Abraham Wald’s formalization of the sequential probability ratio test in the crucible of World War II is one of the more famous cases in the history of statistics of the interplay of statistical theory and real-world applications. Focusing entirely on the moments around its creation, however, obscures the way in which it was also a continuation of previous work he had done in the late 1930s, and in particular, Wald’s development of decision theory and his approach to using inverse probability. By situating the origins of the sequential probability ratio test in a broader history, we see not only how inverse probability initially made its way into sequential analysis but also the ongoing importance of the role of applications in motivating the development of statistical theory.

In this study, we propose a group sequential design for multi-arm multi-stage trials with treatment selection for ordinal endpoints. The proposed method is based on the property of Brownian motion process of efficient score tests. Thus, by applying the sequential conditional probability ratio test, the proposed group sequential design provides analytical solutions for both futility and efficacy boundaries for arbitrary number of stages and number of arms and avoids complicated computations implemented in the method proposed by Jaki and Margirr. Simulations are conducted to study operating characteristics of the proposed method.

ABSTRACT This study introduces the power odd Lindley half‐logistic distribution (POLiHLD), a novel statistical distribution developed to provide enhanced flexibility for modeling diverse data sets. This distribution is derived by combining the characteristics of the odd Lindley and half‐logistic distributions through the power transformation, resulting in a model capable of capturing various shapes and tail behaviors. We explore the fundamental statistical properties of the POLiHLD, including moments and moment‐generating functions, a sequential probability ratio test, and average sample number, among others. Extensive simulation studies were conducted to validate the estimation method used to estimate the parameters of the developed distribution. These simulations highlight the robustness of the estimation method used. The POLiHLD's flexibility is shown through its fitting to two real datasets: the first data set represents the ordered failure of components, and the second data set captures economic data. Comparative analyses with existing distributions show that the POLiHLD provides a better fit for the analyzed datasets. A regression model was developed to ascertain the predictive ability of the proposed model.

For the classical problem of sequential binary hypothesis testing (SHT) studied by Wald for independent and identically distributed (i.i.d.) data, the optimal test is the sequential probability ratio test (SPRT). When the data is no longer i.i.d., the SPRT’s exact or strong optimality property is lost. However, the SPRT is asymptotically optimal for general non-i.i.d. data under mild conditions, as the error probabilities go to zero. In this paper, the problem of SHT is studied for a special class of non-i.i.d. processes, and an exact optimal solution is obtained. This special class is the class of statistically periodic processes encountered in many applications in science and engineering. The objective for SHT chosen in the paper is an average risk criterion containing time-varying penalties for collecting samples and making decision errors. It is shown that the optimal solution is the SPRT with a time-varying sequence of thresholds. It is further shown that a constant threshold variant is asymptotically optimal. The constant threshold test is then applied to electrocardiogram (ECG) data to perform energy-efficient detection of heart arrhythmia.

The Rayleigh distribution is essential for modeling and analyzing duration in medical and scientific applications, life testing experiments, reliability analysis, etc. This article aims to propose the one-sided and two-sided Sequential Probability Ratio Test (SPRT) control charts to track the changes in the scale parameter of the Rayleigh distributed process. The proposed control charts are the Phase II applications. Statistical performance metrics average number of observations and samples to signal for one-sided and two-sided control charts are obtained through the Markov chain technique. The effectiveness of the proposed control charts studied by comparing them to the existing control charts. The performance study shows that the newly proposed charts perform much better than Shewhart, cumulative sum, and Exponentially weighted moving average, showing a low out-of-control average number of observations to signal. Examples have been provided to demonstrate how one-sided and two-sided SPRT charts work.

Ideally, the sequential monitoring of adverse events following post-licensed drugs and vaccines is correctly adjusted for confounding variables, such as gender and age, that may have an effect on the quality of the events. This is the idea behind the usual fully randomized, the placebo-control, and the self-control designs. Two prominent methods for conducting sequential analysis of the safety of post-market drugs and vaccines are the maximized sequential probability ratio test (MaxSPRT), and its conditional version, the CMaxSPRT. However, even when the assumption of sample homogeneity is realistic prior to the drug/vaccine administration, the effects caused by the drugs and vaccines on the risk of an adverse event, if any, can still vary according to observable covariates. For binomial and Poisson data, a straightforward sequential test method is introduced in order to accommodate a regression structure in the MaxSPRT. The proposed sequential regression test is also applicable for the CMaxSPRT, that is, the regression works for comparing historical and surveillance Poisson data with unknown heterogeneous baseline rates, taking into account seasonality and any other observable confounding covariates. To illustrate the usefulness of such a regression method, we describe the potential applications of the method to monitor vaccine-adverse events in Manitoba, Canada. The numeric results and examples were executed with the RSequential package.

Many approaches have been proposed to identify malicious anomalous traffic. Statistical models are techniques that rely on the analysis and investigation of network traffic to obtain a deeper understanding. Combining the Sequential Probability Ratio Test (SPRT) and Entropy (E) is an effective technique that can be used to detect anomalies. The most common anomalies targeting servers are Distributed Denial of Service (DDoS) attacks, which are designed to prevent legitimate users from accessing services provided by a targeted server or controller. The first goal of this study is to detect malicious traffic and identify two different types of DDoS anomalies, NTP and DNS anomalies, which are commonly exploited in reflection or amplification attacks due to their stateless UDP-based nature, by implementing an Entropy and Sequential Probability Ratio Test approach (ESPRT). The second is to select relevant features to improve the detection performance by implementing a Pearson Correlation Coefficient (PCC) approach. The CIC-DDoS2019 dataset was utilized to evaluate the proposed approach. ESPRT achieved high accuracy, ranging from 97.27 to 96.23% when the number of features ranged from 5 to 55, and had a low False Positive Rate (FPR), ranging from 0.01 to 0.03.

In recent years, researchers have integrated the historically separate, reinforcement learning (RL), and evidence-accumulation-to-bound approaches to decision modeling. A particular outcome of these efforts has been the RL-DDM, a model that combines value learning through reinforcement with a diffusion decision model (DDM). While the RL-DDM is a conceptually elegant extension of the original DDM, it faces a similar problem to the DDM in that it does not scale well to decisions with more than two options. Furthermore, in its current form, the RL-DDM lacks flexibility when it comes to adapting to rapid, context-cued changes in the reward environment. The question of how to best extend combined RL and DDM models so they can handle multiple choices remains open. Moreover, it is currently unclear how these algorithmic solutions should map to neurophysical processes in the brain, particularly in relation to so-called go/no-go-type models of decision making in the basal ganglia. Here, we propose a solution that addresses these issues by combining a previously proposed decision model based on the multichoice sequential probability ratio test (MSPRT), with a dual-pathway model of decision threshold learning in the basal ganglia region of the brain. Our model learns decision thresholds to optimize the trade-off between time cost and the cost of errors and so efficiently allocates the amount of time for decision deliberation. In addition, the model is context dependent and hence flexible to changes to the speed-accuracy trade-off (SAT) in the environment. Furthermore, the model reproduces the magnitude effect, a phenomenon seen experimentally in value-based decisions and is agnostic to the types of evidence and so can be used on perceptual decisions, value-based decisions, and other types of modeled evidence. The broader significance of the model is that it contributes to the active research area of how learning systems interact by linking the previously separate models of RL-DDM to dopaminergic models of motivation and risk taking in the basal ganglia, as well as scaling to multiple alternatives.

In practical scenarios, data measurements like ratios and proportions often fall within the 0 to 1 range, posing unique modeling challenges. While beta and Kumaraswamy distributions are widely used, alternative models often yield better performance, though no clear consensus exists. This paper introduces a new bounded probability distribution based on a transformation of the Weibull distribution, with properties such as moments, entropies, and a quantile function. Additionally, we have developed the sequential probability ratio test (SPRT) for the proposed model. The maximum likelihood estimation method was employed to estimate the model parameters. A Monte Carlo simulation was conducted to evaluate the performance of parameter estimation for the model. Finally, we formulated a quantile regression model and applied it to data sets related to risk assessment and educational attainment, demonstrating its superior performance over alternative regression models. These results highlight the importance of our contributions to enhancing the statistical toolkit for analyzing bounded variables across different scientific fields.

Data Drift refers to the phenomenon where the generating model behind the data changes over time. Due to data drift, any model built on the past training data becomes less relevant and inaccurate over time. Thus, detecting and controlling for data drift is critical in machine learning models. Hierarchical Temporal Memory (HTM) is a machine learning model developed by Jeff Hawkins, inspired by how the human brain processes information. It is a biologically inspired model of memory similar in structure to the neocortex and whose performance is claimed to be comparable to state of the art models in detecting anomalies in time series data. Another unique benefit of HTMs is their independence from training and testing cycles; all the learning takes place online with streaming data, and no separate training and testing cycle is required. In the sequential learning paradigm, the Sequential Probability Ratio Test (SPRT) offers unique benefits for online learning and inference. This paper proposes a novel hybrid framework combining HTM and SPRT for real-time data drift detection and anomaly identification. Unlike existing data drift methods, our approach eliminates frequent retraining and ensures low false positive rates. HTMs currently work with one dimensional or univariate data. In a second study, we also propose an application of HTM in a multidimensional supervised scenario for anomaly detection by combining the outputs of multiple HTM columns, one for each data dimension, through a neural network. Experimental evaluations demonstrate that the proposed method outperforms conventional drift detection techniques like the Kolmogorov-Smirnov (KS) test, Wasserstein distance, and Population Stability Index (PSI) in terms of accuracy, adaptability, and computational efficiency. Our experiments also provide insights into optimizing hyperparameters for real-time deployment in domains such as Telecom.

Globally, enterprises are undergoing significant transformation in line with developments based on industrial revolution by leveraging extensive computing resources, data capture technologies, information processing systems, and advanced data science models that span analytics, optimization, and algorithmic intelligence. The global market's increasing demand, diverse resource supply options, global competition, and environmental protection needs are driving organizations to adopt sustainable strategies. These involve utilizing information technology and analytics more effectively, innovating manufacturing and service support systems, and employing novel problem-solving methods. The awareness of these challenges and opportunities inspired the theme of the joint event: 56th Annual Convention of ORSI (2023-ORSI) and the 10th International Conference on Business Analytics and Intelligence (2023-ICBAI), held at Indian Institute of Science, Bangalore, India, from December 18 to 20, 2023. The Operational Research Society of India (ORSI) Karnataka, the Department of Management Studies, IISc Bangalore, and the Analytics Society of India (ASI), DCAL, IIM Bangalore jointly organized this event. The joint event aimed to establish a premier platform for knowledge sharing among distinguished practitioners, academics, and researchers from industry and academia, focusing on the current applications of Operations Research (OR), Business Analytics (BA), and Business Intelligence (BI). The conference received over 655+ paper submissions, with 455 selected for presentation. 66 papers were deemed particularly interesting, and authors of 13 promising articles were invited to submit extended versions for a special issue of International Journal of Mathematical, Engineering and Management Sciences (IJMEMS). After rigorous peer review, eight papers were accepted for publication in this special issue, addressing common challenges in Operations Research, Business Analytics, and Business Intelligence. This Special Issue of the IJMEMS explores recent developments in Operations Research, Business Analytics, and Business Intelligence. It presents cutting-edge trends and substantial contributions to key areas such as Scheduling problems, Transshipment problems, E-commerce, Nanofluids, Blockchain Technology, Generative AI, Augmented Analytics, Machine Learning, and real-time Anomaly Detection. This Special Issue delves into following eight topics: Unmasking Content Clarity: Advancements in Defining, Measuring and Enhancing Readability: The authors present a novel method using natural language processing and Generative AI to quantitatively evaluate readability and comprehension. This approach surpasses traditional readability indices, offering substantial benefits for content creation and knowledge management in fields like education, business, technical support, and policy platforms. Strategic Insights into Blockchain Adoption in Automotive Supply Chains: A Comparative AHP-TOPSIS and TISM-MICMAC Analysis The authors explore blockchain adoption in the automotive industry using a multidisciplinary approach involving AHP, TOPSIS, TISM, and MICMAC analyses. This study identifies key enablers and their relationships, offering actionable insights and practical recommendations for automotive managers considering blockchain adoption. Avoid Maximum Cost Method for Solving Linear Fractional Transshipment Problem: The authors introduce a mathematical model for the linear fractional transshipment problem (LFTP) and suggest “Avoid Maximum Cost Method” to obtain an initial basic feasible solution for LFTP. This study conducts a comparative analysis with existing methods to demonstrate the efficiency of the proposed approach. Mathematical Study of Dispersion of Nano Biosensors in an Artery with Multiple Stenosis: This work examines nano-biosensors in a diseased artery with multiple stenoses, determining the temperature, velocity of nanofluid, and transport coefficients. The results lay the groundwork for developing nano-biosensors to diagnose, treat, and manage cardiovascular disease. The mathematical model had possible scope for target detection and drug delivery at stenosed sites. Integrating Generative AI in Business Intelligence: A Practical Framework for Enhancing Augmented Analytics: This study offers a practical framework for integrating generative AI (Gen AI) into Business Intelligence (BI). By adopting it, businesses can maximize GenAI and BI's potential, enhancing analytics, operations, and fostering a collaborative, data-driven culture. Data Monetization Through Cross Industry Collaboration in Retail Banking: This paper examines how data sharing between banks and e-commerce platforms, facilitated by data monetization, can improve banking customer experiences. This study proposes a framework using propensity models to identify promising customers and offer personalized products and promotions. Development of Dispatching Rule based Heuristic Algorithms for Real-Time Dynamic Scheduling of Non-identical Parallel Burn-in Ovens with Machine Eligibility Restriction: This study tackles a realistic problem in semiconductor manufacturing by scheduling non-identical parallel Burn-in ovens. The study proposes 25 heuristic algorithms for real-time dynamic scheduling with machine eligibility restrictions. Through empirical and statistical analysis, this study identifies top-performing algorithms. A Hybrid Framework for Real-Time Data Drift and Anomaly Identification Using Hierarchical Temporal Memory and Statistical Tests: This paper introduces a hybrid framework combining Hierarchical Temporal Memory and Sequential Probability Ratio Test for real-time data drift detection and anomaly identification. Retraining and false positives were minimized, outperforming traditional methods in experiments. Challenges and Future Directions 1. Enhanced Decision-Making: Addressing uncertainty and complexity in decision-making processes to improve outcomes. 2. Regulatory Frameworks: Conducting further research to establish flexible yet robust regulatory structures that can effectively adapt to the rapid evolution of blockchain technology. 3. Optimization Algorithms: Developing efficient algorithms to solve linear fractional transshipment problem with multi-objective linear fractional functions. 4. AI in Business Intelligence: Investigating long-term impacts of AI-enabled Business Intelligence tools on data-driven decision-making and organizational performance. 5. Ethical AI Considerations: Addressing ethical concerns such as data privacy, fairness, and biases in AI systems to ensure responsible use. 6. Digital Collaboration Frameworks: Developing frameworks that integrate digital footprints and cross-industry collaboration data to enhance strategic partnerships. 7. Advanced Scheduling Algorithms: Creating advanced meta-heuristic algorithms using efficient dispatching rule-based heuristics for dynamic scheduling of non-identical parallel batch processing machines with eligibility constraints. 8. Hybrid Anomaly Detection: Proposing a hybrid framework that combines multivariate extension of Hierarchical Temporal Memory with multivariate Sequential Probability Ratio Test for enhanced anomaly detection. 9. Advanced Text Generation: Utilizing advanced text generation techniques like prompt engineering and fine-tuning to produce more readable and engaging content. We extend our sincere appreciation to all contributing authors for their significant contributions and anonymous reviewers for their dedication and sincere evaluation of submissions. Their timely and excellent responses have been truly gratifying. Additionally, we would like to express our heartfelt thanks to Professor Mangey Ram, Editor-in-Chief of the International Journal of Mathematical, Engineering and Management Sciences, for his support in accepting this special issue and providing unwavering backing from its inception. Guest Editors

In the area of real-time analytics, the ability to detect concept drift shifts in data distribution over time is vital for maintaining the reliability of predictive models. This analysis presents a comprehensive comparative analysis for five Unsupervised Concept Drift Detection Algorithms Adaptive Boosting (AdaBoost), Diversity-Induced Ensemble (DIE), Adaptive Sliding Window (ADWIN), Sequential Probability Ratio Test (SPRT), and Page-Hinkley Test (PHT) with a focus on high-dimensional biomedical data streams. The evaluation is conducted using three large-scale and diverse biomedical datasets: MIMIC-III/IV, UK Biobank, and MedMNIST, each representing a distinct challenge in terms of dimensionality, temporal variability and data type (tabular, genomic, and imaging). Performance is assessed across key metrics including Detection Delay, Memory Usage, Execution Time, and post-drift classification effectiveness (Precision, Recall, F1-Score, and Accuracy). Both synthetic and real-world drifts are incorporated to simulate dynamic environments. The findings reveal that ensemble-based methods such as AdaBoost and DIE outperform statistical approaches in handling noisy, sparse, and high-dimensional streams, offering superior adaptability and robustness. This research contributes a systematic evaluation framework and empirical insights to guide the deployment of unsupervised drift-aware systems in healthcare and other data-intensive domains.

The aircraft braking system is critical to ensure the safe take-off and landing of the aircraft. However, the braking system is often exposed to high temperatures and strong vibration working environments, which makes the sensor prone to failure. Sensor failure has the potential to compromise aircraft safety. In order to improve the safety of the aircraft braking system, a fault detection and fault-tolerant control (FDFTC) strategy for the aircraft brake pressure sensor is designed. Firstly, a model based on a bidirectional long short-term memory (Bi-LSTM) network is constructed to estimate the brake pressure. Then, the residual sequence is obtained by comparing the measured pressure with the estimated pressure. On this basis, the improved sequential probability ratio test (SPRT) method based on mathematical statistics is applied to analyze the residual sequence to detect the fault. Finally, simulation and hardware-in-the-loop (HIL) testing results indicate that the proposed FDFTC strategy can detect sensor faults in time and efficiently complete braking when faults occur. Hence, the proposed FDFTC strategy can effectively deal with the faults of the aircraft brake pressure sensor, which is of great significance to improve the reliability and safety of the aircraft.

Active monitoring of health outcomes after COVID-19 vaccination provides early detection of rare outcomes post-licensure. We evaluated health outcomes following bivalent COVID-19 Pfizer-BioNTech (BNT162b2) and Moderna (mRNA-1273.222) vaccination in the United States. Multiple health outcomes were monitored monthly from August 2022 to July 2023 in four administrative claims databases (CVS Health, Carelon Research, Optum, and Medicare). The study included individuals 6 months and older who received a bivalent COVID-19 BNT162b2 or mRNA-1273.222 vaccination during the study period and met a minimum continuous enrollment requirement in a medical insurance plan prior to COVID-19 vaccination. Descriptive analyses monitored counts of vaccinations, outcomes, and concomitant COVID-19 and influenza vaccination. Maximized Sequential Probability Ratio Testing (MaxSPRT) tested for elevations in the observed incidence rate of outcomes post-vaccination compared to annual historical rates estimated from 2019 or 2020, adjusted for claims delay in the observed rate. Where case counts permitted, historical rates were standardized by age and/or sex for all persons, and race and/or nursing home residency status for Medicare persons only. Overall, 13.9 million individuals 6 months and older received a bivalent COVID-19 vaccine. A statistical signal occurred for two outcomes in one database (significance level of 1%): anaphylaxis following both bivalent COVID-19 vaccines in persons 18-64 years and myocarditis/pericarditis following bivalent BNT162b2 vaccines in individuals 18-35 years. Among 642 142 vaccinated children 6 months-17 years, no signals were identified. Results were consistent with published COVID-19 vaccine safety studies and support the safety profile of bivalent COVID-19 mRNA vaccines.

Abstract As the primary power equipment in the oil transport system, the running status of the oil pump is that such a system is safe and reliable operation. The monitored samples in the oil pump are often from various sensors, in which the key signal features need to be extracted and integrated to enhance the capability of anomaly diagnosis. Owing to the complexity and concealment of running information, it is crucial to explore an effective method for anomaly diagnosis of the oil pump. With the rapid progress of artificial intelligence, an intelligent anomaly diagnosis method is proposed for the oil pump by fusing multi-type information in this paper. First, the canonical correlation analysis (CCA) is employed to extract key signal features from multi-type data information. Then, the multi-layer perceptron (MLP) with one output node is implemented to identify anomalies by fusing various signals of the oil pump. Additionally, the anomaly warning decision is achieved by the sequential probability ratio test (SPRT). Finally, the proposed intelligent anomaly diagnosis of the oil pump is validated in a real-world case, demonstrating the effectiveness for diagnosing and warning anomaly information.

The early diagnosis of Chronic Kidney Disease (CKD) remains a crucial challenge in medical research. This study investigates the robustness of the Modified Sequential Probability Ratio Test (MSPRT) in kidney diagnosis, focusing on its response to non-normality and outliers. Additionally, the study evaluates the diagnostic performance of MSPRT by analyzing the average sample size and the operating characteristics curve (OC) in conjunction with the Receiver Operating Characteristic (ROC) curve and the Maxwell-Boltzmann Distribution (MBD). Using patient data from the University of Maiduguri Teaching Hospital (UMTH), the study applies these statistical methods to assess their effectiveness in CKD classification. The results demonstrate the adaptability of MSPRT in non-ideal data conditions and its efficiency in minimizing sample size while maintaining high diagnostic accuracy. The findings recommend the importance of integrating statistical models such as MBD in refining diagnostic decision-making processes for CKD.

This study presents a comprehensive analysis of maternal and foetal outcomes associated with pregnancy-related jaundice, employing a sequential analysis methodology to identify critical risk factors and optimize intervention timing. Through retrospective evaluation of 10 years of hospital records (n=200 cases) and systematic literature review, we identified viral hepatitis (58.3%) and HELLP syndrome (64.86%) as the predominant etiological factors in our study population. The findings reveal alarming mortality and morbidity rates, with maternal mortality reaching 20% and significant fetal complications, including preterm delivery (39.6%) and stillbirth (8.3%). The application of sequential probability ratio testing demonstrated particular efficacy in this clinical context, enabling early termination of data collection upon reaching statistically conclusive results (p<0.0001) while maintaining rigorous standards. This methodological approach not only confirmed the time-sensitive nature of jaundice management but also highlighted its potential for resource-efficient research in obstetric settings. The results underscore the critical need for enhanced antenatal care protocols, particularly in low-resource environments where diagnostic and treatment gaps persist. We advocate for (1) standardized screening programs for hepatic and hematologic disorders in pregnancy, (2) community-based education initiatives to improve early recognition of jaundice symptoms, and (3) targeted healthcare worker training on emergent management of pregnancy-related liver dysfunction. These evidence-based recommendations aim to address the substantial disparities in maternal-fetal outcomes observed in resource-limited settings while demonstrating the value of adaptive research methodologies in clinical obstetrics.

BackgroundThis study developed a sequential winning-percentage prediction model for badminton competitions using the expert system sequential probability ratio test (EXSPRT), aiming to calculate the difficulty of each event within a match and establish the initial prior probability.MethodsWe utilized data from 100 men's singles matches (222 games) held by the Badminton World Federation (BWF) in 2018 to evaluate event difficulty across six models for each determining factor. For setting the initial prior probability calculation method, 30 men's singles matches (74 games) organized by the BWF in 2019 were randomly selected. The odds for these matches were obtained from www.oddsportal.com.ResultsThe efficacy of the six models was assessed based on application rates (15%, 20%, 25%, and 30%) of the collected odds, with the initial prior probability reflecting 25% of the odds chosen owing to its superior validity.ConclusionsThis research yielded six sequential winning percentage prediction models capable of offering real-time predictions during matches in badminton competitions by leveraging EXSPRT. These models enhance spectator engagement and provide foundational data for developing similar prediction models for other sports. Future research should focus on developing a program to identify the most effective model among the six and implement it practically.

To explore the application of sequential analysis in post-market safety dynamic surveillance of vaccines. Under the dynamic monitoring data of vaccines post-market approval, this research introduces the fundamental principles of maximizing sequential probability ratio test (MaxSPRT) and Bayesian sequential analysis, employing R software. Through an example of dynamic safety monitoring data of vaccines post-market approval, we analyze using the MaxSPRT and Bayesian sequential analysis. The MaxSPRT identified a safety signal in week 4 (P<0.05), while Bayesian sequential analysis indicated that the 95% highest density interval for the RR value at week 4 is 1.13-3.27, suggesting the first appearance of a safety signal at week 4. The MaxSPRT and Bayesian sequential analysis effectively leverage continuously accumulating dynamic monitoring data, thereby serving as a valuable method for post-market safety surveillance of vaccines.

Supply chain optimization not only affects the production efficiency and product quality of enterprises, but also directly impacts their cost control and profitability. This article focuses on the spare parts provided by suppliers, the multi-stage production process of enterprises, and quality control during the production process. A Markov decision process was used to construct an optimization decision model aimed at improving production efficiency and reducing defect rates through sampling testing and cost optimization. This provides decision-making support and a basis for optimizing the production process for enterprises.This article makes a decision on whether a company should purchase a batch of spare parts with a defect rate not exceeding a certain nominal value while minimizing the number of inspections. Describing the sampling process with a binomial distribution, establishing a confidence level based sampling detection model to estimate the defect rate, using a one-sided inspection method to determine whether the defect rate of spare parts exceeds the nominal value by minimizing the number of inspections, and making the optimal decision for the enterprise. Based on this, the acceptable defect rate for enterprises is limited to 0.05~0.2. Using statistical methods, when the reliability is 95%, the defect rate is 0.199, corresponding to the minimum sample size that needs to be tested, which is 104; When the reliability is 90% and the defect rate is 0.063, the corresponding minimum sample size to be tested is 335. At the same time, the sequential probability ratio test was used in the article to optimize the model. By selecting a small number of samples and making a decision on whether to continue sampling based on the results, the number of experiments was saved under the same reliability.