The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart

In this paper, we proposed a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis and Loukas (1998). 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 properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential geometric distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches. (C) 2011 Elsevier B.V. All rights reserved.

Reliability properties under a stopping time shift

Considering a series representation of a coherent system using a shift transform of the components lifetime T-i, at its critical level Y-i, we study two problems. First, under such a shift transform, we analyse the preservation properties of the non-parametric distribution classes and secondly the association preserving property of the components lifetime under such transformations. (c) 2007 Elsevier B.V. All rights reserved.

Effect of different ferrule designs on the fracture resistance and failure pattern of endodontically treated teeth restored with fiber posts and all-ceramic crowns

OBJECTIVE: This study investigated the effect of different ferrule heights on endodontically treated premolars. MATERIAL AND METHODS: Fifty sound mandibular first premolars were endodontically treated and then restored with 7-mm fiber post (FRC Postec Plus #1 Ivoclar-Vivadent) luted with self-polymerized resin cement (Multilink, Ivoclar Vivadent) while the coronal section was restored with hybrid composite core build-up material (Tetric Ceram, Ivoclar-Vivadent), which received all-ceramic crown. Different ferrule heights were investigated: 1-mm circumferential ferrule without post and core (group 1 used as control), a circumferential 1-mm ferrule (group 2), non-uniform ferrule 2-mm buccally and 1-mm lingually (group 3), non-uniform ferrule 3-mm buccally and 2-mm lingually (group 4), and finally no ferrule preparation (group 5). The fracture load and failure pattern of the tested groups were investigated by applying axial load to the ceramic crowns (n=10). Data were analyzed statistically by one-way ANOVA and Tukey's post-hoc test was used for pair-wise comparisons (α=0.05). RESULTS: There were no significant differences among the failure load of all tested groups (P<0.780). The control group had the lowest fracture resistance (891.43±202.22 N) and the highest catastrophic failure rate (P<0.05). Compared to the control group, the use of fiber post reduced the percentage of catastrophic failure while increasing the ferrule height did not influence the fracture resistance of the restored specimens. CONCLUSIONS: Within the limitations of this study, increasing the ferrule length did not influence the fracture resistance of endodontically treated teeth restored with glass ceramic crowns. Insertion of a fiber post could reduce the percentage of catastrophic failure of these restorations under function.

The complementary exponential power lifetime model

In this paper we propose a new lifetime distribution which can handle bathtub-shaped unimodal increasing and decreasing hazard rate functions The model has three parameters and generalizes the exponential power distribution proposed by Smith and Bain (1975) with the inclusion of an additional shape parameter The maximum likelihood estimation procedure is discussed A small-scale simulation study examines the performance of the likelihood ratio statistics under small and moderate sized samples Three real datasets Illustrate the methodology (C) 2010 Elsevier B V All rights reserved

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998) This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Gawk 2009) which contains several lifetime models such as exponential geometric (Adamidis and Loukas 1998) exponential Poisson (Kus 2007) and exponential logarithmic (Tahmasbi and Rezaei 2008) distributions The hazard function of our class can be increasing decreasing and upside down bathtub shaped among others while the hazard function of an EPS distribution is only decreasing We obtain several properties of the WPS distributions such as moments order statistics estimation by maximum likelihood and inference for a large sample Furthermore the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints Special distributions are studied in some detail Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions (C) 2010 Elsevier B V All rights reserved

Accelerating autonomous learning by using heuristic selection of actions

This paper investigates how to make improved action selection for online policy learning in robotic scenarios using reinforcement learning (RL) algorithms. Since finding control policies using any RL algorithm can be very time consuming, we propose to combine RL algorithms with heuristic functions for selecting promising actions during the learning process. With this aim, we investigate the use of heuristics for increasing the rate of convergence of RL algorithms and contribute with a new learning algorithm, Heuristically Accelerated Q-learning (HAQL), which incorporates heuristics for action selection to the Q-Learning algorithm. Experimental results on robot navigation show that the use of even very simple heuristic functions results in significant performance enhancement of the learning rate.

High Carbon Ferro-chromium Production by Self-reducing Process: Effects of Fe-Si and Fluxing Agent Additions

The technology of self-reducing pellets for ferro-alloys production is becoming an emerging process due to the lower electric energy consumption and the improvement of metal recovery in comparison with the traditional process. This paper presents the effects of reduction temperature, addition of ferro-silicon and addition of slag forming agents for the production of high carbon ferro-chromium by utilization of self-reducing pellets. These pellets were composed of Brazilian chromium ore (chromite) concentrate, petroleum coke, Portland cement, ferro-silicon and slag forming components (silica and hydrated lime). The pellets were processed at 1 773 K, 1 823 K and 1 873 K using an induction furnace. The products obtained, containing slag and metallic phases, were analyzed by scanning electron microscopy and chemical analyses (XEDS). A large effect on the reduction time was observed by increasing the temperature from 1 773 K to 1 823 K for pellets without Fe-Si addition: around 4 times faster at 1 823 K than at 1 773 K for reaction fraction close to one. However, when the temperature was further increased from 1 823 K to 1 873 K the kinetics improved by double. At 1 773 K, the addition of 2% of ferro-silicon in the pellet resulted in an increasing reaction rate of around 6 times, in comparison with agglomerate without it. The addition of fluxing agents (silica and lime), which form initial slag before the reduction is completed, impaired the full reduction. These pellets became less porous after the reduction process.

High Carbon Ferro-Chromium by Self-Reducing Process

This paper discusses the effects of temperature, addition of ferro-silicon and fluxing agents for the production of high carbon ferro-chromium by self-reducing process. The use of self-reducing agglomerates for ferro-alloys production is becoming an emerging processing technology due to lowering the electric energy consumption and improving the metal recovery in comparison with traditional ones. The self-reducing pellets were composed by chromite, petroleum coke, cement and small (0.1% - 2%) addition of ferro-silicon. The slag composition was adjusted by addition of fluxing agents. The reduction of pellets was carried out at 1773K (1500 degrees C), 1823K (1550 degrees C) and 1873K (1600 degrees C) by using induction furnace. The products obtained, containing slag and metallic phases, were analyzed by scanning electron microscopy and chemical analyses (XEDS). By increasing temperature from 1773K to 1823K large effect on the reduction time was observed. It decreased from 30 minutes to 10 minutes, for reaching around 0.98 reduction fraction. No significant effect on reduction time was observed when the reduction temperature was increased from 1823K to 1873K. At 1773K, the addition of 2% of ferro-silicon in the pellet resulted in an increasing reaction rate of around 6 times, in comparison with agglomerate without this addition. The addition of fluxing agents (silica and hydrated lime) has effect on reduction time (inverse relationship) and the pellets become less porous after reduction.

The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

The beta modified Weibull distribution

A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

A log-extended Weibull regression model

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which has the ability to deal with bathtub-shaped failure rate functions. We use the method of maximum likelihood to estimate the model parameters and some inferential procedures are presented. We reanalyze a real data set under the new model and the log-modified Weibull regression model. We perform a model check based on martingale-type residuals and generated envelopes and the statistics AIC and BIC to select appropriate models. (C) 2009 Elsevier B.V. All rights reserved.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 Elsevier B.V. All rights reserved.

General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.