Iterative Sampling Research Articles

Cluster-based learning and evolution algorithm for optimization

In this work, we present a cluster-based learning and evolution optimizer (CLEO) for solving optimization problems. CLEO is a metaheuristic algorithm that uses cluster-based manipulation of the problem space during the exploration phase, followed by fine-tuning solutions in the exploitation phase using updated knowledge of the problem space. We propose two approaches based on this new algorithm: one using only Latin hypercube sampling (LHS) and the other using LHS in combination with reservoir engineering insights. In addition to ensuring realistic simulation scenarios, we employed intuitive engineering insights to reveal how empirical knowledge enhances efficiency. Also, we propose simulating the partial life instead of the complete lifespan in the second approach. Technical results obtained at the end of this period are processed and used to find the optimized field development plan (FDP). We conducted both deterministic and probabilistic studies to assess the performance of the proposed approaches for various decision variables, both numerous and restricted. We validated the algorithm by optimizing the FDP for a simple numerical simulation model and a giant field-scale model, and compared our approaches to four well-established optimizers (particle swarm optimization (PSO), differential evolution (DE), designed exploration controlled evolution (DECE), and iterative discrete Latin hypercube sampling method (IDLHC)) in terms of simulation time and objective function results. Overall, the comparison demonstrates the advantages of the newly proposed algorithm. The results indicate that our first approach performs as well as any well-established optimizer, notably when working with large scale optimization problems. The second approach has slightly lower objective function results than the first one, but it is the most efficient among the compared algorithms, as the best FDP can be obtained by covering as little as 40% of the field's life. This attribute makes it an excellent alternative for developing oil and gas fields, which are fraught with uncertainty and errors in time-consuming simulation models. As a feasibility study on a complex and expensive compositional model, using second approach resulted in a 75% increase in efficiency while saving 120 days.

Probability propagation for faster and efficient point cloud segmentation using a neural network

Neural networks (NN) have shown promising performance in point cloud segmentation (PCS). However, the measured points are too numerous to be used as model input at once. It results in a long inference time and high computational cost due to iterative sampling and inference. This study proposes Probability Propagation (PP) as a stochastic upsampling method. PP propagates the predicted probability of a sampled part of a point cloud into the other unpredicted points by considering proximity. By replacing the iterative inference of NN with PP, large point clouds can be dealt with quickly and efficiently. We investigated the effectiveness of PP using the ShapeNet benchmark on various settings: sampling methods (random, farthest point, and Poisson disk sampling) with sampling ratios (5%, 10%, 20%, 39%, and 78%) for NN and the stochastic mapping conditions (uniform, linear, cosine, Gaussian, and exponential distributions) for PP. Using NN with PP achieved higher performance and faster inference speed than when using NN alone. For the farthest point sampling method of 5% sampling ratio, NN+PP improved the instance mIoU by 2.457%p with 102 times faster speed compared to that when using NN alone. The result indicates that PP can significantly contribute to the improvement of performance and efficiency in PCS when used in edge AI systems.

Predictors of transportation-related barriers to healthcare access in a North American suburb.

To identify predictors of transportation-related barriers to healthcare access in a North American suburb. Data from the 2022 Scarborough Survey were used, comprising n = 528 adults living in Scarborough, which is a subu<rb of Toronto, Canada, recruited through iterative sampling. Log binomial regression models identified demographic, socioeconomic, health and transportation predictors of a composite of: (1) delaying a primary care appointment, (2) missing a primary care appointment or (3) postponing or declining a vaccination due to transportation issues. Of the sampled individuals, 34.5% experienced the outcome. In the multivariable model, younger age (RR = 3.03), disability (RR = 2.60), poor mental health (RR = 1.70) and reliance on public transit (RR = 2.09) were associated with greater risk of experiencing the outcome. Full-time employment, reliance on active travel and reliance on others for transportation were specifically associated with greater risk of experiencing a transportation-related barrier to vaccination. In suburban areas such as Scarborough, transportation-related barriers to healthcare access have a disproportionate impact on groups defined by important demographic, health and transportation-related characteristics. These results corroborate that transportation is an important determinant of health in suburban areas, the absence of which may exacerbate existing inequities among the most vulnerable individuals in a given population.

Semi-supervised invertible neural operators for Bayesian inverse problems

Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces. In this work, we employ physics-informed Neural Operators in the context of high-dimensional, Bayesian inverse problems. Traditional solution strategies necessitate an enormous, and frequently infeasible, number of forward model solves, as well as the computation of parametric derivatives. In order to enable efficient solutions, we extend Deep Operator Networks (DeepONets) by employing a RealNVP architecture which yields an invertible and differentiable map between the parametric input and the branch-net output. This allows us to construct accurate approximations of the full posterior, irrespective of the number of observations and the magnitude of the observation noise, without any need for additional forward solves nor for cumbersome, iterative sampling procedures. We demonstrate the efficacy and accuracy of the proposed methodology in the context of inverse problems for three benchmarks: an anti-derivative equation, reaction-diffusion dynamics and flow through porous media.

Landmarking for Improved Digital Product Creation

Sampling is a critical step in the concept-to-style workflow for digitally created products. Virtual environments allow sampling without the costs associated with physical prototyping However, current practice often still requires physical prototyping. Here we consider how landmarking contributes to the need for iterative sampling, thereby inhibiting a fully digital product creation DPC process. In the process, the opportunity for error within traditional anthropometric study is highlighted and a path toward global standardized landmarking and measuring (L&amp;M) is presented. Landmarks denote anatomical reference points common to all humans. They are critical to every stage of DPC: measuring, product development, virtual sampling, rigging, size selection, and try-on. Cross-platform use of humanoids (models of humans) and body-worn products will introduce errors if landmarking protocols do not align across three-dimensional body processing (3DBP) technologies. Here we discuss how to avoid these discrepancies by combining Clone Block™ theory with current ISO standards. Further study should validate the findings here for the implementation of global standardized L&amp;M to facilitate 3D technology interoperability, fully DPC, and greater adoption of 3D technologies for improved fit of body-worn products.

A localization scheme based on Improving Dynamic Population Monte Carlo Localization method for large‐scale mobile wireless aquaculture sensor networks

AbstractLocalization is one of the essential problems in wireless sensor applications (WSNs). Most range‐free localization schemes for mobile WSNs are based on the Sequential Monte Carlo (SMC) algorithm. Multiple iterations, sample impoverishment and less sample diversity, leading to low localizing efficiency, are the most usual problems demanding to be solved in these SMC‐based methods. An improved localization scheme for mobile aquaculture WSNs based on the Improving Dynamic Population Monte Carlo Localization (I‐DPMCL) method is proposed. A population of probability density functions is proposed to approximate the unknown location distribution based on a set of observations through an iterative mixture importance sampling procedure, accompanied by node dynamic behaviours being analysed quantitatively or definitely. Threefold constrain rules are put forward in the I‐DPMCL scheme to decrease the iteration number and trade off iteration number and enough valid samples to obtain the optimum iteration number. Then, these localization behaviours, especial delay, are predicted based on the statistical point of view. Moreover, performance comparisons of I‐DPMCL with other SMC‐based schemes are also proposed. Simulation results show that delay of I‐DPMCL has some superiority to those of other schemes, and accuracy and energy consumption are improved in some cases of lower mobile velocity.

Iterative sampling of expensive simulations for faster deep surrogate training*

AbstractDeep neural network (DNN) surrogates of expensive physics simulations are enabling a rapid change in the way that common experimental design and analysis tasks are approached. Surrogate models allow simulations to be performed in parallel and separately from downstream tasks, thereby enabling analyses that would be impossible with the simulation in‐the‐loop; surrogates based on DNNs can effectively emulate diverse non‐scalar data of the types collected in fusion and laboratory‐astrophysics experiments. The challenge is in training the surrogate model, for which large ensembles of physics simulations must be run, preferably without wasting computational effort on uninteresting simulations. In this paper, we present an iterative sampling scheme that can preferentially propose simulations in interesting regions of parameter space without neglecting unexplored regions, allowing high‐quality and wide‐ranging surrogate models to be trained using 2–3 times fewer simulations compare to space‐filling designs. Our approach uses an explicit importance function defined on the simulation output space, balanced against a measure of simulation density which serves as a proxy for surrogate accuracy. It is easy to implement and can be tuned to find interesting simulations early in the study, allowing surrogates to be trained quickly and refined as new simulations become available; this represents an important step towards the routine generation of deep surrogate models quickly enough to be truly relevant to experimental work.

Patient‐reported experiences with migraine‐related cognitive symptoms: Results of the MiCOAS qualitative study

To capture patients' perspectives on migraine-related cognitive symptoms during pre-headache, headache, post-headache, and interictal periods. Migraine-related cognitive symptoms are reported by people with migraine both during and between attacks. Associated with disability, they are increasingly viewed as a priority target for treatment. The Migraine Clinical Outcome Assessment System (MiCOAS) project is focused on developing a patient-centered core set of outcome measures for the evaluation of migraine treatments. The project focuses on incorporating the experience of people living with migraine and the outcomes most meaningful to them. This includes an examination of the presence and functional impact of migraine-related cognitive symptoms and their perceived impact on quality of life and disability. Forty individuals with self-reported medically diagnosed migraine were recruited via iterative purposeful sampling for semi-structured qualitative interviews conducted using audio-only web conferencing. Thematic content analysis was performed to identify key concepts around migraine-related cognitive symptoms. Recruitment continued until concept saturation was achieved. Participants described symptoms consistent with migraine-related deficits in language/speech, sustained attention, executive function, and memory that manifest during pre-headache (36/40 [90%] reported ≥1 cognitive feature), headache (35/40 [88%] reported ≥1 cognitive feature), post-headache (27/40 [68%] reported ≥1 cognitive feature), and interictal periods (13/40 [33%] reported ≥1 cognitive feature). Among participants reporting cognitive symptoms during pre-headache, 32/40 (81%) endorsed 2-5 cognitive symptoms. Findings were similar during the headache phase. Participants reported language/speech problems consistent with, for example, impairments in receptive language, expressive language, and articulation. Issues with sustained attention included fogginess, confusion/disorientation, and trouble with concentration/focus. Deficits in executive function included difficulty processing information and reduced capacity for planning and decision-making. Memory issues were reported across all phases of the migraine attack. This patient-level qualitative study suggests that cognitive symptoms are common for persons with migraine, particularly in the pre-headache and headache phases. These findings highlight the importance of assessing and ameliorating these cognitive problems.

Scattered Train Bolt Point Cloud Segmentation Based on Hierarchical Multi-Scale Feature Learning.

In view of the difficulty of using raw 3D point clouds for component detection in the railway field, this paper designs a point cloud segmentation model based on deep learning together with a point cloud preprocessing mechanism. First, a special preprocessing algorithm is designed to resolve the problems of noise points, acquisition errors, and large data volume in the actual point cloud model of the bolt. The algorithm uses the point cloud adaptive weighted guided filtering for noise smoothing according to the noise characteristics. Then retaining the key points of the point cloud, this algorithm uses the octree to partition the point cloud and carries out iterative farthest point sampling in each partition for obtaining the standard point cloud model. The standard point cloud model is then subjected to hierarchical multi-scale feature extraction to obtain global features, which are combined with local features through a self-attention mechanism, while linear interpolation is used to further expand the perceptual field of local features of the model as a basis for segmentation, and finally the segmentation is completed. Experiments show that the proposed algorithm could deal with the scattered bolt point cloud well, realize the segmentation of train bolt and background, and could achieve high segmentation accuracy, which has important practical significance for train safety detection.

A multi-fidelity model management framework for multi-objective aerospace design optimisation

This paper presents a multi-fidelity meta-modelling and model management framework designed to efficiently incorporate increased levels of simulation fidelity from multiple, competing sources into early-stage multidisciplinary design optimisation scenarios. Phase specific/invariant low-fidelity physics-based subsystem models are adaptively corrected via iterative sampling of high(er)-fidelity simulators. The correction process is decomposed into several distinct parametric/non-parametric stages, each leveraging alternate aspects of the available model responses. Globally approximating surrogates are constructed at each degree of fidelity (low, mid, and high) via an automated hyper-parameter selection and training procedure. The resulting hierarchy drives the optimisation process, with local refinement managed according to a confidence-based multi-response adaptive sampling procedure, with bias given to global parameter sensitivities. An application of this approach is demonstrated via the aerodynamic response prediction of a parametrized re-entry vehicle, subjected to a static/dynamic parameter optimisation for three separate single-objective problems. It is found that the proposed data correction process facilitates increased efficiency in attaining a desired approximation accuracy relative to a single-fidelity equivalent model. When applied within the proposed multi-fidelity management framework, clear convergence to the objective optimum is observed for each examined design optimisation scenario, outperforming an equivalent single-fidelity approach in terms of computational efficiency and solution variability.

Understanding Digital Mental Health Needs and Usage With an Artificial Intelligence-Led Mental Health App (Wysa) During the COVID-19 Pandemic: Retrospective Analysis.

There has been a surge in mental health concerns during the COVID-19 pandemic, which has prompted the increased use of digital platforms. However, there is little known about the mental health needs and behaviors of the global population during the pandemic. This study aims to fill this knowledge gap through the analysis of real-world data collected from users of a digital mental health app (Wysa) regarding their engagement patterns and behaviors, as shown by their usage of the service. This study aims to (1) examine the relationship between mental health distress, digital health uptake, and COVID-19 case numbers; (2) evaluate engagement patterns with the app during the study period; and (3) examine the efficacy of the app in improving mental health outcomes for its users during the pandemic. This study used a retrospective observational design. During the COVID-19 pandemic, the app's installations and emotional utterances were measured from March 2020 to October 2021 for the United Kingdom, the United States of America, and India and were mapped against COVID-19 case numbers and their peaks. The engagement of the users from this period (N=4541) with the Wysa app was compared to that of equivalent samples of users from a pre-COVID-19 period (1000 iterations). The efficacy was assessed for users who completed pre-post assessments for symptoms of depression (n=2061) and anxiety (n=1995) on the Patient Health Questionnaire-9 (PHQ-9) and Generalized Anxiety Disorder-7 (GAD-7) test measures, respectively. Our findings demonstrate a significant positive correlation between the increase in the number of installs of the Wysa mental health app and the peaks of COVID-19 case numbers in the United Kingdom (P=.02) and India (P<.001). Findings indicate that users (N=4541) during the COVID period had a significantly higher engagement than the samples from the pre-COVID period, with a medium to large effect size for 80% of these 1000 iterative samples, as observed on the Mann-Whitney test. The PHQ-9 and GAD-7 pre-post assessments indicated statistically significant improvement with a medium effect size (PHQ-9: P=.57; GAD-7: P=.56). This study demonstrates that emotional distress increased substantially during the pandemic, prompting the increased uptake of an artificial intelligence-led mental health app (Wysa), and also offers evidence that the Wysa app could support its users and its usage could result in a significant reduction in symptoms of anxiety and depression. This study also highlights the importance of contextualizing interventions and suggests that digital health interventions can provide large populations with scalable and evidence-based support for mental health care.

Rare osteohistological evidence of skeletal maturity in the early diverging traversodontid Scalenodon angustifrons, with comments on histological sampling coverage in Cynodontia

ABSTRACT To date, 25 species of non-mammalian cynodonts have been histologically sampled, but few record a definitive and well-developed external fundamental system (EFS) indicative of skeletal maturity. Here, I report an EFS in the femoral histology of Scalenodon angustifrons and discuss the factors that could explain why skeletally mature tissue is rarely documented in cynodont osteohistology. My sample includes two equivalently sized individuals that document marked histological variation, as only one shows evidence of slowing growth rate and an EFS. Variation in the bone histology between femora of the same size suggests that attainment of skeletal maturity does not follow a discrete developmental pattern for S. angustifrons, a pattern that is also seen in the bone histology of other traversodontids and some non-gomphodontian cynodonts. From these results, a flexible growth strategy is inferred for S. angustifrons. To contextualize the validity of this pattern among other cynodont species, I summarize the sampling coverage of cynodonts that have been thin-sectioned and report limited coverage across size classes/ inferred development stages. This is often a result of sampling one isolated element that is not standardized to one skeletal element, which contributes to a poorly constrained comparative sample (in terms of size coverage, spatial and temporal resolution, and taxonomic coverage). Despite this, many cynodont species show shifts towards slow growth, but very few instances of unequivocal evidence of skeletal maturity. This result underscores the need for standardized iterative histological sampling to assess longevity, life history, and developmental patterns of non-mammalian cynodonts more accurately.

Iterative Random Training Sampling Convolutional Neural Network for Hyperspectral Image Classification

Convolution neural network (CNN) has received considerable interest in hyperspectral image classification (HSIC) lately due to its excellent spectral-spatial feature extraction capability. To improve CNN, many approaches have been directed to exploring the infrastructure of its network by introducing different paradigms. This paper takes a rather different approach by developing an iterative CNN which extends a CNN by including a feedback system to repeatedly process the same CNN in an iterative manner. Its idea is to take advantage of a recently developed iterative training sampling spectral-spatial classification (IRTS-SSC) that allows CNN to update its spatial information of classification maps through a feedback spatial filtering system via IRTS. The resulting CNN is called iterative random training sampling CNN (IRTS-CNN) with several unique features. First, IRTS-CNN combines CNN and IRTS-SSC into one paradigm, an architecture which has never investigated in the past. Second, it implements a series of spatial filters to capture spatial information of classified data samples and further feeds this information back via an iterative process to expand the current input data cube for the next iteration. Third, it utilizes the expanded data cube to randomly re-select training samples and then to re-implement CNN iteratively. Last but not least, IRTS-CNN provides a general framework which can implement any arbitrary CNN as an initial classifier to improve its performance through an iterative process. Extensive experiments are conducted to demonstrate that IRTS-CNN indeed significantly improves CNN, specifically, when only a small size of limited training samples is used.

A framework using nested partitions algorithm for convergence analysis of population distribution-based methods

Stochastic optimization algorithms such as genetic algorithm (GA), particle swarm optimization (PSO), estimation of distribution algorithms (EDAs), and nested partitions algorithm (NPA) are used in many problems including nonlinear model predictive control and task assignment. Some of these algorithms, however, lack global convergence guarantee such as PSO, or require strict convergence assumptions such as NPA. To enhance these methods in terms of convergence, a common underlying framework towards representing the seemingly unrelated methods is established as the updating of the distribution of the population through iterative sampling, and the methods that fit into this framework are called population distribution-based methods. Global convergence conditions for this framework are innovatively developed by building a shadow NPA structure for the population evolution process. The result is generic and is capable of analyzing convergence of many methods including GA, PSO, EDA, and NPA. It can be further exploited to improve convergence by modifying these methods. The existing and modified variants of these methods are then applied to case studies to show the improvement.

Estimating traffic density using transformer decoders

We propose a combined particle-based density prediction model consisting of three components: trajectory prediction for existing particles, entering particle prediction, and iterative sampling. At initialization, the combined model takes in a set of trajectories for trajectory prediction and a sequence of observation vectors for entering particle prediction. Then, the iterative sampling module generates the density prediction for the next time instance. It will also sample a pool of particles and pass on their trajectories to the next trajectory prediction model for future density prediction.

An Iterative Random Sampling Algorithm for Rapid and Scalable Estimation of Matrix Spectra

An easy-to-implement iterative algorithm that enables efficient and scalable spectral analysis of dense matrices is presented. The algorithm relies on the approximation of a matrix's singular values by those of a series of smaller matrices formed from uniform random sampling of its rows and columns. It is shown that, for sufficiently incoherent and rank-deficient matrices, the singular values [are expected to] decay at the same rate as those of matrices formed via this sampling scheme, which permits such matrices' ranks to be accurately estimated from the smaller matrices' spectra. Moreover, for such a matrix of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m \times n$</tex-math></inline-formula> , it is shown that the dominant singular values are [expected to be] <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sqrt {mn} /k$</tex-math></inline-formula> times those of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k \times k$</tex-math></inline-formula> matrix formed by randomly sampling <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> of its rows and columns. Starting from a small initial guess <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k\ = {k}_0\ $</tex-math></inline-formula> , the algorithm repeatedly doubles <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> until two convergence criteria are met; the criteria to ensure that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> is sufficiently large to estimate the singular values, to the desired accuracy, are presented. The algorithm's properties are analyzed theoretically and its efficacy is studied numerically for small to very-large matrices that result from discretization of integral-equation operators, with various physical kernels common in electromagnetics and acoustics, as well as for artificial matrices of various incoherence and rank-deficiency properties.

Acoustic Signals Recovering for Rubbing From Arbitrarily Structured Noise With Joint Iterative Probabilistic Sampling

Acoustic Signals Recovering for Rubbing From Arbitrarily Structured Noise With Joint Iterative Probabilistic Sampling

Data selection and data-enabled predictive control for a fuel cell system

Data-enabled predictive control is applied for power tracking of a fuel cell system and algorithmic aspects are investigated. For the system realization, the column subset selection algorithms norm sampling, iterative norm sampling, leverage score sampling, and selection based on the strong rank-revealing QR factorization are compared. Regularization using the 1-norm and the squared 2-norm on the column combination vector g is evaluated in terms of runtime and closed-loop results. The results indicate that column selection based on a strong rank-revealing QR (sRRQR) decomposition and leverage score sampling lead to consistently small closed-loop costs even with comparatively few columns in the data matrix resulting in reduced computation time. The closed-loop performance with 1-norm and squared 2-norm is similar, with lower turnaround times for the latter.

Accelerating Falcon Post-Quantum Digital Signature Algorithm on Graphic Processing Units

Since 2016, the National Institute of Standards and Technology (NIST) has been performing a competition to standardize post-quantum cryptography (PQC). Although Falcon has been selected in the competition as one of the standard PQC algorithms because of its advantages in short key and signature sizes, its performance overhead is larger than that of other lattice-based cryptosystems. This study presents multiple methodologies to accelerate the performance of Falcon using graphics processing units (GPUs) for server-side use. Direct GPU porting significantly degrades performance because the Falcon reference codes require recursive functions in its sampling process. Thus, an iterative sampling approach for efficient parallel processing is presented. In this study, the Falcon software applied a fine-grained execution model and reported the optimal number of threads in a thread block. Moreover, the polynomial multiplication performance was optimized by parallelizing the number-theoretic transform (NTT)-based polynomial multiplication and the fast Fourier transform (FFT)-based multiplication. Furthermore, dummy-based parallel execution methods have been introduced to handle the thread divergence effects. The presented Falcon software on RTX 3090 NVIDA GPU based on the proposed methods with Falcon-512 and Falcon-1024 parameters outperform at 35.14, 28.84, and 34.64 times and 33.31, 27.45, and 34.40 times, respectively, better than the central processing unit (CPU) reference implementation using Advanced Vector Extensions 2 (AVX2) instructions on a Ryzen 9 5900X running at 3.7 GHz in key generation, signing, and verification, respectively. Therefore, the proposed Falcon software can be used in servers managing multiple concurrent clients for efficient certificate verification and be used as an outsourced key generation and signature generation server for Signature as a Service (SaS).

Amputated Life Testing for Weibull-Fréchet Percentiles: Single, Double and Multiple Group Sampling Inspection Plans with Applications

When a life test is terminated at a predetermined time to decide whether to accept or refuse the submitted batches, the types of group sampling inspection plans (single, two, and multiple-stages) are introduced. The tables in this study give the optimal number of groups for various confidence levels, examination limits, and values of the ratio of the determined experiment time to the fixed percentile life. At various quality levels, the operating characteristic functions and accompanying producer's risk are derived for various types of group sampling inspection plans. At the determined producer's risk, the optimal ratios of real percentile life to a fixed percentile life are obtained. Three case studies are provided to illustrate the processes described here. Comparisons of single-stage and iterative group sampling plans are introduced. The first, second, and third sample minimums must be used to guarantee that the product's stipulated mean and median lifetimes are reached at a certain degree of customer trust. The suggested sample plans' operational characteristic values and the producer's risk are given. In order to show how the suggested approaches based on the mean life span and median life span of the product may function in reality, certain real-world examples are examined.