This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha p...This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha power transformed Weibull distribution.The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions,which are quite familiar in environmental investigations.Its hazard rate function can be decreasing,increasing,bathtub and upside-down then bathtub shaped.Diverse structural properties of the proposed model are acquired including quantile function,moments,entropies,order statistics,residual life and reversed failure rate function.The parameters of the distribution were estimated using the maximum likelihood function.The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed.Via a simulation study,the performance of the point and interval estimates are compared using different criteria.Employing real lifetime data sets,we verify that the offered model furnishes a better fit than some other lifetime models including Weibull,gamma and alpha powerWeibull models.展开更多
The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of...The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.展开更多
In this paper, we introduce a class of Lindley and Weibull distributions (LW) that are useful for modeling lifetime data with a comprehensive mathematical treatment. The new class of generated distributions includes s...In this paper, we introduce a class of Lindley and Weibull distributions (LW) that are useful for modeling lifetime data with a comprehensive mathematical treatment. The new class of generated distributions includes some well-known distributions, such as exponential, gamma, Weibull, Lindley, inverse gamma, inverse Weibull, inverse Lindley, and others. We provide closed-form expressions for the density, cumulative distribution, survival function, hazard rate function, moments, moments generating function, quantile, and stochastic orderings. Moreover, we discuss maximum likelihood estimation and the algorithm for computing the parameters estimates. Some sub models are discussed as an illustration with real data sets to show the flexibility of this class.展开更多
In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confiden...In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution</span><span style="font-family:""> </span><span style="font-family:Verdana;">under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.展开更多
In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are ...In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of </span><span style="font-family:Verdana;">maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.展开更多
Given the steady increase in use of alternative energy sources to supply part of the energy demand of the world, and considering that Mexico has enough wind resources to produce all the electricity required by the cou...Given the steady increase in use of alternative energy sources to supply part of the energy demand of the world, and considering that Mexico has enough wind resources to produce all the electricity required by the country, in this work, it is carried out the development of a system of wind resource assessment to determine the volume of water that a windmill pumping system can provide in a specific area. To this end, it has developed a computer program for wind resource assessment by measurements of wind speed, direction, temperature, barometric pressure and relative humidity. Measuring equipments were mounted in a wind measurement tower of 10 m high, within the premises of the University of Quintana Roo which is located along the coast. Until this day, there are records over a period of five months of the variables of wind speed, wind direction, temperature, relative humidity and atmospheric pressure. These variables were used for statistical calculations using the Weibull distributions. To give a better use of the calculated data, they were applied to the evaluation of a Pumping System.展开更多
In this paper, the location parameter δ_(a) in Weibull distribution i.e. the lower limiting CTOD toughness of high strength steel weldments is evaluated from Gleeble simulated coarse grained specimens. The Charpy-V t...In this paper, the location parameter δ_(a) in Weibull distribution i.e. the lower limiting CTOD toughness of high strength steel weldments is evaluated from Gleeble simulated coarse grained specimens. The Charpy-V transition temperature obtained from these specimens is transformed to a fracture toughness K_(IC) value at a given temperature using Sanz' relation. Then, the location parameter a is δ_(a) evaluated. The predicted location parameter arrives at agreement with the lowest CTOD value as obtained from thick multilayer weldments. The improvement of the fracture toughness of multilayer weldments needs the increase of the lowering limiting CTOD.toughness i.e. the toughness of the coarse grained zone.展开更多
The lifetime data of products with multiple failure modes which are collected from life testing are often fitted by the mixed Weibull distributions. Since the mixed Weibull distributions contain no less than five para...The lifetime data of products with multiple failure modes which are collected from life testing are often fitted by the mixed Weibull distributions. Since the mixed Weibull distributions contain no less than five parameters,the parameter estimation is difficult and inaccurate. In order to enhance the accuracy,a new method of parameter estimation based on Cuckoo search( CS) is proposed. An optimization model for the mixed Weibull distribution is formulated by minimizing the residual sum of squares. The optimal parameters are searched via CS algorithm. In the case study,the lifetime data come from the life testing of diesel injectors and are fitted by the twocomponent Weibull mixture. Regarding the maximum absolute error and the accumulative absolute error between estimated and observed values as the accuracy index of parameter estimation,the results of four parameter estimation methods that the graphic estimation method,the nonlinear least square method,the optimization method based on particle swarm optimization( PSO) and the proposed method are compared. The result shows that the proposed method is more efficient and more accurate than the other three methods.展开更多
Product testing is a key ingredient in maintaining the quality of a pro-duction process.The production process is considered an efficient process if it is capable of quick identification of faulty products.The items p...Product testing is a key ingredient in maintaining the quality of a pro-duction process.The production process is considered an efficient process if it is capable of quick identification of faulty products.The items produced by any production process are usually packed and acceptance or rejection of the pack depends upon its conformity to some specified quality level.Generally,the specified quality level is based upon the number of defective items found in the inspected number of items.Such decisions are based upon some rules and usually acceptance of the pack is based upon a fewer number of defective items in the pack.Such questions can be answered by using acceptance sampling plans.The acceptance sampling plans assume the fact that the quality level of the item follows some probability distribution.The sampling plans based upon some classical probability distributions are available but often it happens that the quality behavior of the product does not follow a simple probability model and hence the available sampling plans fail.In this paper,we have developed acceptance sampling plans when the product life follows a general Weibull distribution.The sampling plans have been constructed by considering the crisp and fuzzy behavior of the acceptance probability.These sampling plans have been constructed by assuming an infinite lot size.It has been found that the number of items required for inspection decreases with an increase in some parameters.展开更多
Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,f...Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.展开更多
Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Se...Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Several situations arise where joint modeling of two random phenomenon is required.In such cases the bivariate distributions are needed.Development of the bivariate distributions necessitates certain conditions,in a field where few work has been performed.This paper deals with a bivariate beta-inverse Weibull distribution.The marginal and conditional distributions from the proposed distribution have been obtained.Expansions for the joint and conditional density functions for the proposed distribution have been obtained.The properties,including product,marginal and conditional moments,joint moment generating function and joint hazard rate function of the proposed bivariate distribution have been studied.Numerical study for the dependence function has been implemented to see the effect of various parameters on the dependence of variables.Estimation of the parameters of the proposed bivariate distribution has been done by using the maximum likelihood method of estimation.Simulation and real data application of the distribution are presented.展开更多
Previous studies have shown that the fatigue life distribution of metal materials fabricated with Additive Manufacturing(AM) methods, such as Direct Energy Deposited(DED) Ti-6.5Al-2Zr-1Mo-1V alloys, exhibits two peaks...Previous studies have shown that the fatigue life distribution of metal materials fabricated with Additive Manufacturing(AM) methods, such as Direct Energy Deposited(DED) Ti-6.5Al-2Zr-1Mo-1V alloys, exhibits two peaks. To promote the application of AM in aerospace and other engineering fields, developing a fatigue strength evaluation method suitable for AM materials based on their unique fatigue behaviours and fatigue life distributions is necessary. In this paper, a novel Detail Fatigue Rating(DFR) method was developed to evaluate the fatigue strength of DED Ti-6.5Al-2Zr-1Mo-1V based on a bimodal Weibull distribution and the excessive restriction on the allowable stress of potential was improved. Meanwhile, a Bimodal Weibull distribution model for fatigue life and its parameter estimation method were established based on a twoparameter Weibull distribution. The fatigue life at a specific reliability level and confidence level was calculated by using the bootstrap method. The calculation results showed that fatigue life estimated by using the bimodal Weibull distribution at the high reliability level and high confidence level is higher than that estimated by using the two-parameter Weibull distribution. Furthermore,The S-N curve at the specified confidence level and reliability level was fitted.展开更多
The loss on drying method,which is regarded as the standard method of rice moisture content analysis,provides the most reliable results but is both labor intensive and time consuming.In order to improve the detection ...The loss on drying method,which is regarded as the standard method of rice moisture content analysis,provides the most reliable results but is both labor intensive and time consuming.In order to improve the detection efficiency of the loss on drying method,this study investigated the drying characteristics of milled rice and developed an information fusion algorithm with which to predict milled rice moisture content based on the Weibull distribution and Levenberg-Marquardt(LM)algorithm.Application of the Weibull distribution model was investigated regarding its description of the drying kinetics of milled rice during infrared drying.An adaptive mechanism was applied to algorithm design,with the starting point of the estimation algorithm determined by calculating the drying rate at each measuring point,and the end-point distinguished using a two-level threshold algorithm.The calculated results were then compared with the measured data regarding the infrared drying of milled rice.For milled rice samples varying in moisture content from 14.44%-17.67%(dry basis),the relative error between predicted and observed values ranged 0.0037-0.0589,with a reduction in test time of 50.71%-67.87%.展开更多
In this work,we consider the problem of estimating the parameters and predicting the unobserved or removed ordered data for the progressive type II censored flexible Weibull sample.Frequentist and Bayesian analyses ar...In this work,we consider the problem of estimating the parameters and predicting the unobserved or removed ordered data for the progressive type II censored flexible Weibull sample.Frequentist and Bayesian analyses are adopted for conducting the estimation and prediction problems.The likelihood method as well as the Bayesian sampling techniques is applied for the inference problems.The point predictors and credible intervals of unobserved data based on an informative set of data are computed.Markov ChainMonte Carlo samples are performed to compare the so-obtained methods,and one real data set is analyzed for illustrative purposes.展开更多
In this paper,a new 4-parameter exponentiated generalized inverse flexible Weibull distribution is proposed.Some of its statistical properties are studied.The aim of this paper is to estimate the model parameters via ...In this paper,a new 4-parameter exponentiated generalized inverse flexible Weibull distribution is proposed.Some of its statistical properties are studied.The aim of this paper is to estimate the model parameters via several approaches,namely,maximum likelihood,maximum product spacing and Bayesian.According to Bayesian approach,several techniques are used to get the Bayesian estimators,namely,standard error function,Linex loss function and entropy loss function.The estimation herein is based on complete and censored samples.Markov Chain Monte Carlo simulation is used to discuss the behavior of the estimators for each approach.Finally,two real data sets are analyzed to obtain the flexibility of the proposed model.展开更多
In random network models, sizes for pores and throats are distributed according to a truncated Weibull distribution. As a result, parameters defining the shape of the distribution are critical for the characteristic o...In random network models, sizes for pores and throats are distributed according to a truncated Weibull distribution. As a result, parameters defining the shape of the distribution are critical for the characteristic of the network. In this paper, an algorithm to distribute pores and throats in random network was established to more representatively describe the topology of porous media. First, relations between Weibull parameters and the distribution of dimensionless throat sizes were studied and a series of standard curves were obtained. Then, by analyzing the capillary pressure curve of the core sample, frequency distribution histogram of throat sizes was obtained. All the sizes were transformed to dimensionless numbers ranged from 0 to 1. Curves of the core were compared to the standard curves, and truncated Weibull parameters could be determined according an inverse algorithm. Finally, aspect ratio and average length of throats were adjusted to simultaneously fit the porosity and the capillary pressure curves and the whole network was established. The predicted relative permeability curves were in good agreement with the experimental data of cores, indicating the validity of the algorithm.展开更多
In this paper,we introduce a new four-parameter version of the traditional Weibull distribution.It is able to provide seven shapes of hazard rate,including constant,decreasing,increasing,unimodal,bathtub,unimodal then...In this paper,we introduce a new four-parameter version of the traditional Weibull distribution.It is able to provide seven shapes of hazard rate,including constant,decreasing,increasing,unimodal,bathtub,unimodal then bathtub,and bathtub then unimodal shapes.Some basic characteristics of the proposedmodel are studied,including moments,entropies,mean deviations and order statistics,and its parameters are estimated using the maximum likelihood approach.Based on the asymptotic properties of the estimators,the approximate confidence intervals are also taken into consideration in addition to the point estimators.We examine the effectiveness of the maximum likelihood estimators of the model’s parameters through simulation research.Based on the simulation findings,it can be concluded that the provided estimators are consistent and that asymptotic normality is a good method to get the interval estimates.Three actual data sets for COVID-19,engineering and blood cancer are used to empirically demonstrate the new distribution’s usefulness inmodeling real-world data.The analysis demonstrates the proposed distribution’s ability in modeling many forms of data as opposed to some of its well-known sub-models,such as alpha powerWeibull distribution.展开更多
In this article, we study a model of a single variable sampling plan with Type I censoring.Assume that the quality of an item in a batch is measured by a random variable which follows aWeibull distribution W(λ,m), wi...In this article, we study a model of a single variable sampling plan with Type I censoring.Assume that the quality of an item in a batch is measured by a random variable which follows aWeibull distribution W(λ,m), with scale parameter A and shape parameter m having a gammadiscrete prior distribution or θ=1/λ and m having an inverse gamma-uniform prior distribution.The decision function is based on the Kaplan-Meter estimator. Then, the explicit expressions ofthe Bayes risk are derived. In addition, an algorithm is suggested so that an optimal samplingplan can be determined approximately after a finite number of searching steps.展开更多
This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of t...This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.展开更多
As part of the national strategy to further develop the wind energy sector,the eight prefectures of Upper Guinea have been selected.Using meteorological data recorded over thirty years(1991-2021)at a height of 20 m,we...As part of the national strategy to further develop the wind energy sector,the eight prefectures of Upper Guinea have been selected.Using meteorological data recorded over thirty years(1991-2021)at a height of 20 m,we assessed wind resources in terms of characteristic speeds,power and available energy.To this end,the Weibull distribution method was used and the following values were obtained:3.66 m/s for the average speed;1,102.83 W/m^(2)for the available power and 8,747.06 kWh/m^(2)/year for the annual available energy.展开更多
基金funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project No.(PNURSP2022R50),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha power transformed Weibull distribution.The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions,which are quite familiar in environmental investigations.Its hazard rate function can be decreasing,increasing,bathtub and upside-down then bathtub shaped.Diverse structural properties of the proposed model are acquired including quantile function,moments,entropies,order statistics,residual life and reversed failure rate function.The parameters of the distribution were estimated using the maximum likelihood function.The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed.Via a simulation study,the performance of the point and interval estimates are compared using different criteria.Employing real lifetime data sets,we verify that the offered model furnishes a better fit than some other lifetime models including Weibull,gamma and alpha powerWeibull models.
基金funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project No. (PNURSP2022R50),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.
文摘In this paper, we introduce a class of Lindley and Weibull distributions (LW) that are useful for modeling lifetime data with a comprehensive mathematical treatment. The new class of generated distributions includes some well-known distributions, such as exponential, gamma, Weibull, Lindley, inverse gamma, inverse Weibull, inverse Lindley, and others. We provide closed-form expressions for the density, cumulative distribution, survival function, hazard rate function, moments, moments generating function, quantile, and stochastic orderings. Moreover, we discuss maximum likelihood estimation and the algorithm for computing the parameters estimates. Some sub models are discussed as an illustration with real data sets to show the flexibility of this class.
文摘In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution</span><span style="font-family:""> </span><span style="font-family:Verdana;">under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.
文摘In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of </span><span style="font-family:Verdana;">maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.
文摘Given the steady increase in use of alternative energy sources to supply part of the energy demand of the world, and considering that Mexico has enough wind resources to produce all the electricity required by the country, in this work, it is carried out the development of a system of wind resource assessment to determine the volume of water that a windmill pumping system can provide in a specific area. To this end, it has developed a computer program for wind resource assessment by measurements of wind speed, direction, temperature, barometric pressure and relative humidity. Measuring equipments were mounted in a wind measurement tower of 10 m high, within the premises of the University of Quintana Roo which is located along the coast. Until this day, there are records over a period of five months of the variables of wind speed, wind direction, temperature, relative humidity and atmospheric pressure. These variables were used for statistical calculations using the Weibull distributions. To give a better use of the calculated data, they were applied to the evaluation of a Pumping System.
文摘In this paper, the location parameter δ_(a) in Weibull distribution i.e. the lower limiting CTOD toughness of high strength steel weldments is evaluated from Gleeble simulated coarse grained specimens. The Charpy-V transition temperature obtained from these specimens is transformed to a fracture toughness K_(IC) value at a given temperature using Sanz' relation. Then, the location parameter a is δ_(a) evaluated. The predicted location parameter arrives at agreement with the lowest CTOD value as obtained from thick multilayer weldments. The improvement of the fracture toughness of multilayer weldments needs the increase of the lowering limiting CTOD.toughness i.e. the toughness of the coarse grained zone.
文摘The lifetime data of products with multiple failure modes which are collected from life testing are often fitted by the mixed Weibull distributions. Since the mixed Weibull distributions contain no less than five parameters,the parameter estimation is difficult and inaccurate. In order to enhance the accuracy,a new method of parameter estimation based on Cuckoo search( CS) is proposed. An optimization model for the mixed Weibull distribution is formulated by minimizing the residual sum of squares. The optimal parameters are searched via CS algorithm. In the case study,the lifetime data come from the life testing of diesel injectors and are fitted by the twocomponent Weibull mixture. Regarding the maximum absolute error and the accumulative absolute error between estimated and observed values as the accuracy index of parameter estimation,the results of four parameter estimation methods that the graphic estimation method,the nonlinear least square method,the optimization method based on particle swarm optimization( PSO) and the proposed method are compared. The result shows that the proposed method is more efficient and more accurate than the other three methods.
文摘Product testing is a key ingredient in maintaining the quality of a pro-duction process.The production process is considered an efficient process if it is capable of quick identification of faulty products.The items produced by any production process are usually packed and acceptance or rejection of the pack depends upon its conformity to some specified quality level.Generally,the specified quality level is based upon the number of defective items found in the inspected number of items.Such decisions are based upon some rules and usually acceptance of the pack is based upon a fewer number of defective items in the pack.Such questions can be answered by using acceptance sampling plans.The acceptance sampling plans assume the fact that the quality level of the item follows some probability distribution.The sampling plans based upon some classical probability distributions are available but often it happens that the quality behavior of the product does not follow a simple probability model and hence the available sampling plans fail.In this paper,we have developed acceptance sampling plans when the product life follows a general Weibull distribution.The sampling plans have been constructed by considering the crisp and fuzzy behavior of the acceptance probability.These sampling plans have been constructed by assuming an infinite lot size.It has been found that the number of items required for inspection decreases with an increase in some parameters.
基金The work was funded by the University of Jeddah,Saudi Arabia under Grant Number UJ–02–093–DR.The authors,therefore,acknowledge with thanks the University for technical and financial support.
文摘Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.
基金funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah under grant number(D-153-130-1441).The author,therefore,gratefully acknowledge the DSR technical and financial support.
文摘Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Several situations arise where joint modeling of two random phenomenon is required.In such cases the bivariate distributions are needed.Development of the bivariate distributions necessitates certain conditions,in a field where few work has been performed.This paper deals with a bivariate beta-inverse Weibull distribution.The marginal and conditional distributions from the proposed distribution have been obtained.Expansions for the joint and conditional density functions for the proposed distribution have been obtained.The properties,including product,marginal and conditional moments,joint moment generating function and joint hazard rate function of the proposed bivariate distribution have been studied.Numerical study for the dependence function has been implemented to see the effect of various parameters on the dependence of variables.Estimation of the parameters of the proposed bivariate distribution has been done by using the maximum likelihood method of estimation.Simulation and real data application of the distribution are presented.
基金the support from the National Key Research and Development Program of China(No.2017YFB1104003)National Natural Science Foundation of China(No.11772027)Aeronautical Science Foundation of China(No.201909051002)。
文摘Previous studies have shown that the fatigue life distribution of metal materials fabricated with Additive Manufacturing(AM) methods, such as Direct Energy Deposited(DED) Ti-6.5Al-2Zr-1Mo-1V alloys, exhibits two peaks. To promote the application of AM in aerospace and other engineering fields, developing a fatigue strength evaluation method suitable for AM materials based on their unique fatigue behaviours and fatigue life distributions is necessary. In this paper, a novel Detail Fatigue Rating(DFR) method was developed to evaluate the fatigue strength of DED Ti-6.5Al-2Zr-1Mo-1V based on a bimodal Weibull distribution and the excessive restriction on the allowable stress of potential was improved. Meanwhile, a Bimodal Weibull distribution model for fatigue life and its parameter estimation method were established based on a twoparameter Weibull distribution. The fatigue life at a specific reliability level and confidence level was calculated by using the bootstrap method. The calculation results showed that fatigue life estimated by using the bimodal Weibull distribution at the high reliability level and high confidence level is higher than that estimated by using the two-parameter Weibull distribution. Furthermore,The S-N curve at the specified confidence level and reliability level was fitted.
基金This study supported by a grant from the National Natural Science Foundation of China(No.61663039)Natural Science Foundation of Ningxia Hui Autonomous Region(No.NZ1648)the Natural Science Funds of Ningxia University(ZR15010).
文摘The loss on drying method,which is regarded as the standard method of rice moisture content analysis,provides the most reliable results but is both labor intensive and time consuming.In order to improve the detection efficiency of the loss on drying method,this study investigated the drying characteristics of milled rice and developed an information fusion algorithm with which to predict milled rice moisture content based on the Weibull distribution and Levenberg-Marquardt(LM)algorithm.Application of the Weibull distribution model was investigated regarding its description of the drying kinetics of milled rice during infrared drying.An adaptive mechanism was applied to algorithm design,with the starting point of the estimation algorithm determined by calculating the drying rate at each measuring point,and the end-point distinguished using a two-level threshold algorithm.The calculated results were then compared with the measured data regarding the infrared drying of milled rice.For milled rice samples varying in moisture content from 14.44%-17.67%(dry basis),the relative error between predicted and observed values ranged 0.0037-0.0589,with a reduction in test time of 50.71%-67.87%.
文摘In this work,we consider the problem of estimating the parameters and predicting the unobserved or removed ordered data for the progressive type II censored flexible Weibull sample.Frequentist and Bayesian analyses are adopted for conducting the estimation and prediction problems.The likelihood method as well as the Bayesian sampling techniques is applied for the inference problems.The point predictors and credible intervals of unobserved data based on an informative set of data are computed.Markov ChainMonte Carlo samples are performed to compare the so-obtained methods,and one real data set is analyzed for illustrative purposes.
文摘In this paper,a new 4-parameter exponentiated generalized inverse flexible Weibull distribution is proposed.Some of its statistical properties are studied.The aim of this paper is to estimate the model parameters via several approaches,namely,maximum likelihood,maximum product spacing and Bayesian.According to Bayesian approach,several techniques are used to get the Bayesian estimators,namely,standard error function,Linex loss function and entropy loss function.The estimation herein is based on complete and censored samples.Markov Chain Monte Carlo simulation is used to discuss the behavior of the estimators for each approach.Finally,two real data sets are analyzed to obtain the flexibility of the proposed model.
文摘In random network models, sizes for pores and throats are distributed according to a truncated Weibull distribution. As a result, parameters defining the shape of the distribution are critical for the characteristic of the network. In this paper, an algorithm to distribute pores and throats in random network was established to more representatively describe the topology of porous media. First, relations between Weibull parameters and the distribution of dimensionless throat sizes were studied and a series of standard curves were obtained. Then, by analyzing the capillary pressure curve of the core sample, frequency distribution histogram of throat sizes was obtained. All the sizes were transformed to dimensionless numbers ranged from 0 to 1. Curves of the core were compared to the standard curves, and truncated Weibull parameters could be determined according an inverse algorithm. Finally, aspect ratio and average length of throats were adjusted to simultaneously fit the porosity and the capillary pressure curves and the whole network was established. The predicted relative permeability curves were in good agreement with the experimental data of cores, indicating the validity of the algorithm.
基金The Deanship of Scientific Research(DSR)at King Abdulaziz University,Jeddah,Saudi Arabia has funded this project under Grant No.(G-102-130-1443).
文摘In this paper,we introduce a new four-parameter version of the traditional Weibull distribution.It is able to provide seven shapes of hazard rate,including constant,decreasing,increasing,unimodal,bathtub,unimodal then bathtub,and bathtub then unimodal shapes.Some basic characteristics of the proposedmodel are studied,including moments,entropies,mean deviations and order statistics,and its parameters are estimated using the maximum likelihood approach.Based on the asymptotic properties of the estimators,the approximate confidence intervals are also taken into consideration in addition to the point estimators.We examine the effectiveness of the maximum likelihood estimators of the model’s parameters through simulation research.Based on the simulation findings,it can be concluded that the provided estimators are consistent and that asymptotic normality is a good method to get the interval estimates.Three actual data sets for COVID-19,engineering and blood cancer are used to empirically demonstrate the new distribution’s usefulness inmodeling real-world data.The analysis demonstrates the proposed distribution’s ability in modeling many forms of data as opposed to some of its well-known sub-models,such as alpha powerWeibull distribution.
文摘In this article, we study a model of a single variable sampling plan with Type I censoring.Assume that the quality of an item in a batch is measured by a random variable which follows aWeibull distribution W(λ,m), with scale parameter A and shape parameter m having a gammadiscrete prior distribution or θ=1/λ and m having an inverse gamma-uniform prior distribution.The decision function is based on the Kaplan-Meter estimator. Then, the explicit expressions ofthe Bayes risk are derived. In addition, an algorithm is suggested so that an optimal samplingplan can be determined approximately after a finite number of searching steps.
基金the Science,Research and Innovation Promotion Funding(TSRI)(Grant No.FRB660012/0168)managed under Rajamangala University of Technology Thanyaburi(FRB66E0646O.4).
文摘This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.
文摘As part of the national strategy to further develop the wind energy sector,the eight prefectures of Upper Guinea have been selected.Using meteorological data recorded over thirty years(1991-2021)at a height of 20 m,we assessed wind resources in terms of characteristic speeds,power and available energy.To this end,the Weibull distribution method was used and the following values were obtained:3.66 m/s for the average speed;1,102.83 W/m^(2)for the available power and 8,747.06 kWh/m^(2)/year for the annual available energy.