Refine Search

New Search

Results: 62

(searched for: Compound Weibull Lifetime Distribution-I)
Save to Scifeed
Page of 2
Articles per Page
by
Show export options
  Select all
Gadicharla Sirisha
European Journal of Mathematics and Statistics, Volume 3, pp 51-54; https://doi.org/10.24018/ejmath.2022.3.5.117

Abstract:
In this paper a new lifetime distribution named as ‘Compound Weibull Lifetime Distribution-I’ is derived. The basic assumptions, derivation of the model and some useful characteristics, like mean, variance, distribution function, reliability function, hazard function and cumulative hazard function of the distribution are derived.
Antoni Drapella
Quality and Reliability Engineering International, Volume 9, pp 385-386; https://doi.org/10.1002/qre.4680090427

The publisher has not yet granted permission to display this abstract.
Amos E. Gera
Quality and Reliability Engineering International, Volume 10, pp 355-358; https://doi.org/10.1002/qre.4680100417

The publisher has not yet granted permission to display this abstract.
Saeid Tahmasebi, Ali Akbar Jafari
Published: 30 March 2015
Abstract:
In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power series, generalized exponential-power series, generalized linear failure rate-power series, exponentiated Weibull-power series, generalized modified Weibull-power series, generalized Gompertz-power series and exponentiated extended Weibull distributions as special cases. We obtain several properties of this new class of distributions such as Shannon entropy, mean residual life, hazard rate function, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented.
, Armin Pourkhanali, Saralees Nadarajah
Communications in Statistics - Theory and Methods, Volume 47, pp 4006-4020; https://doi.org/10.1080/03610926.2017.1367811

Abstract:
A new class of lifetime distributions, which can exhibit with upside-down bathtub-shaped, bathtub-shaped, decreasing, and increasing failure rates, is introduced. The new distribution is constructed by compounding generalized Weibull and logarithmic distributions, leading to improvement on the lifetime distribution considered in Dimitrakopoulou et al. ( 2007 Dimitrakopoulou, T. , K. Adamidis, and S. Loukas. 2007. A lifetime distribution with an upside-down bathtub-shaped hazard function. IEEE Transactions on Reliability 56:308–11. [Crossref], [Web of Science ®] , [Google Scholar] ) by having no restriction on the shape parameter and extending the result studied by Tahmasbi and Rezaei ( 2008 Tahmasbi, R. , and S. Rezaei. 2008. A two-parameter lifetime distribution with decreasing failure rate. Computational Statistics and Data Analysis 52:3889–901. [Crossref], [Web of Science ®] , [Google Scholar] ) in the general form. The proposed model includes the exponential–logarithmic and Weibull–logarithmic distributions as special cases. Various statistical properties of the proposed class are discussed. Furthermore, estimation via the maximum likelihood method and the Fisher information matrix are discussed. Applications to real data demonstrate that the new class of distributions is more flexible than other recently proposed classes.
Jin Qin, Baoguang Yan, Yossi Shoshany, Druker Roy, Hezi Rahamim, Haim Marom, Joseph B. Bernstein
Abstract:
NBTI has been extensively studied to understand physics of degradation in recent years. However, little has been done to find out the lifetime distributions of NBTI at both transistor and product level, which are important in reliability prediction and improvement. In this paper, Monte-Carlo simulation is carried out to study the NBTI lifetime distribution at transistor level. Lognormal distribution is found to have the best fit. Product level NBTI lifetime distribution is studied through rare event simulation. Result shows that Weibull distribution has a better fit than lognormal distribution at product level. Acceleration test result of 90nm SRAM cache NBTI degradation is compared with the simulation results and a good agreement is observed.
Jin Qin, Baoguang Yan, Yossi Shoshany, Druker Roy, Hezi Rahamim, Haim Marom, Joseph B. Bernstein
Abstract:
Simulation provides more insights of NBTI at low cumulative failure which is not easy to obtain through measurement. Monte-Carlo simulation has demonstrated that NBTI lifetime distribution at transistor level follows lognormal distribution. Rare-Event simulation shows that Weibull distribution fits better than lognormal distribution at product level. Analysis of 90nm SRAM NBTI accelerated test results confirms the product level simulation result.
Eisa Mahmoudi, Afsaneh Sepahdar, Artur Lemonte
Published: 21 February 2014
Abstract:
In this paper, we introduce a new four-parameter generalization of the exponentiated Weibull (EW) distribution, called the exponentiated Weibull-logarithmic (EWL) distribution, which obtained by compounding EW and logarithmic distributions. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub-shaped hazard rate functions, depending on its parameters and contains several lifetime sub-models such as: generalized exponential-logarithmic (GEL), complementary Weibull-logarithmic (CWL), complementary exponential-logarithmic (CEL), exponentiated Rayleigh-logarithmic (ERL) and Rayleigh-logarithmic (RL) distributions. We study various properties of the new distribution and provide numerical examples to show the flexibility and potentiality of the model.
Xuezhong Wu, Chenyue Ma, Xinnan Lin
Abstract:
In this study, impact of traps located at SiO2/Si interface on the time-dependent dielectric breakdown (TDDB) lifetime is investigated by modeling the Weibull distribution in high-k (HK) dielectric stacks. The results show that the interface traps will cause the distortion of Weibull slope of TDDB lifetime, decreasing the growing rate of the probability of breakdown after a long time.
Shovan Chowdhury
Published: 1 January 2014
Abstract:
A unified approach is proposed in this paper to study a family of lifetime distributions of a system consisting of random number of components in series and in parallel. While the lifetimes of the components are assumed to follow generalized (exponentiated) Weibull distribution, a zero-truncated Poisson is assigned to model the random number of components in the system. The resulting family of compounded distributions describes several well-known distributions as well as some new models with some of their statistical and reliability properties. Various ageing classes of life distributions including increasing, decreasing, bath-tub, upside-down-bathtub and roller coaster shaped failure rates are covered by the family of compounded distributions. The simplest algorithm for maximum likelihood method of estimation of the model parameters is discussed. Some numerical results are obtained via Monte-Carlo Simulation. The asymptotic variance-covariance matrices of the estimators are also obtained. Five different real data sets are used to validate the distributions and the results demonstrate that the family of distributions can be considered as a suitable model under several real situations.
Published: 8 March 2019
Abstract:
We propose a new four-parameter lifetime distribution obtained by compounding twouseful distributions: the Weibull and Burr XII distributions. Among interesting features,it shows a great flexibility with respect to its crucial functions shapes; the probability density function can exhibit unimodal (symmetrical and right-skewed), bimodal and decreasing shapes, and the hazard rate function can accommodate increasing, decreasing, bathtub, upside-down bathtub and decreasing-increasing-decreasing shapes. Some mathematicalproperties of the new distribution are obtained such as the quantiles, moments, generatingfunction, stress-strength reliability parameter and stochastic ordering. The maximum likelihood estimation is employed to estimate the model parameters. A Monte Carlo simulationstudy is carried out to assess the performance of the maximum likelihood estimates. Wealso propose a flexible cure rate survival model by assuming that the number of competingcauses of the event of interest has the Poisson distribution and the time for the event followsthe proposed distribution. Four empirical illustrations of the new distribution are presentedto real-life data sets. The results of the proposed model are better in comparison to thoseobtained with the exponential-Weibull, odd Weibull-Burr and Weibull-Lindley models.
Published: 8 March 2019
Abstract:
We propose a new four-parameter lifetime distribution obtained by compounding twouseful distributions: the Weibull and Burr XII distributions. Among interesting features,it shows a great flexibility with respect to its crucial functions shapes; the probability density function can exhibit unimodal (symmetrical and right-skewed), bimodal and decreasing shapes, and the hazard rate function can accommodate increasing, decreasing, bathtub, upside-down bathtub and decreasing-increasing-decreasing shapes. Some mathematicalproperties of the new distribution are obtained such as the quantiles, moments, generatingfunction, stress-strength reliability parameter and stochastic ordering. The maximum likelihood estimation is employed to estimate the model parameters. A Monte Carlo simulationstudy is carried out to assess the performance of the maximum likelihood estimates. Wealso propose a flexible cure rate survival model by assuming that the number of competingcauses of the event of interest has the Poisson distribution and the time for the event followsthe proposed distribution. Four empirical illustrations of the new distribution are presentedto real-life data sets. The results of the proposed model are better in comparison to thoseobtained with the exponential-Weibull, odd Weibull-Burr and Weibull-Lindley models.
Journal of Statistics and Management Systems, Volume 23, pp 887-913; https://doi.org/10.1080/09720510.2019.1677315

Abstract:
In this paper we analyze a unified approach to study a family of lifetime distributions of a system consisting of random number of components in series and in parallel proposed by Chowdhury (2014). While the lifetimes of the components are assumed to follow generalized (exponentiated) Weibull distribution, a zero-truncated Poisson is assigned to model the random number of components in the system. The resulting family of compounded distributions describes several well-known distributions as well as some new models. Bivariate extension of the proposed family of distribution is also introduced. Some important statistical and reliability properties of the family of distributions are investigated. The distribution is found to exhibit both monotone and non-monotone failure rates. Parameters of the proposed distributions are estimated by the expectation maximization (EM) algorithm. Some numerical results are obtained through Monte-Carlo simulation. The asymptotic variance-covariance matrices of the estimators are also derived. Potential of the distribution is explored through two real data sets and compared with similar compounded distribution and the results demonstrate that the family of distributions can be considered as a suitable model under several real situations.
Published: 8 March 2019
Abstract:
We propose a new four-parameter lifetime distribution obtained by compounding twouseful distributions: the Weibull and Burr XII distributions. Among interesting features,it shows a great flexibility with respect to its crucial functions shapes; the probability density function can exhibit unimodal (symmetrical and right-skewed), bimodal and decreasing shapes, and the hazard rate function can accommodate increasing, decreasing, bathtub, upside-down bathtub and decreasing-increasing-decreasing shapes. Some mathematicalproperties of the new distribution are obtained such as the quantiles, moments, generatingfunction, stress-strength reliability parameter and stochastic ordering. The maximum likelihood estimation is employed to estimate the model parameters. A Monte Carlo simulationstudy is carried out to assess the performance of the maximum likelihood estimates. Wealso propose a flexible cure rate survival model by assuming that the number of competingcauses of the event of interest has the Poisson distribution and the time for the event followsthe proposed distribution. Four empirical illustrations of the new distribution are presentedto real-life data sets. The results of the proposed model are better in comparison to thoseobtained with the exponential-Weibull, odd Weibull-Burr and Weibull-Lindley models.
Qingling Guan, , Piet C. P. Bouten, Gijsbertus de With
Published: 7 June 2013
Journal of applied physics, Volume 113; https://doi.org/10.1063/1.4809542

Abstract:
Mechanical failure resulting from subcritical crack growth in the SiNx inorganic barrier layer applied on a flexible multilayer structure was studied by an electro-mechanical two-point bending method. A 10 nm conducting tin-doped indium oxide layer was sputtered as an electrical probe to monitor the subcritical crack growth in the 150 nm dielectric SiNx layer carried by a polyethylene naphthalate substrate. In the electro-mechanical two-point bending test, dynamic and static loads were applied to investigate the crack propagation in the barrier layer. As consequence of using two loading modes, the characteristic failure strain and failure time could be determined. The failure probability distribution of strain and lifetime under each loading condition was described by Weibull statistics. In this study, results from the tests in dynamic and static loading modes were linked by a power law description to determine the critical failure over a range of conditions. The fatigue parameter n from the power law reduces greatly from 70 to 31 upon correcting for internal strain. The testing method and analysis tool as described in the paper can be used to understand the limit of thin-film barriers in terms of their mechanical properties.
, Satoshi Okubo, Kiyotaka Horikawa,
Published: 21 April 2018
Journal of applied physics, Volume 123; https://doi.org/10.1063/1.5022338

Abstract:
Atomic-layer-deposited (ALD) Al2O3 films are the most promising surface passivation and gate insulation layers in non-Si semiconductor devices. Here, we carried out an extensive study on the time-dependent dielectric breakdown characteristics of ALD-Al2O3 films formed on homo-epitaxial GaN substrates using two different oxidants at two different ALD temperatures. The breakdown times were approximated by Weibull distributions with average shape parameters of 8 or larger. These values are reasonably consistent with percolation theory predictions and are sufficiently large to neglect the wear-out lifetime distribution in assessing the long-term reliability of the Al2O3 films. The 63% lifetime of the Al2O3 films increases exponentially with a decreasing field, as observed in thermally grown SiO2 films at low fields. This exponential relationship disproves the correlation between the lifetime and the leakage current. Additionally, the lifetime decreases with measurement temperature with the most remarkable reduction observed in high-temperature (450 °C) O3-grown films. This result agrees with that from a previous study, thereby ruling out high-temperature O3 ALD as a gate insulation process. When compared at 200 °C under an equivalent SiO2 field of 4 MV/cm, which is a design guideline for thermal SiO2 on Si, high-temperature H2O-grown Al2O3 films have the longest lifetimes, uniquely achieving the reliability target of 20 years. However, this target is accomplished by a relatively narrow margin and, therefore, improvements in the lifetime are expected to be made, along with efforts to decrease the density of extrinsic Al2O3 defects, if any, to promote the practical use of ALD Al2O3 films.
D. Hoogeland, , , W. F. A. Besling, ,
Published: 8 December 2009
Journal of applied physics, Volume 106; https://doi.org/10.1063/1.3267299

Abstract:
By employing plasma-assisted atomic layer deposition, thin films of Al2O3 and TiN are subsequently deposited in a single reactor at a single substrate temperature with the objective of fabricating high-quality TiN/Al2O3/p-Si metal-oxide-semiconductor capacitors. Transmission electron microscopy and Rutherford backscattering spectroscopy analyses show well-defined interfaces and good Al2O3 stoichiometry, respectively. Electrical investigation of as-deposited test structures demonstrates leakage current densities as low as 1nA/cm2 . Current-voltage (I-V) measurements demonstrate clear Fowler–Nordheim tunneling with an average TiN/Al2O3 barrier height of 3.3 eV. Steep Weibull distributions of the breakdown electric field around 7.5 MV/cm indicate good reliability of these devices. Time-dependent dielectric breakdown measurements demonstrate that the devices can sustain high operating electric fields of 3–4 MV/cm for the 10 year lifetime criterion. From capacitance-voltage (C-V) measurements, a dielectric constant (k) of 8.7±0.1 was extracted for the Al2O3 . No direct dependence on the deposition temperature was found in the range 350400°C , although the stack deposited at 400°C demonstrates significantly lower C-V hysteresis of 50mV . A negative fixed oxide charge density of (9.6±0.2)×1012cm2 was found to be present at the Al2O3/p-Si interface.
T. Shimizu, N. Suzumura, K. Ohgata, H. Tsuchiya, H. Aono, M. Ogasawara
Abstract:
We investigated the time-dependent clustering (TDC) model for time-dependent dielectric breakdown (TDDB) of non-uniform dielectrics and revealed for the first time that the TDC model is a compound Weibull model that is expressed as a superposition of Weibull distributions. The Weibull model has two statistical parameters, scale parameter η and shape parameter β We clarified the precondition that the TDC model holds when term η β of the Weibull model is distributed according to an inverse-gamma distribution. By using our finding, we proposed a new method to directly estimate the variations of electric field and effective space from TDDB data. We found that the corresponding electric field distribution is a generalization of extreme value distribution, which is a natural consequence since the lifetime is determined by the maximum value of the electric field.
, M. H. Alamatsaz, V. Nekoukhou
Communications in Statistics - Simulation and Computation, Volume 44, pp 1389-1404; https://doi.org/10.1080/03610918.2013.819918

Abstract:
In this article, the exponentiated Weibull distribution is extended by the Marshall-Olkin family. Our new four-parameter family has a hazard rate function with various desired shapes depending on the choice of its parameters and, thus, it is very flexible in data modeling. It also contains two mixed distributions with applications to series and parallel systems in reliability and also contains several previously known lifetime distributions. We shall study some basic distributional properties of the new distribution. Some closed forms are derived for its moment generating function and moments as well as moments of its order statistics. The model parameters are estimated by the maximum likelihood method. The stress–strength parameter and its estimation are also investigated. Finally, an application of the new model is illustrated using two real datasets.
Jiabei He, Jin Wei, Song Yang, Mengyuan Hua, KaiKun Zhong, Kevin J. Chen
Abstract:
This paper experimentally investigates the time-dependent gate degradation of Schottky-type p-GaN gate transistors subjected to positive gate voltage stress. By means of combined static/dynamic gate stress and temperature-dependent analysis, the dependence of time-to-breakdown ( tBD) on stress mode and temperature are unveiled. It is demonstrated that tBD is Weibull distributed and the mean-time-to-failure (MTTF) is comparable under static and dynamic stress conditions. Both the gate breakdown voltage and MTTF exhibit positive temperature dependence. The maximum applicable gate voltage for a 10-year lifetime is extrapolated at different stress conditions. Moreover, the mechanism of the gate degradation is discussed by comparing the devices' performance before and after the progressive breakdown. It is revealed that electrons accelerated in the depletion region of the p-GaN layer under large forward gate bias would gain enough energy and induce defects near the metal/ p-GaN interface, resulting in the time-dependent gate degradation.
Published: 7 October 2010
Computational Statistics & Data Analysis, Volume 55, pp 1410-1425; https://doi.org/10.1016/j.csda.2010.09.030

The publisher has not yet granted permission to display this abstract.
Published: 9 June 2018
by MDPI
Journal: Stats
Stats, Volume 1, pp 77-91; https://doi.org/10.3390/stats1010006

Abstract:
A new compound distribution called Burr XII-Weibull-Logarithmic (BWL) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Burr XII-Exponential-Logarithmic, Burr XII-Rayleigh-Logarithmic, Burr XII-Logarithmic, Lomax-Exponential-Logarithmic, Lomax–Rayleigh-Logarithmic, Weibull, Rayleigh, Lomax, Lomax-Logarithmic, Weibull-Logarithmic, Rayleigh-Logarithmic, and Exponential-Logarithmic distributions. Some statistical properties of the proposed distribution including moments and conditional moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.
, Canan Hamurkaroğlu, Nazan Danacıoğlu
International Journal of Quality & Reliability Management; https://doi.org/10.1108/ijqrm-07-2021-0201

Abstract:
Purpose: Acceptance sampling plans are a decision-making process on the basis of a randomly selected sampling from a party, where it is not possible to completely scan the products for reasons such as time and cost being limited or the formation of damaged products during the inspection. For some products, the life span (time from beginning to failure) may be an important quality characteristic. In this case, the quality control adequacy of the products can be checked with an acceptance sampling plan based on the truncated life test with a censored scheme for the lifetime of the products. In this study, group acceptance sampling plans (GASPs) based on life tests are studied under the Type-I censored scheme for the compound Weibull-exponential (CWE) distribution. Design/methodology/approach: GASPs based on life tests under the Type-I censored scheme for the CWE distribution are developed by using both the producer's risk and the consumer's risk. Findings: In this study, optimum sample size, optimum number of groups and acceptance number are obtained under the Type-I censored scheme for the CWE distribution. Real data set illustration is given to show GASPs how to be used for the industry applications. Originality/value: Different from acceptance sampling plans with just considering the producer's risk, GASPs are constructed by using two-point approach included both the producer's risk and the consumer's risk for CWE distribution.
, Gayan Warahena-Liyanage, Mavis Pararai
Journal of Statistical Computation and Simulation, Volume 86, pp 1363-1391; https://doi.org/10.1080/00949655.2015.1064409

Abstract:
A new class of distributions called the log-logistic Weibull–Poisson distribution is introduced and its properties are explored. This new distribution represents a more flexible model for lifetime data. Some statistical properties of the proposed distribution including the expansion of the density function, quantile function, hazard and reverse hazard functions, moments, conditional moments, moment generating function, skewness and kurtosis are presented. Mean deviations, Bonferroni and Lorenz curves, Rényi entropy and distribution of the order statistics are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the confidence interval for each parameter and finally applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.
Published: 1 December 1981
Journal: Metrika
Metrika, Volume 28, pp 263-271; https://doi.org/10.1007/bf01902900

The publisher has not yet granted permission to display this abstract.
Published: 16 March 2022
Abstract:
Statisticians are interested in improving the ability of classical distributions to appropriately fit real-world data and accurately describe its characteristics. Typically, this can be achieved by extending known distributions by incorporating extra parameters or compounding distributions. In this paper, a flexible general method to obtain new families of distributions is proposed. A number of known methods turn out to be special cases of the proposed method in this paper. Some examples are given to demonstrate the power of the proposed method such as the exponential and the Weibull distribution.
Communications in Statistics - Theory and Methods, Volume 46, pp 4296-4310; https://doi.org/10.1080/03610926.2015.1081949

Abstract:
In this paper, the researchers attempt to introduce a new generalization of the Weibull-geometric distribution. The failure rate function of the new model is found to be increasing, decreasing, upside-down bathtub, and bathtub-shaped. The researchers obtained the new model by compounding Weibull distribution and discrete generalized exponential distribution of a second type, which is a generalization of the geometric distribution. The new introduced model contains some previously known lifetime distributions as well as a new one. Some basic distributional properties and moments of the new model are discussed. Estimation of the parameters is illustrated and the model with two known real data sets is examined.
A. R. Sydor
Abstract:
For unsymmetrical compound electromagnetic systems ramified to level 2, models of main reliability characteristics are worked out for the cases when the lifetime of ageing output elements is circumscribed by the Weibull distribution. These models make it possible to compare variants of system structures depending on requirements of production process
Jimut Bahan Chakrabarty,
Communications in Statistics - Simulation and Computation, Volume 48, pp 2012-2033; https://doi.org/10.1080/03610918.2018.1429623

Abstract:
In this paper two probability distributions are analyzed which are formed by compounding inverse Weibull with zero-truncated Poisson and geometric distributions. The distributions can be used to model lifetime of series system where the lifetimes follow inverse Weibull distribution and the subgroup size being random follows either geometric or zero-truncated Poisson distribution. Some of the important statistical and reliability properties of each of the distributions are derived. The distributions are found to exhibit both monotone and non-monotone failure rates. The parameters of the distributions are estimated using the expectation-maximization algorithm and the method of minimum distance estimation. The potentials of the distributions are explored through three real life data sets and are compared with similar compounded distributions, viz. Weibull-geometric, Weibull-Poisson, exponential-geometric and exponential-Poisson distributions.
Said H. Alkarni
American Review of Mathematics and Statistics, Volume 3; https://doi.org/10.15640/arms.v3n2a8

Abstract:
Generalizedextended Weibull Power Series Family of Distributions Said H. Alkarni Abstract In this study, we introduce a new familyof models for lifetime data called generalized extended Weibullpower series family of distributions by compoundinggeneralizedextended Weibull distributions and power series distributions. The compounding procedure follows the same setup carried out by Adamidis (1998). The proposed family contains all types of combinations between truncated discrete with generalized and nongeneralized Weibull distributions. Some existing power series and subclasses of mixed lifetime distributions become special cases of the proposed family, such as the compound class of extended Weibull power seriesdistributions proposed by Silva et al. (2013) and the generalized exponential power series distributionsintroduced by Mahmoudi and Jafari (2012).Some mathematical properties of the new class are studied, includingthe cumulative distribution function, density function, survival function, and hazard rate function. The method of maximum likelihood is used for obtaining a general setup for estimating the parameters of any distribution in this class. An expectation-maximization algorithm is introduced for estimating maximum likelihood estimates.Special subclasses and applications for some models in areal datasetare introduced to demonstrate the flexibility and the benefit of this new family. Full Text: PDF DOI: 10.15640/arms.v3n2a8
A R Sydor, D. Marunchak
Abstract:
A method of investigation of reliability parameters of compound systems by means of generating functions is developed taking account of aging of the system's output elements. Main reliability characteristics of compound electromagnetic systems are examined in this paper. Expressions for the failure probability, the failure frequency and the failure rate are worked out in the cases when the lifetime of ageing output elements is circumscribed by the Weibull distribution
Avinash Agrawal
Abstract:
Computer software for analyzing life test data with a Weibull distribution is given. The programs calculate and plot the 95, 90, 50 and 5% highest probability density contours and the maximum likelihood estimators on the same frame for all sets of data. They also calculate the maximum likelihood estimator of mean life and conservative 95, 90, 50 and 5% credible intervals on mean life. The programs are used to analyze data on the lifetimes of Kevlar/Epoxy spherical vessels and the results are given.
Published: 30 May 2015
Ciência e Natura, Volume 37; https://doi.org/10.5902/2179460x16680

Abstract:
DOI: http://dx.doi.org/10.5902/2179460X16680 In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power series, generalized exponential-power series, generalized linear failure rate-power series, exponentiated Weibull-power series, generalized modified Weibull-power series, generalized Gompertz-power series and exponentiated extended Weibull distributions as special cases. We obtain several properties of this new class of distributions such as Shannon entropy, mean residual life, hazard rate function, quantiles and moments. Sub-models of this distribution are studied in details, and the maximum likelihood estimation procedure via a EM-algorithm is presented.
Irene Dekomwine Angbing, , Dioggban Jakperik
International Journal of Mathematics and Mathematical Sciences, Volume 2022, pp 1-13; https://doi.org/10.1155/2022/1798278

Abstract:
In this study, two new distributions are developed by compounding Sine-Weibull and zero-truncated geometric distributions. The quantile and ordinary moments of the distributions are obtained. Plots of the hazard rate functions of the distributions show that the distributions exhibit nonmonotonic failure rates. Also, plots of the densities of the distributions show that they exhibit decreasing, skewed, and approximately symmetric shapes, among others. Mixture and nonmixture cure rate models based on these distributions are also developed. The estimators of the parameters of the cure rate models are shown to be consistent via simulation studies. Covariates are introduced into the cure rate models via the logit link function. Finally, the performance of the distributions and the cure rate and regression models is demonstrated using real datasets. The results show that the developed distributions can serve as alternatives to existing models for survival data analyses.
Essam K. Al-Hussaini
Published: 1 April 2003
Journal of Statistical Planning and Inference, Volume 113, pp 15-24; https://doi.org/10.1016/s0378-3758(01)00297-x

The publisher has not yet granted permission to display this abstract.
, Basma Ahmed
Pakistan Journal of Statistics and Operation Research, Volume 14, pp 333-358; https://doi.org/10.18187/pjsor.v13i3.2060

Abstract:
In this paper, acceptance sampling plans as, double for the lifetime tests is truncated at pre-fixed time to determine on acceptance or rejection of the submitted lots are provided. The probability distributions of the lifetime of the product are determined based on three distributions: generalized inverse Weibull, skew-generalized inverse Weibull and compound inverse Rayleigh. The median lifetime of the test unit as the quality parameter is considered. The minimum sample sizes to assure that the actual median life is more than the specified life, OC values according to different quality levels and the minimum ratios of the actual median life to the specified life at the determined level of producer's risk for acceptance sampling plans are obtained. Numerical cases are introduced to illustrate the applications of acceptance sampling plans.
, Horst Lewitschnig,
Quality and Reliability Engineering International, Volume 30, pp 363-373; https://doi.org/10.1002/qre.1577

The publisher has not yet granted permission to display this abstract.
, Hanaa Sagor
Journal of Statistical Computation and Simulation, Volume 85, pp 1883-1901; https://doi.org/10.1080/00949655.2014.907800

Abstract:
In this paper we introduce a three-parameter lifetime distribution following the Marshall and Olkin [New method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika. 1997;84(3):641–652] approach. The proposed distribution is a compound of the Lomax and Logarithmic distributions (LLD). We provide a comprehensive study of the mathematical properties of the LLD. In particular, the density function, the shape of the hazard rate function, a general expansion for moments, the density of the rth order statistics, and the mean and median deviations of the LLD are derived and studied in detail. The maximum likelihood estimators of the three unknown parameters of LLD are obtained. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance–covariance matrix. Finally, a real data set is analysed to show the potential of the new proposed distribution.
, Ali Akbar Jafari
Published: 31 May 2016
Ciência e Natura, Volume 38; https://doi.org/10.5902/2179460x19496

Abstract:
In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power series, generalized exponential-power series, generalized linear failure rate-power series, exponentiated Weibull-power series, generalized modifiedWeibull-power series, generalized Gompertz-power series and exponentiated extendedWeibull distributions as special cases. We obtain several properties of this new class of distributions such as Shannon entropy, mean residual life, hazard rate function, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented.
Published: 15 August 2014
Journal: Metron
Metron, Volume 73, pp 303-315; https://doi.org/10.1007/s40300-014-0052-1

The publisher has not yet granted permission to display this abstract.
Tengiz Mdzinarishvili, Simon Sherman
Published: 1 January 2010
Cancer Informatics, Volume 9; https://doi.org/10.4137/cin.s5460

Abstract:
Mathematical modeling of cancer development is aimed at assessing the risk factors leading to cancer. Aging is a common risk factor for all adult cancers. The risk of getting cancer in aging is presented by a hazard function that can be estimated from the observed incidence rates collected in cancer registries. Recent analyses of the SEER database show that the cancer hazard function initially increases with the age, and then it turns over and falls at the end of the lifetime. Such behavior of the hazard function is poorly modeled by the exponential or compound exponential-linear functions mainly utilized for the modeling. In this work, for mathematical modeling of cancer hazards, we proposed to use the Weibull-like function, derived from the Armitage-Doll multistage concept of carcinogenesis and an assumption that number of clones at age t developed from mutated cells follows the Poisson distribution. This function is characterized by three parameters, two of which ( r and λ) are the conventional parameters of the Weibull probability distribution function, and an additional parameter ( C0) that adjusts the model to the observational data. Biological meanings of these parameters are: r—the number of stages in carcinogenesis, λ—an average number of clones developed from the mutated cells during the first year of carcinogenesis, and C0—a data adjustment parameter that characterizes a fraction of the age-specific population that will get this cancer in their lifetime. To test the validity of the proposed model, the nonlinear regression analysis was performed for the lung cancer (LC) data, collected in the SEER 9 database for white men and women during 1975–2004. Obtained results suggest that: (i) modeling can be improved by the use of another parameter A- the age at the beginning of carcinogenesis; and (ii) in white men and women, the processes of LC carcinogenesis vary by A and C0, while the corresponding values of r and λ are nearly the same. Overall, the proposed Weibull-like model provides an excellent fit of the estimates of the LC hazard function in aging. It is expected that the Weibull-like model can be applicable to fit estimates of hazard functions of other adult cancers as well.
Anuwoje Ida L. Abonongo, Albert Luguterah, Suleman Nasiru
Asian Journal of Probability and Statistics pp 28-51; https://doi.org/10.9734/ajpas/2022/v17i230417

Abstract:
The power series generalised power Weibull class of distributions were developed in this study by compounding the power series family of distributions and the generalised power Weibull distribution. The statistical properties of this new class were derived. Maximum likelihood parameter estimators were derived for the parameters of the power series generalised power Weibull class of distributions. Four sub-families of distributions were developed from the power series generalised power Weibull class of distribution; the generalised power Weibull geometric distribution, generalised power Weibull Poisson distribution, generalised power Weibull binomial distribution and the generalised power Weibull logarithmic distribution. The hazard rate and probability density function plots of the four sub families of distributions showed that, they can model both monotonic and non-monotonic lifetime data. Monte Carlo simulations performed on these sub-distributions showed that, their estimators were consistent estimators. Application of these sub-distributions to failure data from air conditioning system of an aircraft showed that, the generalised power Weibull geometric distribution provides a better fit to the data. Also, the generalised power Weibull Poisson distribution provides a better fit to the data on service times of 63 aircraft.
Mizal H Alobaidi, Pelumi E Oguntunde, Mundher A Khaleel
Published: 1 May 2021
Journal of Physics: Conference Series, Volume 1879; https://doi.org/10.1088/1742-6596/1879/2/022104

Abstract:
The Transmuted Topp Leone Flexible Weibull distribution was developed in this paper using the Transmuted Topp Leone family of distributions and its basic statistical properties were established. Estimation of model parameters was considered using the maximum likelihood estimation (MLE) method and three real life applications were provided. The TTLFW distribution is a promising model as its performance relative to other compounds probability models like the Exponentiated Flexible Weibull, Weibull Flexible Weibull, Kumaraswamy Flexible Weibull, Beta Flexible Weibull, Gamma Flexible Weibull, and Exponentiated Generalized Flexible Weibull distributions is quite credible.
, Francis Ogbemudia Oyegue, Sunday Martins Ogbonmwan
Journal of Statistics and Management Systems, Volume 25, pp 549-584; https://doi.org/10.1080/09720510.2021.1917799

Abstract:
A new flexible probability distribution which extends the classical Burr XII distribution for fitting unimodal datasets with various shape and tail behaviors is introduced in this paper. The distribution is so-called the Weibull – Burr XII {log logistic} Poisson distribution and was realized by compounding the Weibull – Burr XII {log logistic} distribution from the T – R {Y} family of probability distributions and the Poisson distribution and hence, the distribution belongs to the T – R {Y} Poisson class. A detailed account of the statistical properties of the distribution including moments, quantiles, mode and mean deviations are presented. The maximum likelihood estimation method is suggested for the estimation of the parameters of the distribution and Monte Carlo simulations study is used to assess its performance. Three data sets with various shape and tail properties are further used to test the applicability of the new distribution.
J.E. Fernández Rico, I. Minondo, D. García Cuervo, R. Tucho
International Journal of Surface Science and Engineering, Volume 5; https://doi.org/10.1504/ijsurfse.2011.044279

Abstract:
This work evaluates the rolling contact fatigue life of AISI steel bearing balls with a lubricant made up of a neutral mineral oil and synthetic polyester. This second oil can be considered as environmental friendly, non-toxic and biodegradable. The obtained results were compared with the corresponding pure oils identified by means of infrared spectrums. The failure mechanism evaluation was made through rolling contact fatigue test in a modified Stanhope Seta-Shell according to IP 300 standard at 1,475 rpm with a load of 600 kg. A specific software, Weibull++ by Reliasoft, was used to procure life data analysis and to obtain lifetime distribution diagrams. Reliability plots, like SN curves, mean life, failure rate and L
Peng Liu, , Xingwen Tan, Xiang Lin,
Journal of Materials Science: Materials in Electronics, Volume 31, pp 6313-6320; https://doi.org/10.1007/s10854-020-03187-z

The publisher has not yet granted permission to display this abstract.
Published: 13 January 2020
by MDPI
Journal: Polymers
Abstract:
Undispersed filler agglomerates or other substantial inclusions/contaminants in rubber can act as large crack precursors that reduce the strength and fatigue lifetime of the material. To demonstrate this, we use tensile strength (stress at break, σb) data from 50 specimens to characterize the failure distribution behavior of carbon black (CB) reinforced styrene-butadiene rubber (SBR) compounds. Poor mixing was simulated by adding a portion of the CB late in the mixing process, and glass beads (microspheres) with 517 μm average diameter were introduced during milling to reproduce the effects of large inclusions. The σb distribution was well described with a simple unimodal Weibull distribution for the control compound, but the tensile strengths of the poor CB dispersion material and the compounds with the glass beads required bimodal Weibull distributions. For the material with the lowest level of glass beads—corresponding to less than one microsphere per test specimen—the bimodal failure distribution spanned a very large range of σb from 13.7 to 22.7 MPa in contrast to the relatively narrow σb distribution for the control from 18.4 to 23.8 MPa. Crack precursor size (c0) distributions were also inferred from the data, and the glass beads introduced c0 values in the 400 μm range compared to about 180 μm for the control. In contrast to σb, critical tearing energy (tear strength) was unaffected by the presence of the CB agglomerates and glass beads, because the strain energy focuses on the pre-cut macroscopic crack in the sample during tear testing rather than on the microscopic crack precursors within the rubber. The glass beads were not detected by conventional filler dispersion measurements using interferometric microscopy, indicating that tensile strength distribution characterization is an important complementary approach for identifying the presence of minor amounts of large inclusions in rubber.
, Amani Abdullah Alahmadi, Ibrahim Elbatal, Ibrahim E. Ragab, ,
Published: 5 November 2021
Mobile Information Systems, Volume 2021, pp 1-14; https://doi.org/10.1155/2021/9550156

Abstract:
This paper is devoted to a new lifetime distribution having three parameters by compound the exponential model and the transmuted Topp-Leone-G. The new proposed model is called the transmuted Topp-Leone exponential model; it is useful in lifetime data and reliability. The new model is very flexible; its pdf can be right skewness, unimodal, and decreasing shaped, but the hrf of the suggested model can be unimodal, constant, and decreasing. Numerous statistical characteristics of the new model, notably the quantile function, moments, incomplete moments, conditional moments, mean residual life, mean inactivity time, and entropy are produced and investigated. The systems parameters are estimated using the maximum likelihood approach. All estimators should be theoretically convergent, which is supported by a simulation analysis. Finally, two real-world datasets from the engineering and medical disciplines explore the new models relevance and adaptability in comparison to the alternatives models such as the beta exponential, the MarshallOlkin generalized exponential, the exponentiated Weibull, the modified Weibull, and the transmuted Burr type X models.
Pedro R.D. Marinho, , Rodrigo B. Silva, Gauss M. Cordeiro
Published: 1 January 2019
by SciELO
Anais da Academia Brasileira de Ciencias, Volume 91; https://doi.org/10.1590/0001-3765201920180480

Abstract:
Abstract: In this paper, we introduce a new three-parameter distribution by compounding the Nadarajah-Haghighi and geometric distributions, which can be interpreted as a truncated Marshall-Olkin extended Weibull. The compounding procedure is based on the work by Marshall and Olkin 1997. We prove that the new distribution can be obtained as a compound model with mixing exponential distribution. It can have decreasing, increasing, upside-down bathtub, bathtub-shaped, constant and decreasing-increasing-decreasing failure rate functions depending on the values of the parameters. Some mathematical properties of the new distribution are studied including moments and quantile function. The maximum likelihood estimation procedure is discussed and a particle swarm optimization algorithm is provided for estimating the model parameters. The flexibility of the new model is illustrated with an application to a real data set.
, Farrukh Jamal, , Ibrahim Elbatal,
Published: 20 March 2020
Journal: PLOS ONE
Abstract:
In this paper, we introduce the exponentiated power generalized Weibull power series (EPGWPS) family of distributions, obtained by compounding the exponentiated power generalized Weibull and power series distributions. By construction, the new family contains a myriad of new flexible lifetime distributions having strong physical interpretations (lifetime system, biological studies…). We discuss the characteristics and properties of the EPGWPS family, including its probability density and hazard rate functions, quantiles, moments, incomplete moments, skewness and kurtosis. The main vocation of the EPGWPS family remains to be applied in a statistical setting, and data analysis in particular. In this regard, we explore the estimation of the model parameters by the maximum likelihood method, with accuracy supported by a detailed simulation study. Then, we apply it to two practical data sets, showing the applicability and competitiveness of the EPGWPS models in comparison to some other well-reputed models.
Page of 2
Articles per Page
by
Show export options
  Select all
Back to Top Top