Weibull Distributed Research Articles

Research on the P‐S‐N Curve Fitting Method of Notched Specimens Considering Small Sample Properties

ABSTRACTAiming at the issue of fatigue test data for large‐scale mechanical components of building steel are very limited, a method for fitting P‐S‐N curves under small sample data of notched specimens is proposed to predict fatigue life. First, a fatigue life subsample augmented and its reliability assessment method are established, based on Bayesian hierarchical modeling and modified Monte Carlo method. Second, a clustering combination weighting method is proposed, to define weights of hidden variables of the binomial mixture Weibull distribution, and the expectation–maximization algorithm is used to determine probability density function of the distribution. Finally, the P‐S‐N curves under various failure probabilities are fitted with Weibull distributed life models, and the convergence and prediction accuracy of the different models are compared. The results show that the fatigue data of small samples can be predicted better by using mixed Weibull distribution, and the fitting P‐S‐N curve is more reliable and accurate.

CLOUD DATA PROTECTION USING WEIBULL DISTRIBUTED RECURRENT NEURAL ERGODIC SIGNCRYPTION

Cloud computing has become an integral part of modern computing, offering scalable storage and processing resources. However, the security of data stored in the cloud remains a major concern, especially when dealing with sensitive information. Traditional encryption schemes, while effective, often face limitations in terms of computational overhead and vulnerability to advanced attacks. To address these challenges, we propose a novel Weibull Distributed Recurrent Neural Ergodic Skewed Certificateless Signcryption scheme aimed at enhancing data protection in cloud environments. The key problem addressed by this work is the inherent inefficiency of existing cryptographic solutions that either rely on certificate-based systems or suffer from high computational and communication costs. This is especially crucial in cloud systems where real-time data processing is essential. Our approach integrates Weibull distribution for key management and optimization, recurrent neural networks (RNNs) for secure data transmission prediction, and ergodic skewed signcryption to eliminate the need for certificate authorities. This results in improved security, reduced computational overhead, and efficient communication, ensuring that the data remains secure even in dynamic cloud environments. The proposed scheme was tested using various metrics, including encryption/decryption time, data throughput, and attack resistance. Results demonstrate a significant reduction in computational cost by approximately 28% compared to traditional certificateless encryption. Furthermore, encryption times decreased from an average of 1.8 ms to 1.2 ms, and the scheme showed robustness against man-in-the-middle and chosen-ciphertext attacks with a detection accuracy of 98.6%. These results confirm the efficacy of the proposed system for enhancing security in cloud computing environments while maintaining high performance.

An efficient weapon detection system using NSGCU-DCNN classifier in surveillance

Weapon detection systems play a significant role in ensuring public safety, specifically in surveillance scenarios. But, poor performance has been shown by the prevailing research methodologies towards occluded and customized weapons. Thus, to resolve this issue, a Non-linear and Scalar Growing Cosine Unit based Deep Convolutional Neural Network (NSGCU-DCNN)-based efficient weapon detection system in the surveillance video is proposed. Primarily, the input video is converted into frames. The pre-processing process is applied for each frame. By utilizing Gaussian Kernelized Double Plateau Histogram Equalization (GKDPHE), contrast enhancement is performed grounded on the frame’s brightness. After that, for each frame, the motions are estimated by using the Frobenius Norm-based Three Step Search (FN-TSS) algorithm. Thereafter, by utilizing Weibull Distributed Viola Jones (WDVJ), the objects are detected, and the detected objects are cropped for further analysis. Next, the edge information of each object is determined by the Canny Edge Detection (CED) algorithm. Then, the frame is further converted into a 3x3 block. Afterward, the silhouette coefficient is calculated between the frames and the mask images. Further, the features are extracted and selected from the silhouette estimated frame. The NSGCU-DCNN classifies the weapons grounded on the selected features. The experimental outcomes exhibited that when contrasted with the prevailing techniques, the proposed mechanism withstands high-accuracy rates.

Life truncated multiple dependent state plan for imprecise Weibull distributed data

This paper aims to provide a multiple dependent state (MDS) sampling technique for light-emitting diode luminous intensities under indeterminacy by employing time truncated sampling schemes and the Weibull distribution. This indicates that ASN is significantly impacted by the indeterminacy parameter. Furthermore, a comparison is shown between the existing, indeterminate sampling plans and the recommended sample designs. The projected sampling technique is illustrated by calculating the luminous intensities of LEDs using the Weibull distribution. Based on the findings and practical example, we conclude that the suggested strategy needs a smaller sample size than SSP and the current MDS sampling plan.

Reliability Analysis of the Shaft Subjected to Twisting Moment and Bending Moment for The Exponential and Weibull Distributed Strength and Stress

Objectives: The purpose of the present work is to design a shaft subjected to twisting moment, bending moment and combined twisting and bending moment by determine the reliability of the shaft. Methods: Probabilistic approach is considered to find the lifetime of shaft by taking stress as random variable. Exponential and Weibull distributions are used to find lifetime of the equipment stress is considered as exponential and Weibull random variable. When the shaft is subjected to combined twisting and bending moment, the stress is found by using the two theories: (i) The maximum shear stress theory is used for ductile materials such as mild steel. (ii) The maximum normal stress theory is used for brittle materials such as cast iron. Findings: Reliability of the shaft is derived subjected to twisting and bending moments. The reliability is computed and compared for changing of the twisting moment, bending moment and diameter of the shaft. Novelty: To design a shaft by using reliability theory and to find reliability of the shaft by using the exponential and Weibull distribution is the novel idea. Keywords: Reliability, Weibull distribution, Shaft, Twisting moment, Bending moment, Combined twisting and bending moment, Exponential distribution, Maximum normal stress theory, Maximum shear stress theory

Tumor Volume Distributions Based on Weibull Distributions of Maximum Tumor Diameters

(1) Background: The distribution of tumor volumes is important for various aspects of cancer research. Unfortunately, tumor volume is rarely documented in tumor registries; usually only maximum tumor diameter is. This paper presents a method to derive tumor volume distributions from tumor diameter distributions. (2) Methods: The hypothesis is made that tumor maximum diameters d are Weibull distributed, and tumor volume is proportional to dk, where k is a parameter from the Weibull distribution of d. The assumption is tested by using a test dataset of 176 segmented tumor volumes and comparing the k obtained by fitting the Weibull distribution of d and from a direct fit of the volumes. Finally, tumor volume distributions are calculated from the maximum diameters of the SEER database for breast, NSCLC and liver. (3) Results: For the test dataset, the k values obtained from the two separate methods were found to be k = 2.14 ± 0.36 (from Weibull distribution of d) and 2.21 ± 0.25 (from tumor volume). The tumor diameter data from the SEER database were fitted to a Weibull distribution, and the resulting parameters were used to calculate the corresponding exponential tumor volume distributions with an average volume obtained from the diameter fit. (4) Conclusions: The agreement of the fitted k using independent data supports the presented methodology to obtain tumor volume distributions. The method can be used to obtain tumor volume distributions when only maximum tumor diameters are available.

A hybrid method for generating heterogeneous digital models for granites using a conditional filtering process and multiple level Weibull distribution functions

In this study, combining geometric and statistical modelling techniques together, a novel hybrid heterogeneity digital model generation method for granites is developed. It is motivated by the complexity of the digital core method and the limitations of the traditional random Weibull distributed heterogeneous method in reflecting the mechanical behaviour influenced by the spatial distribution of mineral particles. The initial mineral proportion is acquired from the feature extraction of the input image. Then a conditional filtering process is proposed in order to acquire a reasonable mineral particle distribution. Finally, the multiple-level Weibull distribution function is applied to describe the heterogeneity of different minerals. The new method has been validated in particle distribution configuration and mechanical reflection using a simulation software. In contrast to the previous methods, the multiple heterogeneity material assignment results obtained from the conditional filtering process can better reflect the actual mineral particle distribution. Moreover, reflection of failure mode behaviour is greatly improved by the proposed method compared to the traditional single-level heterogeneity model. The current data emphasize the independent and significant influence of each mineral heterogeneity, which can only be investigated using the traditional method, which ignores mineral differences. The present study lays the groundwork for future research into the influences of mineral mechanical properties and mineral particle spatial distribution on macro mechanical behaviour.

Statistics of Weibull Record-Breaking Events

The statistics of record-breaking events plays an important role in the analysis of natural physical systems. It can provide an additional insight into the mechanisms and the occurrence of extreme events. In this work, the statistical aspects of the record-breaking events drawn from the Weibull distribution are considered and analyzed in detail. It is assumed that the underlying sequences of events are independent and identically distributed (i.i.d.). Several statistical measures of record-breaking events are analyzed. Exact analytical expressions are derived for the statistics of records. Particularly, the distributions of record magnitudes and the corresponding average magnitudes of records in case of Weibull distributed events are derived exactly for any specific record order and time step. In addition, a convolution operation is used to derive a recursive formula for the distribution of times of the occurrence of records. The analytical results are compared with the Monte Carlo simulations and their validity is confirmed. The numerical simulations also reveal that the finite-size effects strongly affect the statistics of records and need to be considered during the analysis of numerical experiments or empirical data.

Asymmetric Control Limits for Weighted-Variance Mean Control Chart with Different Scale Estimators under Weibull Distributed Process

Shewhart charts are the most commonly utilised control charts for process monitoring in industries with the assumption that the underlying distribution of the quality characteristic is normal. However, this assumption may not always hold true in practice. In this paper, the weighted-variance mean charts are developed and their population standard deviation is estimated using the three subgroup scale estimators, namely the standard deviation, median absolute deviation and standard deviation of trimmed mean for monitoring Weibull distributed data with different coefficients of skewness. This study aims to compare the out-of-control average run length of these charts with the pre-determined fixed value of the in-control ARL in terms of different scale estimators, coefficients of skewness and sample sizes via extensive simulation studies. The results indicate that as the coefficients of skewness increase, the charts tend to detect the out-of-control signal more rapidly under identical magnitude of shift. Meanwhile, as the size of the shift increases under the same coefficient of skewness, the proposed charts are able to locate the shifts quicker and the similar scenarios arise as a sample size raised from 5 to 10. A real data set from survival analysis domain which, possessing Weibull distribution, was to demonstrate the usefulness and applicability of the proposed chart in practice.

Bayesian estimation of a competing risk model based on Weibull and exponential distributions under right censored data

Abstract In this paper, we investigate the estimation of the unknown parameters of a competing risk model based on a Weibull distributed decreasing failure rate and an exponentially distributed constant failure rate, under right censored data. The Bayes estimators and the corresponding risks are derived using various loss functions. Since the posterior analysis involves analytically intractable integrals, we propose a Monte Carlo method to compute these estimators. Given initial values of the model parameters, the maximum likelihood estimators are computed using the expectation-maximization algorithm. Finally, we use Pitman’s closeness criterion and integrated mean-square error to compare the performance of the Bayesian and the maximum likelihood estimators.

The Effects of Weibull Distribution on Supplier Comparison using Lower Process Capability Index: A Case Study

In supplier comparison, durability, one of the quality dimensions, is important criterion. Lifetime data is widely used to measure the durability and commonly modeled with Weibull distribution. Many researchers employ process capability indices (PCIs) for comparing suppliers about quality aspect. However, applying these methods bring to some misleading results when lifetime data are considered because the methods are developed under normal distribution. This study attempts to develop the new method for comparing supplier using lower process capability index (Cpl) to apply with the lifetime data. To be guideline for developing the new method, this research aims to study the effects of Weibull distribution on supplier comparison using Cpl via a case study. The effect is studied through 2 performance measures, e.g., producer’s risk and the power of test obtained by Monte Carlo simulation. The simulation results for Weibull distribution indicate that the process’s shape influences on the performance measures obviously. For right-skewed process, the producer’s risks are lower than = 0.05, and power of tests do not exceed 0.10. Although power of tests are close to 1.00 in case of left-skewed process, the risks are greater than = 0.05. For symmetric process, the producer’s risks are close to = 0.05, but the power of tests do not exceed 0.40 in all cases. So, this study points out that the process’s shape is an important factor affecting to the performance of supplier comparison using Cpl leading to the possibly misleading results. To better understand the effects, this paper presents the example of supplier comparison using real data. The example shows that although the popular methods for handling Weibull distribution are applied, the supplier comparison results are not the same. So, manufacturers should be aware in supplier comparison regarding to lifetime data.
 HIGHLIGHTS
 
 Studying the effects of lifetime data modeled with Weibull distribution on the supplier comparison to be guideline for developing the new method
 Presenting the example of supplier comparison via real data
 For Weibull distributed process, the process’s shape is an important factor affecting to the performance of supplier comparison
 The supplier comparison leads to the possibly misleading results although the process is symmetric
 
 GRAPHICAL ABSTRACT

A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

Standard regression models focus on the mean response based on covariates. Quantile regression describes the quantile for a response conditioned to values of covariates. The relevance of quantile regression is even greater when the response follows an asymmetrical distribution. This relevance is because the mean is not a good centrality measure to resume asymmetrically distributed data. In such a scenario, the median is a better measure of the central tendency. Quantile regression, which includes median modeling, is a better alternative to describe asymmetrically distributed data. The Weibull distribution is asymmetrical, has positive support, and has been extensively studied. In this work, we propose a new approach to quantile regression based on the Weibull distribution parameterized by its quantiles. We estimate the model parameters using the maximum likelihood method, discuss their asymptotic properties, and develop hypothesis tests. Two types of residuals are presented to evaluate the model fitting to data. We conduct Monte Carlo simulations to assess the performance of the maximum likelihood estimators and residuals. Local influence techniques are also derived to analyze the impact of perturbations on the estimated parameters, allowing us to detect potentially influential observations. We apply the obtained results to a real-world data set to show how helpful this type of quantile regression model is.

An Inventory Model for Weibull Distributed Deteriorating Items Under Ramp Type Demand and Permissible Trade Credit Policy

In a classical inventory economic order quantity (EOQ) model, the stock is depleted due to both market demand and deterioration. Many inventory models are developed for items under variable rate of deterioration. The two parameter Weibull distributed term is a representation of constant, time dependent linear and non-linear, increasing and decreasing rate of deterioration. Again the demand rate is assumed here as time dependent in beginning of cycle and then becomes constant as passage of time. Shortages are allowed and fully backlogged. Moreover the trade credit policy is a win-win payment strategy for sharing profit in the inventory system. This present paper deals with a replenishment policy assuming two parameter Weibull distributed deteriorating items, demand rate a ramp type function of time under permissible trade credit policy. Finally several numerical examples are given to illustrate the model and some particular cases are also discussed along with its’ illustrations along with concluding remarks. Keywords: Inventory, Weibull distribution, deterioration, ramp type, trade credit and shortages. Subject classification: AMS Classification No. 90B05 DOI: 10.7176/EJBM/13-19-03 Publication date: October 31 st 2021

Statistical inference of generalized progressive hybrid censored step-stress accelerated dependent competing risks model for Marshall-Olkin bivariate Weibull distribution

In this article, a step-stress accelerated life test based on the generalized Khamis-Higgins model in the presence of Marshall-Olkin bivariate Weibull distributed dependent competing risks is considered under generalized progressive hybrid censoring. It is assumed that the stress is changed when a pre-specified number of failures take place, and four different failure causes are discussed. The classical and Bayesian statistical methods are used to estimate the unknown parameters. In addition to the maximum likelihood estimation, the stochastic expectation-maximization algorithm is also applied. The Monte Carlo Markov Chain samples with importance sampling are used to obtain the Bayesian estimates under two loss functions, and the Bayesian highest posterior density credible intervals are constructed. Then the parameters and reliability function under normal use stress level are calculated. The Monte Carlo method is applied to compare the performance of the estimation methods. Finally, a real-life data set is analyzed for illustrative purposes.

Sample size calculation for two-arm trials with time-to-event endpoint for nonproportional hazards using the concept of Relative Time when inference is built on comparing Weibull distributions.

Sample size calculations for two-arm clinical trials with a time-to-event endpoint have traditionally used the assumption of proportional hazards (PH) or the assumption of exponentially distributed survival times. Available software provides methods for sample size calculation using a nonparametric logrank test, Schoenfeld's formula for Cox PH model, or parametric calculations specific to the exponential distribution. In cases where the PH assumption is not valid, the first-choice method is to compute sample size assuming a piecewise linear survival curve (Lakatos approach) for both the control and treatment arms with judiciously chosen cut-points. Recent advances in literature have used the assumption of Weibull distributed times for single-arm trials, and, newer methods have emerged that allow sample size calculations for two-arm trials using the assumption of proportional time (PT) while considering non-PH. These methods, however, always assume an instantaneous effect of treatment relative to control requiring that the effect size be defined by a single number whose magnitude is preserved throughout the trial duration. Here, we consider the scenarios where the hypothesized benefit of treatment relative to control may not be constant giving rise to the notion of Relative Time (RT). By assuming that survival times for control and treatment arm come from two different Weibull distributions with different location and shape parameters, we develop the methodology for sample size calculation for specific cases of both non-PH and non-PT. Simulations are conducted to assess the operation characteristics of the proposed method and a practical example is discussed.

Aggregation levels when the time between events is Weibull distributed

Practical applications always require an assessment of an aggregation process that is best for early detection of any outbreak of events including sales, warrantee claims or disease outbreaks. This article provides a means of deciding on the level of temporal aggregation that best suits the needs of whoever aims to monitor a process or a service. This article aims to achieve a practical aggregation level for monitoring events when the in-control time between events (TBE) in the targeted process or service follows a non-homogeneous Weibull distribution. We analyze the impact of various aggregation levels on early detection of outbreaks with different magnitudes using several monitoring schemes including an adaptive exponentially weighted moving average (EWMA) plan and several simultaneous EWMA plans with differing amounts of temporal memory for TBE data. We also consider monitoring the related counting processes to address the problem of deciding on the temporal aggregation level. To the best of our knowledge, the effect of various levels of temporal aggregation on detecting outbreaks in TBEs, when they are Weibull distributed, is not studied thoroughly.

Research on thermal imaging fault detection system based on weibull distributed electrical system

A fault prediction analysis is performed In order to use infrared thermal imaging technology to detect electrical system faults, based on Weibull distribution technology. First, the principle is explained, the key technologies and factors of infrared thermal imaging and the electrical fault monitoring system are analyzed, and the available technologies are summarized. The detection process and analysis research are established with the help of on-site inspection and analysis results for power system fault analysis and research. The research shows that the method is effective for fault detection and trend analysis, and provides a reference for power fault detection and prediction analysis.

Development of New Robust Optimal Score Function for the Weibull Distributed Error Term in Multilevel Models

A popular robust estimation technique for linear models is the rank-based method as an alternative to the ordinary least square (OLS) and restricted maximum likelihood (REML) in the presence of extreme observations. This method is applied in machine reliability analysis and quantum engineering, especially in artificial intelligence and optimization problems where outliers are commonly observed. This technique is also extended for the multilevel model, where the shape of error distribution contributes a significant role in more efficient estimation. In this study, we proposed the Weibull score function for the Weibull distributed error terms in the multilevel model. The efficiency of the proposed score function is compared with the existing Wilcoxon score function and the traditional method REML via Monte Carlo simulations after adding simulated extreme observations. For small values of shape parameter in Weibull distribution of error term showing the presence of outliers, the Weibull score function was found to be efficient as compared to the Wilcoxon and REML methods. However, for a large value of shape parameter, Wilcoxon score appeared either equally efficient than the Weibull score function. REML is observed least precise in all situations. These findings are verified through a real application on test scores data, with a small value of shape parameter, and the Weibull score function turned out the most efficient.

Stochastic modelling of cellulose hydrolysis with Gauss and Weibull distributed transition probabilities

Two Markov-type stochastic models were developed to describe the kinetics of acid hydrolysis of cellulose. One of them involved a Gauss (normal) distribution of probabilities of chemical bond breaking, the other a Weibull distribution. It was considered that the random breaking of cellulose was based on the cleavage of a parent macromolecule into two descendants. Model equations and kinetics of acid hydrolysis of cellulose consisting of 10 and 100 units of cellobiose were presented. The effects of acid concentration and temperature on the kinetics of hydrolysis process were taken into account. The results obtained applying both stochastic models were in a reasonable agreement with those obtained using a deterministic kinetic model. These stochastic models can accurately describe the kinetics of acid hydrolysis and cover the drawbacks of some deterministic kinetic models, e.g., large number of model equations and parameters, modification of parameter values by changing the process conditions.

Weighted Quantile Regression Theory And Its Application Weibull Distribution As An Actuarial Risk Model: Computation Of Its Probability Of Ultimate Ruin And The Moments Of The Time To Ruin, Deficit At Ruin And Surplus Prior To Ruin

The Weibull distribution due to its suitability to adequately model data with high degree of positive skewness which is a typical characteristics of the claim amounts, is considered a versatile model for loss modeling in general Insurance. In this paper, the Weibull distribution is fitted to a set of insurance claim data and the probability of ultimate ruin has been computed for Weibull distributed claim data using two methods, namely the Fast Fourier Transform and the 4 moment Gamma De Vylder approximation. The consistency has been found in the values obtained from the both the methods. For the same model, the first two moments of the time to ruin, deficit at the time of ruin and the surplus just prior to ruin have been computed numerically. The moments are found to be exhibiting behavior consistent to what is expected in practical scenario. The influence of the surplus process being subjected to the force of interest earnings and tax payments on the probability of ultimate ruin, causes the later to be higher than what is obtained in the absence of these factors.