Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

In this article, we study reliability measures such as geometric vitality function and conditional Shannon’s measures of uncertainty proposed by Ebrahimi (1996) and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them

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.

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.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

Complication and failure rates with implant-supported fixed dental prostheses and single crowns: a 10-year retrospective study

PURPOSE Clinical studies related to the long-term outcomes with implant-supported reconstructions are still sparse. The aim of this 10-year retrospective study was to assess the rate of mechanical/technical complications and failures with implant supported fixed dental prostheses (FDPs) and single crowns (SCs) in a large cohort of partially edentulous patients. MATERIALS AND METHODS The comprehensive multidisciplinary examination consisted of a medical/dental history, clinical examination, and a radiographic analysis. Prosthodontic examination evaluated the implant-supported reconstructions for mechanical/technical complications and failures, occlusal analysis, presence/absence of attrition, and location, extension, and retention type. RESULTS Out of three hundred ninety seven fixed reconstructions in three hundred three patients, two hundred sixty eight were SCs and one hundred twenty seven were FDPs. Of these three hundred ninety seven implant-supported reconstructions, 18 had failed, yielding a failure rate of 4.5% and a survival rate of 95.5% after a mean observation period of 10.75 years (range: 8.4-13.5 years). The most frequent complication was ceramic chipping (20.31%) followed by occlusal screw loosening (2.57%) and loss of retention (2.06%). No occlusal screw fracture, one abutment loosening, and two abutment fractures were noted. This resulted in a total mechanical/technical complication rate of 24.7%. The prosthetic success rate over a mean follow-up time of 10.75 years was 70.8%. Generalized attrition and FDPs were associated with statistically significantly higher rates of ceramic fractures when compared with SCs. Cantilever extensions, screw retention, anterior versus posterior, and gender did not influence the chipping rate. CONCLUSIONS After a mean exposure time of 10.75 years, high survival rates for reconstructions supported by Sand-blasted Large-grit Acid-etched implants can be expected. Ceramic chipping was the most frequent complication and was increased in dentitions with attrition and in FDPs compared with SCs.

Predictors For Weight Loss Failure Following Roux-en-y Gastric Bypass.

Weight loss failure is a widely recognized occurrence following Roux-en-Y gastric bypass. This study aims to identify predictors associated with weight loss failure. It is a retrospective cohort which enrolled 187 subjects who underwent RYGB. Comparisons were made between patients' features at baseline and 24 months after surgery. A weight loss failure rate of 11.2% was found. Advanced age and diabetes were statistically associated with failure. The results found were close to previous reports. As weight loss failure represents an important concern, there is the possibility to perform revisional surgeries, which may emphasize the restrictive or malabsorptive characteristics of RYGB, leading to varied results. It is reinforced that weight loss cannot be used as the unique outcome to evaluate the success of surgery.

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 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.

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.

Failure rates modelling for heterogenous populations

Mixture of distributions, decreasing failure rate, increasing failure rate, proportional hazards model, accelerated life model, asymptotic behavior of mixture failure rate

Entrepreneurial success and failure: Confidence and fallible judgement

Excess entry or the high failure rate of market-entry decisions is often attributed tooverconfidence exhibited by entreprene urs. We show analytically that whereas excess entryis an inevitable consequence of imperfect assessments of entrepreneurial skill, it does notimply overconfidence. Judgmental fallibility leads to excess entry even when everyone isunderconfident. Self-selection implies greater confidence (but not necessarilyoverconfidence) among those who start new businesses than those who do not and amongsuccessful entrants than failures. Our results question claims that entrepreneurs areoverconfident and emphasize the need to understand the role of judgmental fallibility inproducing economic outcomes.

Acute neurorehabilitation: does a neurosensory and coordinated interdisciplinary programme reduce tracheostomy weaning time and weaning failure?

BACKGROUND/PURPOSE: A new coordinated interdisciplinary unit was created in the acute section of the department of clinical neurosciences, the Acute NeuroRehabilitation (NRA) unit. The objective was to evaluate the impact of the unit and its neurosensory programme on the management of tracheostomy patients in terms of reduction in the average time taken for weaning, weaning success rate and therapeutic efficiency. METHODS: This 49-month retrospective study compares 2 groups of tracheostomy patients before (n = 34) and after (n = 46) NRA intervention. The outcome measures evaluate the benefits of the NRA unit intervention (time to decannulation, weaning and complication rates) and the benefits of the coordination (time to registration in a rehabilitation centre and rate of non-compliance with standards of care). RESULTS: Weaning failure rate was reduced from 27.3% to 9.1%, no complications or recannulations were observed in the post-intervention group after weaning and time to decannulation following admission to our unit decreased from 19.13 to 12.75 days. The rate of non-compliance with patient standards of care was significantly reduced from 45% to 30% (Mann-Whitney p = 0.003). DISCUSSION/CONCLUSIONS: This interdisciplinary weaning programme helped to reduce weaning time and weaning failure, without increased complications, in the sample studied. Coordination improved the efficiency of the interdisciplinary team in the multiplicity and complexity of the different treatments.

Determinants of methicillin-susceptible Staphylococcus aureus native bone and joint infection treatment failure: a retrospective cohort study.

BACKGROUND: Although methicillin-susceptible Staphylococcus aureus (MSSA) native bone and joint infection (BJI) constitutes the more frequent clinical entity of BJI, prognostic studies mostly focused on methicillin-resistant S. aureus prosthetic joint infection. We aimed to assess the determinants of native MSSA BJI outcomes. METHODS: Retrospective cohort study (2001-2011) of patients admitted in a reference hospital centre for native MSSA BJI. Treatment failure determinants were assessed using Kaplan-Meier curves and binary logistic regression. RESULTS: Sixty-six patients (42 males [63.6%]; median age 61.2 years; interquartile range [IQR] 45.9-71.9) presented an acute (n = 38; 57.6%) or chronic (n = 28; 42.4%) native MSSA arthritis (n = 15; 22.7%), osteomyelitis (n = 19; 28.8%) or spondylodiscitis (n = 32; 48.5%), considered as "difficult-to-treat" in 61 cases (92.4%). All received a prolonged (27.1 weeks; IQR, 16.9-36.1) combined antimicrobial therapy, after surgical management in 37 cases (56.1%). Sixteen treatment failures (24.2%) were observed during a median follow-up period of 63.3 weeks (IQR, 44.7-103.1), including 13 persisting infections, 1 relapse after treatment disruption, and 2 super-infections. Independent determinants of treatment failure were the existence of a sinus tract (odds ratio [OR], 5.300; 95% confidence interval [CI], 1.166-24.103) and a prolonged delay to infectious disease specialist referral (OR, 1.134; 95% CI 1.013-1.271). CONCLUSIONS: The important treatment failure rate pinpointed the difficulty of cure encountered in complicated native MSSA BJI. An early infectious disease specialist referral is essential, especially in debilitated patients or in presence of sinus tract.

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Damage rate is a predictor of fatigue life and creep strain rate in fatigue of tensile human cortical bone samples

We present results on the growth of damage in 29 fatigue tests of human femoral cortical bone from four individuals, aged 53–79. In these tests we examine the interdependency of stress, cycles to failure, rate of creep strain, and rate of modulus loss. The behavior of creep rates has been reported recently for the same donors as an effect of stress and cycles (Cotton, J. R., Zioupos, P., Winwood, K., and Taylor, M., 2003, "Analysis of Creep Strain During Tensile Fatigue of Cortical Bone," J. Biomech. 36, pp. 943–949). In the present paper we first examine how the evolution of damage (drop in modulus per cycle) is associated with the stress level or the "normalized stress" level (stress divided by specimen modulus), and results show the rate of modulus loss fits better as a function of normalized stress. However, we find here that even better correlations can be established between either the cycles to failure or creep rates versus rates of damage than any of these three measures versus normalized stress. The data indicate that damage rates can be excellent predictors of fatigue life and creep strain rates in tensile fatigue of human cortical bone for use in practical problems and computer simulations.