcase the plan's applicability and practicality through a case study. This research contributes to the field of quality control by offering an efficient and cost-effective sampling scheme for lot disposition.

Enhanced patient-based real-time quality control using the graph-based anomaly detection.

Patient-based real-time quality control (PBRTQC) is an alternative tool for laboratories that has gained increasing attention. Despite the progress made by using various algorithms, the problems of data volume imbalance between in-control and out-of-control results, as well as the issue of variation remain challenges. We propose a novel integrated framework using anomaly detection and graph neural network, combining clinical variables and statistical algorithms, to improve the error detection performance of patient-based quality control. The testing results of three representative analytes (sodium, potassium, and calcium) and eight independent variables of patients (test date, time, gender, age, department, patient type, and reference interval limits) were collected. Graph-based anomaly detection network was modeled and used to generate control limits. Proportional and random errors were simulated for performance evaluation. Five mainstream PBRTQC statistical algorithms were chosen for comparison. The framework of a patient-based graph anomaly detection network for real-time quality control (PGADQC) was established and proven feasible for error detection. Compared with classic PBRTQC, the PGADQC showed a more balanced performance for both positive and negative biases. For different analytes, the average number of patient samples until error detection (ANPed) of PGADQC decreased variably, and reductions could reach up to approximately 95 % at a small bias of 0.02 taking calcium as an example. The PGADQC is an effective framework for patient-based quality control, integrating statistical and artificial intelligence algorithms. It improves error detection in a data-driven fashion and provides a new approach for PBRTQC from the data science perspective.

Sequential fusion‐based defense strategy against sophisticated Byzantine attacks in cognitive IoT networks

Abstract5G and 6G promise to be catalysts for the Internet of Things (IoT), enabling ultra‐massive and mission‐critical IoT. The demands of new IoT applications and the large number of connected objects being announced will exacerbate the thorny issue of spectrum scarcity in wireless communications. Cognitive radio (CR) is a revolutionary technology that promises to mitigate the problem of spectrum scarcity through more efficient use of spectrum. Integrating CR into the IoT allows objects to opportunistically access spectrum resources already allocated to a Primary User (PU) without causing interference. Spectrum sensing (SS) allows objects to be aware of the PU's spectrum occupancy status. In radio environments where the PU signal is subject to multipath and shadowing effects that degrade the channel between the PU and objects, SS performed by a single object could be inaccurate and lead to incorrect decisions about the PU's status. Cooperative spectrum sensing (CSS) has been proposed to improve detection performance. However, this cooperation between objects has opened the way to a new form of attack known as the Spectrum Sensing Data Falsification (SSDF) or Byzantine attack. In a SSDF attack, attackers falsify their local sensing results before sharing them in the CSS. This attack is very harmful to the CSS and can lead to a loss of spectrum opportunities or interference with the PU. In this paper, from the attack point of view, a sophisticated Byzantine attack model that generalizes well the simple attack strategies has been proposed and allows an attacker to implement other attack strategies. From a defense point of view, a new and innovative Weighted Sequential Hypothesis Testing (WSPRT) scheme has been suggested. This ensures the security of the CSS while significantly reducing the average number of samples required for overall decision‐making in a very hostile IoT network. The results obtained from simulations carried out in various attacks scenarios show that the proposed secure CSS scheme requires at most six samples to detect the state of the PU without error when the proportion of attackers reaches 80%. This performance far exceeds that of other defense mechanisms such as classic WSPRT, SPRT, and majority rule, with which we have compared it under the same conditions. In general, for the classic WSPRT, SPRT, and majority rule mechanisms, the error rate starts to deteriorate at ratio 40% of attackers and the number of samples is greater than six and reaches 50.

Impact of the COVID-19 pandemic on the real-world diagnostic infrastructure for tuberculosis-An ESGMYC collaborative study.

We determined the impact of the COVID-19 pandemic on mycobacterial diagnostic services. 40 laboratories from 22 countries completed an online questionnaire covering the redeployment of the laboratory infrastructure and/or staff for SARS-CoV-2 testing, staff shortages and supply chain disruptions. 28 laboratories reported monthly numbers of samples processed for mycobacterial investigations and monthly numbers of M. tuberculosis complex (MTBC) PCRs performed between October 1st 2018 and October 31st 2020. More than half (23/40) of the participating TB laboratories reported having performed COVID-19 diagnostics in the early phase of the pandemic, in part with negative impact on the mycobacterial service activities. All participating laboratories reported shortages of consumables and laboratory equipment due to supply chain issues. Average monthly sample numbers decreased by 24% between January 2020 and October 2020 compared to pre-pandemic averages. At the end of the study period, most participating laboratories had not returned to pre-pandemic average MTBC PCR throughput.

Sequential Detection under Correlated Observations using Recursive Method

Sequential analysis has been used in many cases when the decision is supposed to be taken quickly such as for signal detection in statistical signal processing, namely sequential detector. For identical error probabilities, a sequential detector needs a smaller average sample number (ASN) than its counterpart of a fixed sample number quadrature detector based on Neyman-Pearson criteria. The optimum sequential detector was derived based on the assumption that the observations are uncorrelated (independent). However, in realistic scenario, such as in radar, the assumption is commonly violated. Using a sequential detector under correlated observations is sub-optimal and it poses a problem. It demands a high computational complexity, since it needs to recalculate the inverse and the determinant of the signal covariance matrix for each new sample taken. This paper presents a technique for reducing the computational complexity, which involves using recursive matrix inverse to subsequently calculate conditional probability density functions (pdf). This eliminates the need to recalculate the inverse and determinant, leading to a more reasonable solution in real-world scenario. We evaluate the performance of the proposed (recursive) sequential detector by using Monte-Carlo simulations and we use the conventional and non-recursive sequential detectors for comparisons. The results show that the recursive sequential detector has equal probabilities of false alarm and miss-detection with the conventional sequential detector and performs better than the non-recursive sequential detector. In terms of ASN, it maintains comparable results to the two conventional detectors. The recursive approach has reduced the computational complexity for matrix multiplication to from and it also has rendered the calculation of matrix determinant to be unnecessary. Therefore, by having better probabilities of error and reduced computational complexities under correlated observations, the proposed recursive sequential detector may become a viable alternative to obtain a more agile detection system as required in future applications, such as in radar and cognitive radio.

Modified Sequential Probability Ratio Test Based on Truncated Life Tests on the Exponential Distribution Functions

Modified Sequential probability ratio test (MSPRT) technique helps to increase the reliability and speed of stabilization detection on the Non homogenous poison process (NHPP) with the maximum number of software faults to reduce error between the consumer risk and producer risk, with the time cumulative system of hours. Modified sequential probability ratio test can be used to reduce the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. The proposed result suggests MSPRT along with maximum number of faults contained in software would be useful in speeding up decision making while dealings error in a software reliability weekly index, we show the graphical performance of the MSPRT and average sample number (ASN).

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.

Optimal and economic design of modified double sampling plan under new Weibull–Pareto distribution

PurposeThe purpose of this paper is to design a modified version of the double sampling plan to handle the inspection processes requiring a minimum sample size to assure the median life for the products under the new Weibull–Pareto distribution. The economic design of the proposed plan is also considered to assure the product's lifetime with minimum cost.Design/methodology/approachThe authors have developed an optimization model for obtaining the required plan parameters by solving simultaneously two non-linear inequalities and such inequalities have been formed based on the two points on the operating characteristic curve approach.FindingsThe results show that the average sample number, average total inspection and total inspection cost under the proposed plan are smaller than the same of a single sampling plan. This means that the proposed plan will be more efficient than a single sampling plan in reducing inspection effort and cost while providing the desired protection.Originality/valueThe proposed modified double sampling plan designed to assure the median life of the products under the new Weibull–Pareto distribution is not available in the literature. The proposed plan will be very useful in assuring the product median lifetime with minimum sample size as well as minimum cost in all the manufacturing industries.