Search results for: Weibull parameter

Authors: Al Omari Mohammed Ahmed

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This paper focuses on Maximum Likelihood Estimator with Covariate. Covariates are incorporated into the Weibull model. Under this regression model with regards to maximum likelihood estimator, the parameters of the covariate, shape parameter, survival function and hazard rate of the Weibull regression distribution with right censored data are estimated. The mean square error (MSE) and absolute bias are used to compare the performance of Weibull regression distribution. For the simulation comparison, the study used various sample sizes and several specific values of the Weibull shape parameter.

Keywords: weibull regression distribution, maximum likelihood estimator, survival function, hazard rate, right censoring

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Authors: Abd El Hady N. Ebraheim

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This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: exponentiated, inversion method, maximum likelihood estimation, transmutation map

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Authors: Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa

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A generalized log-logistic distribution with variable shapes of the hazard rate was introduced and studied, extending the log-logistic distribution by adding an extra parameter to the classical distribution, leading to greater flexibility in analysing and modeling various data types. The proposed distribution has a large number of well-known lifetime special sub-models such as; Weibull, log-logistic, exponential, and Burr XII distributions. Its basic mathematical and statistical properties were derived. The method of maximum likelihood was adopted for estimating the unknown parameters of the proposed distribution, and a Monte Carlo simulation study is carried out to assess the behavior of the estimators. The importance of this distribution is that its tendency to model both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub shape) or reversed “bathtub” shape hazard rate functions which are quite common in survival and reliability data analysis. Furthermore, the flexibility and usefulness of the proposed distribution are illustrated in a real-life data set and compared to its sub-models; Weibull, log-logistic, and BurrXII distributions and other parametric survival distributions with 3-parmaeters; like the exponentiated Weibull distribution, the 3-parameter lognormal distribution, the 3- parameter gamma distribution, the 3-parameter Weibull distribution, and the 3-parameter log-logistic (also known as shifted log-logistic) distribution. The proposed distribution provided a better fit than all of the competitive distributions based on the goodness-of-fit tests, the log-likelihood, and information criterion values. Finally, Bayesian analysis and performance of Gibbs sampling for the data set are also carried out.

Keywords: hazard rate function, log-logistic distribution, maximum likelihood estimation, generalized log-logistic distribution, survival data, Monte Carlo simulation

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Authors: Taehan Bae

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In this paper, a class of length-biased Weibull mixtures is presented to model loss severity data. The proposed model generalizes the Erlang mixtures with the common scale parameter, and it shares many important modelling features, such as flexibility to fit various data distribution shapes and weak-denseness in the class of positive continuous distributions, with the Erlang mixtures. We show that the asymptotic tail estimate of the length-biased Weibull mixture is Weibull-type, which makes the model effective to fit loss severity data with heavy-tailed observations. A method of statistical estimation is discussed with applications on real catastrophic loss data sets.

Keywords: Erlang mixture, length-biased distribution, transformed gamma distribution, asymptotic tail estimate, EM algorithm, expectation-maximization algorithm

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Authors: Xiang Jia, Zhijun Cheng

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The residual lifetime of a product is the operation time between the current time and the time point when the failure happens. The residual lifetime estimation is rather important in reliability analysis. To predict the residual lifetime, it is necessary to assume or verify a particular distribution that the lifetime of the product follows. And the two-parameter Weibull distribution is frequently adopted to describe the lifetime in reliability engineering. Due to the time constraint and cost reduction, a life testing experiment is usually terminated before all the units have failed. Then the censored data is usually collected. In addition, other information could also be obtained for reliability analysis. The expert judgements are considered as it is common that the experts could present some useful information concerning the reliability. Therefore, the residual lifetime is estimated for Weibull distribution by fusing the censored data and expert judgements in this paper. First, the closed-forms concerning the point estimate and confidence interval for the residual lifetime under the Weibull distribution are both presented. Next, the expert judgements are regarded as the prior information and how to determine the prior distribution of Weibull parameters is developed. For completeness, the cases that there is only one, and there are more than two expert judgements are both focused on. Further, the posterior distribution of Weibull parameters is derived. Considering that it is difficult to derive the posterior distribution of residual lifetime, a sample-based method is proposed to generate the posterior samples of Weibull parameters based on the Monte Carlo Markov Chain (MCMC) method. And these samples are used to obtain the Bayes estimation and credible interval for the residual lifetime. Finally, an illustrative example is discussed to show the application. It demonstrates that the proposed method is rather simple, satisfactory, and robust.

Keywords: expert judgements, information fusion, residual lifetime, Weibull distribution

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Authors: Eduardo C. Guardia, Jose W. M. Lima, Afonso H. M. Santos

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This paper presents a nonparametric method to obtain the hazard rate “Bathtub curve” for power system components. The model is a mixture of the three known phases of a component life, the decreasing failure rate (DFR), the constant failure rate (CFR) and the increasing failure rate (IFR) represented by three parametric Weibull models. The parameters are obtained from a simultaneous fitting process of the model to the Kernel nonparametric hazard rate curve. From the Weibull parameters and failure rate curves the useful lifetime and the characteristic lifetime were defined. To demonstrate the model the historic time-to-failure of distribution transformers were used as an example. The resulted “Bathtub curve” shows the failure rate for the equipment lifetime which can be applied in economic and replacement decision models.

Keywords: bathtub curve, failure analysis, lifetime estimation, parameter estimation, Weibull distribution

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Authors: Kanchan Mondal, Dasharath Koulage, Dattatray Manerikar, Asmita Ghate

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This paper presents an additive reliability model using warranty data and Finite Element Analysis (FEA) data. Warranty data for any product gives insight to its underlying issues. This is often used by Reliability Engineers to build prediction model to forecast failure rate of parts. But there is one major limitation in using warranty data for prediction. Warranty periods constitute only a small fraction of total lifetime of a product, most of the time it covers only the infant mortality and useful life zone of a bathtub curve. Predicting with warranty data alone in these cases is not generally provide results with desired accuracy. Failure rate of a mechanical part is driven by random issues initially and wear-out or usage related issues at later stages of the lifetime. For better predictability of failure rate, one need to explore the failure rate behavior at wear out zone of a bathtub curve. Due to cost and time constraints, it is not always possible to test samples till failure, but FEA-Fatigue analysis can provide the failure rate behavior of a part much beyond warranty period in a quicker time and at lesser cost. In this work, the authors proposed an Additive Weibull Model, which make use of both warranty and FEA fatigue analysis data for predicting failure rates. It involves modeling of two data sets of a part, one with existing warranty claims and other with fatigue life data. Hazard rate base Weibull estimation has been used for the modeling the warranty data whereas S-N curved based Weibull parameter estimation is used for FEA data. Two separate Weibull models’ parameters are estimated and combined to form the proposed Additive Weibull Model for prediction.

Keywords: bathtub curve, fatigue, FEA, reliability, warranty, Weibull

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Authors: Al Omari Moahmmed Ahmed

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In the Bayesian, we developed an approach by using non-informative prior with covariate and obtained by using Gauss quadrature method to estimate the parameters of the covariate and reliability function of the Weibull regression distribution with Type-I censored data. The maximum likelihood seen that the estimators obtained are not available in closed forms, although they can be solved it by using Newton-Raphson methods. The comparison criteria are the MSE and the performance of these estimates are assessed using simulation considering various sample size, several specific values of shape parameter. The results show that Bayesian with non-informative prior is better than Maximum Likelihood Estimator.

Keywords: non-informative prior, Bayesian method, type-I censoring, Gauss quardature

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Authors: Al Omari Moahmmed Ahmed

Abstract:

These papers describe the Bayesian Estimator using Markov Chain Monte Carlo and Lindley’s approximation and the maximum likelihood estimation of the Weibull distribution with Type-I censored data. The maximum likelihood method can’t estimate the shape parameter in closed forms, although it can be solved by numerical methods. Moreover, the Bayesian estimates of the parameters, the survival and hazard functions cannot be solved analytically. Hence Markov Chain Monte Carlo method and Lindley’s approximation are used, where the full conditional distribution for the parameters of Weibull distribution are obtained via Gibbs sampling and Metropolis-Hastings algorithm (HM) followed by estimate the survival and hazard functions. The methods are compared to Maximum Likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the better method in scale and shape parameters, the survival and hazard functions.

Keywords: weibull distribution, bayesian method, markov chain mote carlo, survival and hazard functions

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Authors: Isha Saxena, Behzad Kazemtabrizi, Matthias C. M. Troffaes, Christopher Crabtree

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The calculations done at the beginning of the life of a wind farm are rarely reliable, which makes it important to conduct research and study the failure and repair rates of the wind turbines under various conditions. This miscalculation happens because the current models make a simplifying assumption that the failure/repair rate remains constant over time. This means that the reliability function is exponential in nature. This research aims to create a more accurate model using sensory data and a data-driven approach. The data cleaning and data processing is done by comparing the Power Curve data of the wind turbines with SCADA data. This is then converted to times to repair and times to failure timeseries data. Several different mathematical functions are fitted to the times to failure and times to repair data of the wind turbine components using Maximum Likelihood Estimation and the Posterior expectation method for Bayesian Parameter Estimation. Initial results indicate that two parameter Weibull function and exponential function produce almost identical results. Further analysis is being done using the complex system analysis considering the failures of each electrical and mechanical component of the wind turbine. The aim of this project is to perform a more accurate reliability analysis that can be helpful for the engineers to schedule maintenance and repairs to decrease the downtime of the turbine.

Keywords: reliability, bayesian parameter inference, maximum likelihood estimation, weibull function, SCADA data

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Authors: Ehsanolah Assareh, Mojtaba Biglari, Mojtaba Nedaei

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Sanar village in north of Iran is a remote region with difficult access to electricity, grid and water supply. Thus the aim of this research is to evaluate the potential of wind as a power source either for electricity generation or for water pumping. In this study the statistical analysis has been performed by Weibull distribution function. The results show that the Weibull distribution has fitted the wind data very well. Also it has been demonstrated that wind speed at 40 m height is ranged from 1.75 m/s in Dec to 3.28 m/s in Aug with average value of 2.69 m/s. In this research, different wind speed characteristics such as turbulence intensity, wind direction, monthly air temperature, humidity wind power density and other related parameters have been investigated. Finally it was concluded that the wind energy in the Sanar village may be explored by employing modern wind turbines that require very lower start-up speeds.

Keywords: wind energy, wind turbine, weibull, Sanar village, Iran

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Authors: Mohammed Wadi, Bedri Kekezoglu, Mustafa Baysal, Mehmet Rida Tur, Abdulfetah Shobole

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This paper investigates the technical evaluation of the wind potential for present and future investments in Turkey taking into account the feasibility of sites, installments, operation, and maintenance. This evaluation based on the hourly measured wind speed data for the three years 2008–2010 at 30 m height for Çatalca district. These data were obtained from national meteorology station in Istanbul–Republic of Turkey are analyzed in order to evaluate the feasibility of wind power potential and to assure supreme assortment of wind turbines installing for the area of interest. Furthermore, the data are extrapolated and analyzed at 60 m and 80 m regarding the variability of roughness factor. Weibull bi-parameter probability function is used to approximate monthly and annually wind potential and power density based on three calculation methods namely, the approximated, the graphical and the energy pattern factor methods. The annual mean wind power densities were to be 400.31, 540.08 and 611.02 W/m² for 30, 60, and 80 m heights respectively. Simulation results prove that the analyzed area is an appropriate place for constructing large-scale wind farms.

Keywords: wind potential in Turkey, Weibull bi-parameter probability function, the approximated method, the graphical method, the energy pattern factor method, capacity factor

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Authors: Anurag Savarnya

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The reliability of the various parts of electric mining shovel has been assessed through the application of Weibull Model. The study was initiated to find reliability of components of electric mining shovel. The paper aims to optimize the reliability of components and increase the life cycle of component. A multilevel decomposition of the electric mining shovel was done and maintenance records were used to evaluate the failure data and appropriate system characterization was done to model the system in terms of reasonable number of components. The approach used develops a mathematical model to assess the reliability of the electric mining shovel components. The model can be used to predict reliability of components of the hydraulic mining shovel and system performance. Reliability is an inherent attribute to a system. When the life-cycle costs of a system are being analyzed, reliability plays an important role as a major driver of these costs and has considerable influence on system performance. It is an iterative process that begins with specification of reliability goals consistent with cost and performance objectives. The data were collected from an Indian open cast coal mine and the reliability of various components of the electric mining shovel has been assessed by following a Weibull Model.

Keywords: reliability, Weibull model, electric mining shovel

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Authors: Niroshan K. Walgama Wellalage, Tieling Zhang, Richard Dwight

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State-based Markov deterioration models (SMDM) sometimes fail to find accurate transition probability matrix (TPM) values, and hence lead to invalid future condition prediction or incorrect average deterioration rates mainly due to drawbacks of existing nonlinear optimization-based algorithms and/or subjective function types used for regression analysis. Furthermore, a set of separate functions for each condition state with age cannot be directly derived by using Markov model for a given bridge element group, which however is of interest to industrial partners. This paper presents a new approach for generating Homogeneous SMDM model output, namely, the Modified Weibull approach, which consists of a set of appropriate functions to describe the percentage condition prediction of bridge elements in each state. These functions are combined with Bayesian approach and Metropolis Hasting Algorithm (MHA) based Markov Chain Monte Carlo (MCMC) simulation technique for quantifying the uncertainty in model parameter estimates. In this study, factors contributing to rail bridge deterioration were identified. The inspection data for 1,000 Australian railway bridges over 15 years were reviewed and filtered accordingly based on the real operational experience. Network level deterioration model for a typical bridge element group was developed using the proposed Modified Weibull approach. The condition state predictions obtained from this method were validated using statistical hypothesis tests with a test data set. Results show that the proposed model is able to not only predict the conditions in network-level accurately but also capture the model uncertainties with given confidence interval.

Keywords: bridge deterioration modelling, modified weibull approach, MCMC, metropolis-hasting algorithm, bayesian approach, Markov deterioration models

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Authors: Mohadeseh Shojaei Shahrokhabadi, Ding-Geng (Din) Chen

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Positive continuous outcomes with a substantial number of zero values and incomplete longitudinal follow-up are quite common in medical cost data. To jointly model semi-continuous longitudinal cost data and survival data and to provide marginalized covariate effect estimates, a marginalized two-part joint model (MTJM) has been developed for outcome variables with lognormal distributions. In this paper, we propose MTJM models for outcome variables from a generalized gamma (GG) family of distributions. The GG distribution constitutes a general family that includes approximately all of the most frequently used distributions like the Gamma, Exponential, Weibull, and Log Normal. In the proposed MTJM-GG model, the conditional mean from a conventional two-part model with a three-parameter GG distribution is parameterized to provide the marginal interpretation for regression coefficients. In addition, MTJM-gamma and MTJM-Weibull are developed as special cases of MTJM-GG. To illustrate the applicability of the MTJM-GG, we applied the model to a set of real electronic health record data recently collected in Iran, and we provided SAS code for application. The simulation results showed that when the outcome distribution is unknown or misspecified, which is usually the case in real data sets, the MTJM-GG consistently outperforms other models. The GG family of distribution facilitates estimating a model with improved fit over the MTJM-gamma, standard Weibull, or Log-Normal distributions.

Keywords: marginalized two-part model, zero-inflated, right-skewed, semi-continuous, generalized gamma

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Authors: Ozan Kahraman, Hao Feng

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Several models such as Weibull, Modified Gompertz, Biphasic linear, and Log-logistic models have been proposed in order to describe non-linear inactivation kinetics and used to fit non-linear inactivation data of several microorganisms for inactivation by heat, high pressure processing or pulsed electric field. First-order kinetic parameters (D-values and z-values) have often been used in order to identify microbial inactivation by non-thermal processing methods such as ultrasound. Most ultrasonic inactivation studies employed first-order kinetic parameters (D-values and z-values) in order to describe the reduction on microbial survival count. This study was conducted to analyze the E. coli O157:H7 inactivation data by using five microbial survival models (First-order, Weibull, Modified Gompertz, Biphasic linear and Log-logistic). First-order, Weibull, Modified Gompertz, Biphasic linear and Log-logistic kinetic models were used for fitting inactivation curves of Escherichia coli O157:H7. The residual sum of squares and the total sum of squares criteria were used to evaluate the models. The statistical indices of the kinetic models were used to fit inactivation data for E. coli O157:H7 by MTS at three temperatures (40, 50, and 60 0C) and three pressures (100, 200, and 300 kPa). Based on the statistical indices and visual observations, the Weibull and Biphasic models were best fitting of the data for MTS treatment as shown by high R2 values. The non-linear kinetic models, including the Modified Gompertz, First-order, and Log-logistic models did not provide any better fit to data from MTS compared the Weibull and Biphasic models. It was observed that the data found in this study did not follow the first-order kinetics. It is possibly because of the cells which are sensitive to ultrasound treatment were inactivated first, resulting in a fast inactivation period, while those resistant to ultrasound were killed slowly. The Weibull and biphasic models were found as more flexible in order to determine the survival curves of E. coli O157:H7 treated by MTS on apple-carrot juice.

Keywords: Weibull, Biphasic, MTS, kinetic models, E.coli O157:H7

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Authors: Ch. Sridevi, A. Chalapathi Rao, P. Srinivasulu

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The location accuracy of data products is a critical parameter in assessing the geometric performance of satellite sensors. This study focuses on reliability analysis of onboard sensors to evaluate their performance in terms of location accuracy performance over time. The analysis utilizes field failure data and employs the weibull distribution to determine the reliability and in turn to understand the improvements or degradations over a period of time. The analysis begins by scrutinizing the location accuracy error which is the root mean square (RMS) error of differences between ground control point coordinates observed on the product and the map and identifying the failure data with reference to time. A significant challenge in this study is to thoroughly analyze the possibility of an infant mortality phase in the data. To address this, the Weibull distribution is utilized to determine if the data exhibits an infant stage or if it has transitioned into the operational phase. The shape parameter beta plays a crucial role in identifying this stage. Additionally, determining the exact start of the operational phase and the end of the infant stage poses another challenge as it is crucial to eliminate residual infant mortality or wear-out from the model, as it can significantly increase the total failure rate. To address this, an approach utilizing the well-established statistical Laplace test is applied to infer the behavior of sensors and to accurately ascertain the duration of different phases in the lifetime and the time required for stabilization. This approach also helps in understanding if the bathtub curve model, which accounts for the different phases in the lifetime of a product, is appropriate for the data and whether the thresholds for the infant period and wear-out phase are accurately estimated by validating the data in individual phases with Weibull distribution curve fitting analysis. Once the operational phase is determined, reliability is assessed using Weibull analysis. This analysis not only provides insights into the reliability of individual sensors with regards to location accuracy over the required period of time, but also establishes a model that can be applied to automate similar analyses for various sensors and parameters using field failure data. Furthermore, the identification of the best-performing sensor through this analysis serves as a benchmark for future missions and designs, ensuring continuous improvement in sensor performance and reliability. Overall, this study provides a methodology to accurately determine the duration of different phases in the life data of individual sensors. It enables an assessment of the time required for stabilization and provides insights into the reliability during the operational phase and the commencement of the wear-out phase. By employing this methodology, designers can make informed decisions regarding sensor performance with regards to location accuracy, contributing to enhanced accuracy in satellite-based applications.

Keywords: bathtub curve, geometric performance, Laplace test, location accuracy, reliability analysis, Weibull analysis

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Authors: A. D. Abdellatif, A. N. Ahmed, M. E. Abdelaziz

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The main purpose of this paper is to design a double acceptance sampling plan under the time truncated life test when the product lifetime follows an exponentiated transmuted Weibull distribution. Here, the motive is to meet both the consumer’s risk and producer’s risk simultaneously at the specified quality levels, while the termination time is specified. A comparison between the results of the double and single acceptance sampling plans is conducted. We demonstrate the applicability of our results to real data sets.

Keywords: double sampling plan, single sampling plan, producer’s risk, consumer’s risk, exponentiated transmuted weibull distribution, time truncated experiment, single, double, Marshal-Olkin

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Authors: Kaushal Kishore

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Immense amount of imported fuels are used in Fiji for electricity generation, transportation and for carrying out miscellaneous household work. To alleviate its dependency on fossil fuel, paramount importance has been given to instigate the utilization of renewable energy sources for power generation and to reduce the environmental dilapidation. Amongst the many renewable energy sources, wind has been considered as one of the best identified renewable sources that are comprehensively available in Fiji. In this study the wind resource assessment for three locations in Rakiraki, Fiji has been carried out. The wind resource estimation at Rokavukavu, Navolau and at Tuvavatu has been analyzed. The average wind speed at 55 m above ground level (a.g.l) at Rokavukavu, Navolau, and Tuvavatu sites are 5.91 m/s, 8.94 m/s and 8.13 m/s with the turbulence intensity of 14.9%, 17.1%, and 11.7% respectively. The moment fitting method has been used to estimate the Weibull parameter and the power density at each sites. A high resolution wind resource map for the three locations has been developed by using Wind Atlas Analysis and Application Program (WAsP). The results obtained from WAsP exhibited good wind potential at Navolau and Tuvavatu sites. A wind farm has been proposed at Navolau and Tuvavatu site that comprises six Vergnet 275 kW wind turbines at each site. The annual energy production (AEP) for each wind farm is estimated and an economic analysis is performed. The economic analysis for the proposed wind farms at Navolau and Tuvavatu sites showed a payback period of 5 and 6 years respectively.

Keywords: annual energy production, Rakiraki Fiji, turbulence intensity, Weibull parameter, wind speed, Wind Atlas Analysis and Application Program

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Authors: Meriem Bahij, Ahmed Nafidi, Boujemâa Achchab, Sílvio M. A. Gama, José A. O. Matos

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Stochastic modeling concerns the use of probability to model real-world situations in which uncertainty is present. Therefore, the purpose of stochastic modeling is to estimate the probability of outcomes within a forecast, i.e. to be able to predict what conditions or decisions might happen under different situations. In the present study, we present a model of a stochastic diffusion process based on the bi-Weibull distribution function (its trend is proportional to the bi-Weibull probability density function). In general, the Weibull distribution has the ability to assume the characteristics of many different types of distributions. This has made it very popular among engineers and quality practitioners, who have considered it the most commonly used distribution for studying problems such as modeling reliability data, accelerated life testing, and maintainability modeling and analysis. In this work, we start by obtaining the probabilistic characteristics of this model, as the explicit expression of the process, its trends, and its distribution by transforming the diffusion process in a Wiener process as shown in the Ricciaardi theorem. Then, we develop the statistical inference of this model using the maximum likelihood methodology. Finally, we analyse with simulated data the computational problems associated with the parameters, an issue of great importance in its application to real data with the use of the convergence analysis methods. Overall, the use of a stochastic model reflects only a pragmatic decision on the part of the modeler. According to the data that is available and the universe of models known to the modeler, this model represents the best currently available description of the phenomenon under consideration.

Keywords: diffusion process, discrete sampling, likelihood estimation method, simulation, stochastic diffusion process, trends functions, bi-parameters weibull density function

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Authors: Bouchemha Amel, Chachoui Takieddine, H. Maalem

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Automatic detection of targets in a modern communication system RADAR is based primarily on the concept of adaptive CFAR detector. To have an effective detection, we must minimize the influence of disturbances due to the clutter. The detection algorithm adapts the CFAR detection threshold which is proportional to the average power of the clutter, maintaining a constant probability of false alarm. In this article, we analyze the performance of two variants of adaptive algorithms CA-CFAR and OS-CFAR and we compare the thresholds of these detectors in the marine environment (no-Gaussian) with a Weibull distribution.

Keywords: CFAR, threshold, clutter, distribution, Weibull, detection

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Authors: Nahashon Mwirigi

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The management of HIV/AIDS is a global challenge, demanding precise tools to predict disease progression and guide tailored treatment. CD4 cell count dynamics, a crucial immune function indicator, play an essential role in understanding HIV/AIDS progression and enhancing patient care through effective modeling. While several models assess disease progression, existing methods often fall short in capturing the complex, non-linear nature of HIV/AIDS, especially across diverse demographics. A need exists for models that balance predictive accuracy with clinical applicability, enabling individualized care strategies based on patient-specific progression rates. This study utilizes patient data from Kenyatta National Hospital (2003–2014) to model HIV/AIDS progression across six CD4-defined states. The Exponential, 2-Parameter Weibull, and 3-Parameter Weibull models are employed to analyze failure rates and explore progression patterns by age and gender. Model selection is based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to identify models best representing disease progression variability across demographic groups. The 3-Parameter Weibull model emerges as the most effective, accurately capturing HIV/AIDS progression dynamics, particularly by incorporating delayed progression effects. This model reflects age and gender-specific variations, offering refined insights into patient trajectories and facilitating targeted interventions. One key finding is that older patients progress more slowly through CD4-defined stages, with a delayed onset of advanced stages. This suggests that older patients may benefit from extended monitoring intervals, allowing providers to optimize resources while maintaining consistent care. Recognizing slower progression in this demographic helps clinicians reduce unnecessary interventions, prioritizing care for faster-progressing groups. Gender-based analysis reveals that female patients exhibit more consistent progression, while male patients show greater variability. This highlights the need for gender-specific treatment approaches, as men may require more frequent assessments and adaptive treatment plans to address their variable progression. Tailoring treatment by gender can improve outcomes by addressing distinct risk patterns in each group. The model’s ability to account for both accelerated and delayed progression equips clinicians with a robust tool for estimating the duration of each disease stage. This supports individualized treatment planning, allowing clinicians to optimize antiretroviral therapy (ART) regimens based on demographic factors and expected disease trajectories. Aligning ART timing with specific progression patterns can enhance treatment efficacy and adherence. The model also has significant implications for healthcare systems, as its predictive accuracy enables proactive patient management, reducing the frequency of advanced-stage complications. For resource limited providers, this capability facilitates strategic intervention timing, ensuring that high-risk patients receive timely care while resources are allocated efficiently. Anticipating progression stages enhances both patient care and resource management, reinforcing the model’s value in supporting sustainable HIV/AIDS healthcare strategies. This study underscores the importance of models that capture the complexities of HIV/AIDS progression, offering insights to guide personalized, data-informed care. The 3-Parameter Weibull model’s ability to accurately reflect delayed progression and demographic risk variations presents a valuable tool for clinicians, supporting the development of targeted interventions and resource optimization in HIV/AIDS management.

Keywords: HIV/AIDS progression, 3-parameter Weibull model, CD4 cell count stages, antiretroviral therapy, demographic-specific modeling

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Authors: Jinyoung Choi, Sunmook Lee

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In general, single parameter, i.e. temperature, as an accelerating parameter is used to assess the accelerated stability of Point-of-Care Testing (POCT) diagnostic devices. However, humidity also plays an important role in deteriorating the strip performance since major components of test strips are proteins such as enzymes. 4 different Temp./Humi. Conditions were used to assess the lifetime of strips. Degradation of test strips were studied through the accelerated stability test and the lifetime was assessed using commercial POCT products. The life distribution of strips, which were obtained by monitoring the failure time of test strip under each stress condition, revealed that the weibull distribution was the most proper distribution describing the life distribution of strips used in the present study. Equal shape parameters were calculated to be 0.9395 and 0.9132 for low and high concentrations, respectively. The lifetime prediction was made by adopting Peck Eq. Model for Stress-Life relationship, and the B10 life was calculated to be 70.09 and 46.65 hrs for low and high concentrations, respectively.

Keywords: accelerated degradation, diagnostic device, lifetime assessment, POCT

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Authors: Chang He, Hiroshi Tamura, Hiroshi Katsuchi, Jiaqi Wang

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In this study, the aim is to infer the slip limit (static friction limit) of contact interfaces in bolt friction joints by analyzing other bolt friction joints with the same contact surface but in a different shape. By using the Weibull distribution to deal with microelements on the contact surface statistically, the slip limit of a certain type of bolt joint was predicted from other types of bolt joint with the same contact surface. As a result, this research succeeded in predicting the slip limit of bolt joins with different numbers of contact surfaces and with different numbers of bolt rows.

Keywords: bolt joints, slip coefficient, finite element method, Weibull distribution

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Authors: M. Dahbi, M. Sellam, A. Benatiallah, A. Harrouz

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The wind energy is one of the most significant and rapidly developing renewable energy sources in the world and it provides a clean energy resource, which is a promising alternative in the short term in Algeria The main purpose of this paper is to compared and discuss the wind power potential in three sites located in sahara of Algeria (south west of Algeria) and to perform an investigation on the wind power potential of desert of Algeria. In this comparative, wind speed frequency distributions data obtained from the web site SODA.com are used to calculate the average wind speed and the available wind power. The Weibull density function has been used to estimate the monthly power wind density and to determine the characteristics of monthly parameters of Weibull for these three sites. The annual energy produced by the BWC XL.1 1KW wind machine is obtained and compared. The analysis shows that in the south west of Algeria, at 10 m height, the available wind power was found to vary between 136.59 W/m2 and 231.04 W/m2. The highest potential wind power was found at Adrar, with 21h per day and the mean wind speed is above 6 m/s. Besides, it is found that the annual wind energy generated by that machine lie between 512 KWh and 1643.2 kWh. However, the wind resource appears to be suitable for power production on the sahara and it could provide a viable substitute to diesel oil for irrigation pumps and rural electricity generation.

Keywords: Weibull distribution, parameters of Wiebull, wind energy, wind turbine, operating hours

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Authors: Saleem Z. Ramadan

Abstract:

This paper discusses the effects of using progressive Type-I right censoring on the design of the Simple Step Accelerated Life testing using Bayesian approach for Weibull life products under the assumption of cumulative exposure model. The optimization criterion used in this paper is to minimize the expected pre-posterior variance of the PTH percentile time of failures. The model variables are the stress changing time and the stress value for the first step. A comparison between the conventional and the progressive Type-I right censoring is provided. The results have shown that the progressive Type-I right censoring reduces the cost of testing on the expense of the test precision when the sample size is small. Moreover, the results have shown that using strong priors or large sample size reduces the sensitivity of the test precision to the censoring proportion. Hence, the progressive Type-I right censoring is recommended in these cases as progressive Type-I right censoring reduces the cost of the test and doesn't affect the precision of the test a lot. Moreover, the results have shown that using direct or indirect priors affects the precision of the test.

Keywords: reliability, accelerated life testing, cumulative exposure model, Bayesian estimation, progressive type-I censoring, Weibull distribution

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Authors: M. Akhlaque Ahmed, Maliha Afshan Siddiqui

Abstract:

A study has been carried out to see the prospect of wind power potential of southern Sindh namely Karachi, Hawksbay, Norriabad, Hyderabad, Ketibander and Shahbander using local wind speed data. The monthly average wind speed for these area ranges from 4.5m/sec to 8.5m/sec at 30m height from ground. Extractable wind power, wind energy and Weibul parameter for above mentioned areas have been examined. Furthermore, the power output using fast and slow wind machine using different blade diameter along with the 4Kw and 20 Kw aero-generator were examined to see the possible use for deep well pumping and electricity supply to remote villages. The analysis reveals that in this wind corridor of southern Sindh Hawksbay, Ketibander and Shahbander belongs to wind power class-3 Hyderabad and Nooriabad belongs to wind power class-5 and Karachi belongs to wind power class-2. The result shows that the that higher wind speed values occur between June till August. It was found that considering maximum wind speed location, Hawksbay,Noriabad are the best location for setting up wind machines for power generation.

Keywords: wind energy generation, Southern Sindh, seasonal change, Weibull parameter, wind machines

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Authors: Yoonsuh Jung

Abstract:

As DNA microarray data contain relatively small sample size compared to the number of genes, high dimensional models are often employed. In high dimensional models, the selection of tuning parameter (or, penalty parameter) is often one of the crucial parts of the modeling. Cross-validation is one of the most common methods for the tuning parameter selection, which selects a parameter value with the smallest cross-validated score. However, selecting a single value as an "optimal" value for the parameter can be very unstable due to the sampling variation since the sample sizes of microarray data are often small. Our approach is to choose multiple candidates of tuning parameter first, then average the candidates with different weights depending on their performance. The additional step of estimating the weights and averaging the candidates rarely increase the computational cost, while it can considerably improve the traditional cross-validation. We show that the selected value from the suggested methods often lead to stable parameter selection as well as improved detection of significant genetic variables compared to the tradition cross-validation via real data and simulated data sets.

Keywords: cross validation, parameter averaging, parameter selection, regularization parameter search

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Authors: Madaki Umar Yusuf, Mohd Rizam B. Abubakar

Abstract:

The survival censored data with incomplete covariate data is a common occurrence in many studies in which the outcome is survival time. With model when the missing covariates are categorical, a useful technique for obtaining parameter estimates is the EM by the method of weights. The survival outcome for the class of generalized linear model is applied and this method requires the estimation of the parameters of the distribution of the covariates. In this paper, we propose some clinical trials with ve covariates, four of which have some missing values which clearly show that they were fully censored data.

Keywords: EM algorithm, incomplete categorical covariates, ignorable missing data, missing at random (MAR), Weibull Distribution

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Authors: Swajeeth Panchangam, Arun Rajendran, Swarnim Gupta, Ahmed Zeouita

Abstract:

Semiconductor processing chambers tend to operate in controlled but aggressive operating conditions (chemistry, plasma, high temperature etc.) Owing to this, the design of this equipment requires developing robust and reliable hardware and software. Any equipment downtime due to reliability issues can have cost implications both for customers in terms of tool downtime (reduced throughput) and for equipment manufacturers in terms of high warranty costs and customer trust deficit. A thorough reliability assessment of critical parts and a plan for preventive maintenance/replacement schedules need to be done before tool shipment. This helps to save significant warranty costs and tool downtimes in the field. However, designing a proper reliability test plan to accurately demonstrate reliability targets with proper sample size and test duration is quite challenging. This is mainly because components can fail in different failure modes that fit into different Weibull beta value distributions. Without apriori Weibull beta of a failure mode under consideration, it always leads to over/under utilization of resources, which eventually end up in false positives or false negatives estimates. This paper proposes a methodology to design a reliability test plan with optimal model size/duration/both (independent of apriori Weibull beta). This methodology can be used in demonstration tests and can be extended to accelerated life tests to further decrease sample size/test duration.

Keywords: reliability, stochastics, preventive maintenance

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