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In reliability engineering or medical studies, failure of units or individuals may occurring due to several failure modes which is known by competing risks model. In this paper, we have adopted a competing risks model under consideration that, the failure time has generalized inverted exponential distribution (GIED) and the failure modes are independent and partially observed. Under type-II progressive censoring scheme (type-II PCS), the experiment is designed as a quite popular scheme for collecting data specially, for a highly reliable product. The point estimates of the model parameters are formulated under classical approach (maximum likelihood and bootstrap) and Bayesian approach with respect to the symmetric squared error loss function. Also, the approximate confidence intervals under a large sample theory, bootstrap technique's and Markov chain Monte Carlo method (MCMC) are constructed. The estimators are assessed and compared with building the simulation study. Analysis a set of type-II PCS competing risks mortality data for illustration purpose. [ABSTRACT FROM AUTHOR]

Effective measurement of system resilience provides a comprehensive understanding of the system's characteristics. However, little research has been devoted to the resilience of a technical system that is affected by both the degradation process of the system and the external shocks. In addition, existing studies have mainly evaluated the resilience of systems without considering competing risks, and rarely investigated the transient resilience evaluation subjected to the interaction of shocks and maintenance. In this paper, a new resilience model is proposed for the systems under competing risks. The paper first introduces a competing risk model to depict the failure modes of the single-component system, and then uses semi-Markov processes to describe the state transition process when the system suffers the attacks of multiple shocks. Then, according to the multi-state division of the system, the resistibility index, absorbability index and recoverability index are proposed and the overall resilience is then introduced. Considering that the system needs to meet the reliability requirement, constrained by limit budget for maintenance, a reliability and cost-based resilience model is proposed. Finally, the case of a radar system subjected to shocks of one type and multiple types of shocks is given to illustrate the concept developed in this paper. [ABSTRACT FROM AUTHOR]

The reliability analysis is usually concerned with failures in the time domain which show the difference between the quality control and reliability engineering. Also, It is very common in engineering or biological science units are falling under different causes of failure, which is known by competing risks model. In this paper, we have adopted the competing risks model when the lifetime of units distributed with generalized half-logistic (GHL) distribution. This model is formulated under consideration the failure done with two independent causes of failure. Also, to balance in statistical inference between the minimum number of failure and ideal test time, we are using, the type-I generalized hybrid censoring scheme (GHCS). The model parameters are estimated by maximum likelihood (ML) and Bayes approaches. The approximate confidence intervals, bootstrap confidence intervals and credible intervals are constructed. The developed results are discussed and assessed through Monte Carlo simulation study. A real data set is used and analyzed to report and illustrate the developed results. [ABSTRACT FROM AUTHOR]

• Explored a novel finite mixture modelling approach to deal with dependent competing risks data. • Assumed a more realistic scenario of competing risks data with multiple causes of failure. • Considered a flexible progressive first failure censoring scheme. • Different cause-specific lifetime distributions are assumed to belong to proportional hazard family of distributions. • A Diabetic Retinopathy dataset is analysed in details assuming some important members of the proportional hazard family. This paper proposes a flexible mixture modeling approach to analyze competing risks data with multiple causes of failure under a progressive first-failure censoring scheme where the causes may not be independent. The failure time distributions corresponding to different causes of failure are assumed to belong to the flexible proportional hazard family of distributions, some important members of which are Weibull, Burr XII and Gompertz distributions. We address the problem here from a classical viewpoint. The point estimates of the parameters can be easily obtained by employing the maximum likelihood principle. For interval estimation purposes, we resort to using the asymptotic confidence intervals. An extensive simulation study is carried out to validate our proposed model. Finally, a diabetic retinopathy treatment dataset is used as an application to study the effectiveness of our proposed model assuming some important members of the proportional hazard family. [ABSTRACT FROM AUTHOR]

In this paper, we adopted the competing risks model considering that, the failure time is distributed with the Chen lifetime distribution, causes of failure are partially observed and the individuals are tested under type-I censoring scheme. The model parameters are estimated by maximum likelihood and Bayes estimations. Also, the asymptotic confidence intervals as well as credible interval are constructed. The proposed model is used to analyze two sets of data, real and simulate lifetime data sets for illustrative purposes. [ABSTRACT FROM AUTHOR]

In a reliability theory, the statistical inference under accelerated competing risks model have a great significance. This model proposes the assumption of independence of variables for convenience. But, in general this assumption doesn't agree with the nature of the problem at hand. In this paper, we proposed a step stress accelerated life testing (ALT) model on the dependent competing risk modes of life Lomax distribution (LD). The structural problem of the dependence between variables discussed copula approach. Also, we are considering the units of the product fails under two dependent fatal risks and the failure times accelerated under step stress ALTs and censored with type-I generalized hybrid censoring scheme (GHCS). The parameters of this model are estimated by maximum likelihood method. Also, the confidence intervals are discussed with asymptotic and two bootstrap confidence intervals. The Monte Carlo simulation study conducted to measure the quality of the proposed methods. Finally, we report some points to describe the numerical results. [ABSTRACT FROM AUTHOR]

Time-to- failure under different causes of failure is known as a competing risks model. Practice, competing risks data can be appeared in different applications such as engineering fields or biological and medical lifetime studies as well as other related areas. Also, the causes of failure, which are competing may be partially observed. In this paper, we adopted the competing risks model with partially observed causes of failure when the latent failure times follow Lomax life distribution under type-II generalized hybrid censoring scheme. The maximum likelihood estimators of the model parameters with the associated confidence intervals are discussed. Moreover, Bayes estimators under importance sampling procedure with probability credible intervals are developed. The results are discussed using both real and simulated data sets for illustration purposes. Finally, the Monte Carlo simulation experiments are performed to assess and compare the different proposed methods with some brief comments. [ABSTRACT FROM AUTHOR]

• Competing risks model with aging and continuous-state degradation. • Development of prognostic approach with dynamic corrective mechanisms. • Development of corrected residual life-based maintenance policy with dynamic control policy. • Development of SMDP approach to optimize the multi-objective maintenance model. • Considerably better MRL and maintenance performance compared with published results. The accurate prediction of residual life in deteriorating systems is a challenging task due to uncertainties and idealized assumptions during data acquisition and model construction. To address this challenge, the paper proposes a bi-level maintenance model that incorporates a corrected residual life (CRL) approach for a deteriorating system under competing risks. Specifically, the degradation failure is modeled using a Gamma process, while the competing sudden failure is described by a proportional hazards (PH) model. To reduce inconsistencies in residual life prediction, a CRL model is presented and continuously updated with a dynamic corrective factor at each monitoring epoch. Based on the updated CRL, a bi-level maintenance model is developed, which considers both system availability and maintenance cost objectives, enabling dynamic monitoring of the system's degradation state and residual life. The optimal decision variables in the maintenance model are determined through a multi-objective optimization algorithm formulated within a semi-Markov decision process (SMDP) framework. The unique aspect of this work lies in the consideration of prediction errors in residual life and the incorporation of multi-attribute optimization for maintenance design. The proposed method is validated through a case study on light-emitting diodes, confirming its effectiveness in improving residual life prediction and optimizing maintenance decisions. [ABSTRACT FROM AUTHOR]

The mission-oriented systems (MOS) are often required to operate a consecutive of missions interspersed with finite breaks. For MOS, an appropriate maintenance strategy is the selective maintenance (SM). The SM problem (SMP) aims then to identify an optimal set of components to be maintained under maintenance resource constraints such as limited break durations. However, most existing SM models merely deals with either stochastic independent (s -independent) components in MOS or deterministic mission and break durations. To overcome this unrealistic restriction, this paper develops a novel SM model for optimizing the SMP in MOS operating under stochastic mission and break durations and s -dependent competing risks (CRs). Durations of missions and breaks are respectively governed by normal and uniform distributions, while the s -dependent CRs are captured by the copula function of which the unknown parameters are estimated relying on the two-stage MLE method. Furthermore, due to the stochastic break durations, an integrated importance measure (IIM) is introduced to measure the maintenance priority on selected components. The resulting SM optimization model is therefore formulated as a mixed-integer nonlinear program (MINLP) whose objective is to minimize the total cost while ensuring the required minimum mission reliability. A differential evolution (DE) algorithm is designed to solve the MINLP. Two numerical experiments are conducted on a ball screw system. Results obtained demonstrate the validity of our proposed model, in addition to the robustness of the solution algorithm designed. [ABSTRACT FROM AUTHOR]

The cumulative incidence function (CIF) plays an important role in the comparison of competing risks in a competing risks model. Its value at time t is the probability of failure by time t from a particular type of risk in the presence of other risks. In this paper we consider the estimation of two CIFs, F 1 and F 2 , corresponding to two competing risks when the ratio R (t) ≡ F 1 (t) / F 2 (t) is nondecreasing in t > 0. First, we derive their nonparametric maximum likelihood estimators (NPMLE) of these CIFs in the continuous case under this order constraint and show that they are inconsistent. We then develop projection-type estimators that are uniformly strongly consistent and study the weak convergence of the resulting processes. Through simulations, we compare the finite sample performance of the NPMLEs and our estimators and show that our estimators outperform them in general in terms of mean square error at all the scenarios that we consider. We also develop a test for the presence of this order constraint and extend all these results to the censored case. To illustrate the applicability of the theory we develop, we provide a real life example. • Uniformly consistent estimation of two cumulative incidence functions in a competing risks model when the ratio is monotonic. • Weak convergence of the estimators of two cumulative incidence functions in a competing risks model when the ratio is monotonic. • Test of equality of two cumulative incidence functions against the alternative that their ratio is monotonic in a competing risks model. [ABSTRACT FROM AUTHOR]

Data obtained from destructive one-shot devices are usually studied through a binary response variable indicating failure or success of the device. But, in many practical situations, it may be more realistic to consider that the failure of the device may be due to several competing risks. In this paper, we develop divergence-based inference for one-shot device testing under Weibull lifetimes. This inference is shown to be more robust than the classical MLE-based inference, without a significant loss in efficiency when the data arise from the true model. A detailed simulation study is done to show the behaviour of the proposed estimation method and the associated inference. Finally, the developed methods are applied to a motor insulation dataset for illustrative purposes. [ABSTRACT FROM AUTHOR]

In reliability, failure data often correspond to competing risks, where several failure modes can cause a unit to fail. This paper presents nonparametric predictive inference (NPI) for pairwise comparison with competing risks data, assuming that the failure modes are independent. These failure modes could be the same or different among the two groups, and these can be both observed and unobserved failure modes. NPI is a statistical approach based on few assumptions, with inferences strongly based on data and with uncertainty quantified via lower and upper probabilities. The focus is on the lower and upper probabilities for the event that the lifetime of a future unit from one group, say Y , is greater than the lifetime of a future unit from the second group, say X . The paper also shows how the two groups can be compared based on particular failure mode(s), and the comparison of the two groups when some of the competing risks are combined is discussed. [ABSTRACT FROM AUTHOR]

The competing risks problem is ubiquitous in different areas of life science, in engineering and science where failure of one component causes to fail all the system. Studying life testing experiment of a product or material, usual requires long period of time to monitoring. For the purpose of reducing the testing period, test units may be presented under conditions more severe than normal circumstances, which is called accelerated life tests (ALTs). More precisely, this procedure makes the lives shorter than would be spotted or monitored under normal conditions. Burr XII model has increasingly important in engineering statistics than other model. So, within this paper, maximum likelihood and Bayesian estimations will be discussed under the type-II censored Burr XII life time data. The Burr XII parameters as well as accelerated factor under competing risks model will be estimated. Also, the asymptotic confidence intervals under normality theory and credible intervals are obtained from MCMC sampling method will be drawn. Finally, the maximum likelihood and Bayesian estimations will be considered and a simulation investigation is described and reported by comparing the two approaches. [ABSTRACT FROM AUTHOR]

• Establish the pricing equilibrium for the risk sensitive container shipping lines (CSLs) under competition. • Explore the risk seeking behaviors and show that being risk seeking can do more good than harm. • Discover the risk-attitude convergence effect. • Prove the robustness of results by exploring different forms of demand distribution, asymmetric risk attitude, and uncertain spot market price. Container-shipping-lines (CSLs) operate in a highly competitive market with high demand volatility. Unlike many other industries in which risk-averse attitude is dominating, it is well known that many CSLs exhibit risk-seeking behaviors. In this paper, by using the mean-risk formulation, we analytically study the effects of risk attitude and demand volatility on the service pricing game between two CSLs. We find that the equilibrium prices increase when CSLs can accept more risk, and being slightly risk-seeking can help maximize the expected profits of both CSLs. We discover the risk-attitude convergence effect, which theoretically reveals that the "optimal risk attitudes" for the CSLs move in the same direction. Therefore, our research suggests that both CSLs should hire slightly risk-seeking managers in a competitive shipping market. In addition, we explore the impacts brought by demand volatility and find that the equilibrium prices increase (decrease) in the demand volatility when CSLs are risk-seeking (risk-averse). We uncover that when an individual CSL's risk sensitivity level is small and its rival is risk-seeking, its own expected profit under the decentralized case could be larger than that in centralized case. Finally, for robustness checking of our research findings, we investigate the scenarios with multiplicative randomness of demand, asymmetric information on risk attitude and multiple (more than two) competing CSLs, and find that our main findings still hold. Counterintuitively, in the case with multiplicatively random demand, we analytically find that CSLs may not prefer a large market potential when they are risk-averse. [ABSTRACT FROM AUTHOR]

• Noninformative priors (Jefferys prior and two reference priors) for competing degradation failure model are proposed. • The noninformative priors are shown to have proper posterior distributions and probability matching properties. • Gibbs sampling algorithms for the Jeffreys prior and reference priors are proposed. • The advantages of our model have been illustrated by simulation and real data examples. In this paper, the objective Bayesian method is applied to investigate the competing risks model involving both catastrophic and degradation failures. By modeling soft failure as the Wiener degradation process, and hard failures as a Weibull distribution, we obtain the noninformative priors (Jefferys prior and two reference priors) for the parameters. Moreover, we show that their posterior distributions have good properties and we propose Gibbs sampling algorithms for the Bayesian inference based on the Jefferys prior and two reference priors. Some simulation studies are conducted to illustrate the superiority of objective Bayesian method. Finally, we apply our methods to two real data examples and compare the objective Bayesian estimates with the other estimates. [ABSTRACT FROM AUTHOR]

• We introduce a new package for checking key assumptions in the Cox regression and Fine and Gray regression models. • It implements tests based on cumulative sums of residuals including Anderson-Darling type statistics and is available from CRAN R repositories. • Approximations to the null distribution were obtained using Monte-Carlo methods, and validated using extensive numerical studies. • It may help the spread of recent goodness-of-fit methods in medical applications and other fields, such as finance, criminology and industrial engineering studies. In this paper, we introduce a new R package goftte for goodness-of-fit assessment based on cumulative sums of model residuals useful for checking key assumptions in the Cox regression and Fine and Gray regression models. Monte-Carlo methods are used to approximate the null distribution of cumulative sums of model residuals. To limit the computational burden, the main routines used to approximate the null distributions are implemented in a parallel C++ programming environment. Numerical studies are carried out to evaluate the empirical type I error rates of the different testing procedures. The package and the documentation are available to users from CRAN R repositories. Results from simulation studies suggested that all statistical tests implemented in goftte yielded excellent control of the type I error rate even with modest sample sizes with high censoring rates. As compared to other R packages goftte provides new useful method for testing functionals, such as Anderson-Darling type test statistics for checking assumptions about proportional (sub-) distribution hazards. Approximations for the null distributions of test statistics have been validated through simulation experiments. Future releases will provide similar tools for checking model assumptions in multiplicative intensity models for recurrent data. The package may help to spread the use of recent advocated goodness-of-fit techniques in semiparametric regression for time-to-event data. [ABSTRACT FROM AUTHOR]

• A new Weibull inter-arrival shock process is proposed to model the competing risk process. • The closed forms of reliability function are derived in three shock failure models. • Optimal renewal age is derived numerically by minimizing the long run system cost. In this paper, a new Weibull inter-arrival shock process is proposed for modeling the competing risk process. The dependent competing failure/risk processes exists in many systems and the reliability modeling for those processes has attracted much attention in the recent years. However, the arrivals of random shocks are usually modeled as Poisson process which indicates the constant hazard rate of shock inter-arrival time. Our proposed Weibull inter-arrival shock process generalized the Poisson shock process and can deal with the cases when the shock count data are over-dispersion or under-dispersion. On the other hand, the dependency between the soft failure process and hard failure process is emphasized by assuming the linear dependent damage size. In four different hard failure models, analytic forms of the reliability functions are derived by using the polynomial expansion. The maintenance optimization for the developed model is discussed under different shock failure mechanisms. Numerical examples based on a micro-engine are also presented to illustrate the proposed model. [ABSTRACT FROM AUTHOR]

Abstract: Failure data are often modeled using continuous distributions. However, a discrete distribution can be appropriate for modeling interval or grouped data. When failure data come from a complex system, a simple discrete model can be inappropriate for modeling such data. This paper presents two types of discrete distributions. One is formed by exponentiating an underlying distribution, and the other is a two-fold competing risk model. The paper focuses on two special distributions: (a) exponentiated Poisson distribution and (b) competing risk model involving a geometric distribution and an exponentiated Poisson distribution. The competing risk model has a decreasing-followed-by-unimodal mass function and a bathtub-shaped failure rate. Five classical data sets on bus-motor failures can be simultaneously and appropriately fitted by a general 5-parameter competing risk model with the parameters being functions of the number of successive failures. The lifetime and aging characteristics of the fitted distribution are analyzed. [Copyright &y& Elsevier]

Abstract: Reliability analysis is plagued by a lack of accurate data, leading to suboptimal parameter estimates and inaccurate decisions about replacement intervals and preventive maintenance activities. This paper discusses some of the problems associated with failure and maintenance data extraction from coal-fired power plant maintenance databases. Data from four generating units were observed for over 5 years and a reasonable number of equipment classes reviewed. The coal mills are identified as significant equipment that affects the availability of the generating units. This paper describes the interplay of events which includes failure modes, failure, repair and operating time. We investigate a database showing operation of coal mills, and give an exploratory data analysis in which we investigate engineering hypotheses related to mill operation. A competing risk probability model is proposed which captures some of the observed features of the systems under study. [Copyright &y& Elsevier]

Abstract: It is well known that, given observable data for a competing risk problem, there is always an independent model consistent with the data. It has been pointed out, however, that this independent model does not necessarily have to be one with proper marginals. One purpose of this paper is to explore the extent to which one might try to use the non-parametric assumption that the marginals are proper in order to test whether or not independence holds. This will lead us naturally to a closely related estimation problem—how we estimate the marginals given that a certain quantile of one variable is reached at the same time as a given quantile of the other variable. The problem will be considered using the copula-based approach of Zheng and Klein. Two different methods are discussed. One is a non-parametric maximum likelihood method. The other is a consistent estimator, called the bilinear adjustment estimator, that can be computed quickly and which thus lends itself more readily to simulation methods such as bootstrapping. The ultimate objective of the work in this paper is to provide an additional analytical tool to understand the effectiveness of preventive maintenance. Preventive maintenance censors component failure data and thus provides an important example of competing risk within the reliability area. [Copyright &y& Elsevier]

Competing risks data is often grouped into clusters, such as geographic regions. Shared frailty models can be used to model the correlation between individuals within each cluster. For the better fitting of the model in the competing risks data, one random effect can be used for every type of event in each cluster. But the correlation between random effects in each cluster should also be taken into account. On the other hand, there may also be a spatial correlation between random effects during geographic regions. In this paper, we use cause-specific hazard spatial frailty model with multivariate conditional autoregressive distribution for frailties via Bayesian approach. Simulation studies are used to assess the regression coefficient estimators as well as the variance and correlation of random effects within the clusters. We apply the proposed model to the analysis of the gastrointestinal cancer data of Iran’s National Institute of Health Research and the Louisiana breast cancer data from the Surveillance Epidemiology and End Results database of the National Cancer Institute. [ABSTRACT FROM AUTHOR]

Objective. Tree-based models belong to common, assumption-free methods of data analysis. Their application in survival data is narrowed to univariate models, which partition the feature space with axis-parallel hyperplanes, meaning that each internal node involves a single feature. In this paper, I extend the idea of oblique survival tree induction for competing risks by modifying a piecewise-linear criterion function. Additionally, the use of tree-based ensembles to analyze the competing events is proposed. Method and materials. Two types of competing risks trees are proposed: a single event tree designed for analysis of the event of interest and a composite event tree, in which all the competing events are taken into account. The induction process is similar, except that the calculation of the criterion function is minimized for the individual tree nodes generation. These two tree types were also used for building the ensembles with aggregated cumulative incidence functions as an outcome. Nine real data sets, as well as a simulated data set, were taken to assess performance of the models, while detailed analysis was conducted on the basis of follicular cell lymphoma data. Results. The evaluation was focused on two measures: the prediction error expressed by an integrated Brier score (IBS), and the ranked measure of predictive ability calculated as a time-truncated concordance index (C–index). The proposed techniques were compared with the existing approaches of the Fine–Gray subdistribution hazard model, Fine–Gray regression model with backward elimination, and random survival forest for competing risks. The results for both the IBS and the C–index indicated statistically significant differences between these methods ( p  < .0001). Conclusions. The prediction error of the individual trees was similar to the other methods, but the results of the C–index differ in comparison to the Fine–Gray subdistribution hazard model and the Fine–Gray regression with backward elimination. The ensembles prediction ability was comparable to existing algorithms, but their IBS values were better than either random survival forest or Fine–Gray regression with backward elimination. [ABSTRACT FROM AUTHOR]

Reliability analysis of balanced system has become a key factor for the safe operation of some important equipment and the perfect completion of some important missions. As some real systems consisting of several subsystems with different levels of performance and under degradation processes when in operations are relatively common, they have received widely concerned in the recent years, but are rarely in the new reliability research field of balanced systems, the researches on the balanced systems by considering multi-state are rare, and even few researches are in combination with degradation processes. In this paper, a new balanced system for the multi-state system under degradation processes by considering new failure criteria is put forth. The system consists of two subsystems and fails when either subsystem enters into absorbing states, a new model is proposed and applied to two special cases by assuming that the thresholds of the sojourn time in upcoming unbalanced subsets are constant and random variables respectively, and this paper is the first to extend balanced systems into competing risks. The related expressions of the reliability indexes are derived by employing the theory of aggregated stochastic processes. Finally, numerical examples are presented and some future research topics are also discussed. [ABSTRACT FROM AUTHOR]

Background and objectives The joint modeling of longitudinal and survival data to assess effects of multiple informative dropout mechanisms on longitudinal outcomes inference has received considerable attention during recent years; related statistical programs to apply these methods have been lacking. This paper provides a SAS macro implementation of a shared parameter model to accommodate the analysis of longitudinal outcomes in the presence of multiple competing survival/dropout events. Methods In this macro, we assumed that the associations between the survival and the longitudinal submodels are linked through a set of shared random effects. The submodel for the longitudinal outcome takes the form of a linear mixed effects model, with specifications for the random intercept and/or random slope. The survival submodel allows up to three different competing causes for dropout, each allowing either an exponential or Weibull parametric baseline hazard function. In addition, information criterion fit statistics AIC and BIC are provided to assist with parametric baseline hazard function selection. Results We illustrate the SAS Macro in a cognitive decline study sensitivity analysis using data from the Atherosclerosis Risk in Communities Neurocognitive Study (ARIC-NCS). In addition, we also conduct a simulation study to show that the joint model provides unbiased parameter estimates when informative dropout exists compared against separate model approach which assumes missing at random dropout mechanisms. Conclusions We have presented a SAS macro to implement a shared parameter model for a longitudinal outcome and multiple cause-specific dropouts and made the macro code freely available for download. [ABSTRACT FROM AUTHOR]

In this paper, statistical inference of a competing risks model is developed based on a unified hybrid censoring scheme when the latent failure times follow a general family of inverted exponentiated distributions, which covers a wide range of lifetime distributions. Point and interval estimation methods for estimating the model parameters based on maximum likelihood and Bayesian approaches under non-restricted and restricted parameter spaces are developed. The Bayes estimates are obtained under the squared error loss function with non-informative and informative prior distributions. The existence and uniqueness of the maximum likelihood estimates of the model parameters are proved. A Monte Carlo simulation study is carried out to evaluate the performance of the proposed estimation procedures. To illustrate the proposed inferential procedures, a real data analysis is provided. Finally, some concluding remarks and future research directions are presented. • Competing risks model based on unified hybrid censoring scheme. • Frequentist and Bayesian approached for statistical inference of a general family of inverted exponentiated distributions. • Establish the uniqueness and existence of the maximum likelihood estimates. • Statistical inference under cases with and without ordered restriction on the shape parameters. • Recommendations for the choice of point and interval estimation procedures based on Monte Carlo simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the statistical inference of constant-stress accelerated dependent competing risks model under Type-II hybrid censoring schemes. The dependency structure is modeled by a Marshall–Olkin bivariate Weibull distribution. Both the shape and the scale parameters in the model are assumed to be dependent on the stress levels through a log-linear relationship. The maximum likelihood estimates (MLEs) of the model parameters are derived. Confidence intervals (CIs) of the model parameters are constructed based on the asymptotic normality of MLEs and the bias-corrected percentile bootstrap method. Bayes estimates with the squared error loss function and the highest posterior density (HPD) credible intervals (CIs) are obtained by using an importance sampling method. In addition, the estimates for the accelerated coefficients and the reliability under normal use stress level at mission time are derived. A Monte Carlo simulation study is used to evaluate the performance of the proposed statistical inference methods. A real data example is used to illustrate the methodologies proposed in this paper and to compare the proposed model with the copula model. [ABSTRACT FROM AUTHOR]

The reliability of high-reliable and long-lifespan products in the presence of competing risks are commonly derived based on a known acceleration model and a latent independent competing risks model. For the cases with unknown acceleration models and dependent competing risks, this paper proposes a copula based partially accelerated competing risks model using a tampered random variable transformation. The reliability function and dependence structure of the partially accelerated competing risks data are derived between the real lifetime and the accelerated lifetime of each failure cause. In consideration of the parametric constraints and complicated joint posterior distribution, Hamiltonian Monte Carlo method within MCMC procedures is utilized to obtain Bayesian estimation of model parameters and reliability characteristics by defining unconstrained parameters using a specific transformation function. A simulation study is conducted to investigate the estimation performance, showing that the transformation forms have little influence on the point estimation of model parameters, and the constrained parametric Bayesian estimation method is efficient to evaluate the reliability for the proposed model. Finally, a real data set from a light-emitting diode partially accelerated life test is presented for further illustration of Bayesian reliability analysis. • Copula based step-stress partially accelerated competing risks model is developed. • Properties of reliability function using real and accelerated copulas are studied. • Constrained Bayesian method is proposed to estimate parameters and reliability. • Posterior density function and its partial derivatives in HMC method are derived. [ABSTRACT FROM AUTHOR]

In this paper, complex repairable systems presenting infant failures are considered. Different maintenance activities can be carried out such as corrective maintenances and planned preventive maintenances. The maintenance process is described using the competing risks framework under imperfect maintenance. Asymmetric virtual age models are assumed to characterize the maintenance efficiency. Statistical inference procedures are developed considering whether or not the causes of failure are recorded. Properties of the model are presented along with numerical estimations and an application to real data. [ABSTRACT FROM AUTHOR]

This paper provides an extension of the work of Balakrishnan and Ling [1] by introducing a competing risks model into a one-shot device testing analysis under an accelerated life test setting. An Expectation Maximization (EM) algorithm is then developed for the estimation of the model parameters. An extensive Monte Carlo simulation study is carried out to assess the performance of the EM algorithm and then compare the obtained results with the initial estimates obtained by the Inequality Constrained Least Squares (ICLS) method of estimation. Finally, we apply the EM algorithm to a clinical data, ED01, to illustrate the method of inference developed here. [ABSTRACT FROM AUTHOR]

Traffic incident duration is known to result from a combination of multiple factors, including covariates such as spatial and temporal characteristics, traffic conditions, and existence of secondary accidents but also the clearance method itself. In this paper, a competing risks mixture model is used to investigate the influence of clearance methods and various covariates on the duration of traffic incidents and predict traffic incident duration. The proposed mixture model considers the uncertainty in any of five clearance methods that occurred. The probability of the clearance method is specified in the mixture by using a multinomial logistic model. Three candidate distributions, namely, generalized gamma, Weibull, and log-logistic are tested to determine the most appropriate probability density function of the parametric survival analysis model. The unobserved heterogeneity is also incorporated into the mixture model in a way that allows parameters to vary across observations based on the three candidate distributions. The methods are illustrated with incident data from Singaporean expressways from January 2010 to December 2011. Regression analysis reveals that the probability of different clearance methods and the duration of traffic incidents are both significantly affected by various factors, such as traffic conditions and incident characteristics. Results show that the proposed mixture model is better than the traditional accelerated failure time model, and it predicts traffic incident duration with reasonable accuracy, as shown by the mean average percent error. [ABSTRACT FROM AUTHOR]

In this paper, we seek to propose a model that allows us to evaluate the failure times of a single repairable system represented hierarchically, exposed to competing risks and under a minimal repair framework. Our study can be regarded as an extension of the research presented in Louzada et al. (2019), which comprises the representation of complex systems through a hierarchical structure in series and/or in parallel. For this, we deduce the general form of the model, as well as the likelihood function associated with it, to obtain reliable estimates for the parameters that index the model. In addition, we display the mechanism for generating random numbers based on the presented structure, which enables obtaining point and interval estimates (via parametric bootstrap) in a more convenient way for reliability curves at any level of the system hierarchy. We conduct an extensive Monte Carlo simulation study to evaluate the performance of the proposed maximum likelihood estimators and confidence intervals for the model parameters. Finally, we illustrate the applicability of our model and methods with applications that deal with the reliability modeling of a robotic unit still under development, resulting from a project carried out in partnership between Petrobras and other Brazilian research centers. • Statistical modeling and reliability analysis of single complex repairable systems. • System representation through a hierarchical structure in series and/or in parallel. • Exposition to competing risks and minimal repair regime assuming power-law intensity. • The maximum likelihood estimator and bootstrap techniques are considered. • The approach is used in a data set related to in-pipe robot to assess its reliability. [ABSTRACT FROM AUTHOR]

Having a complete and reliable list of risk factors from routine laboratory blood test for COVID-19 disease severity and mortality is important for patient care and hospital management. It is common to use meta-analysis to combine analysis results from different studies to make it more reproducible. In this paper, we propose to run multiple analyses on the same set of data to produce a more robust list of risk factors. With our time-to-event survival data, the standard survival analysis were extended in three directions. The first is to extend from tests and corresponding p-values to machine learning and their prediction performance. The second is to extend from single-variable to multiple-variable analysis. The third is to expand from analyzing time-to-decease data with death as the event of interest to analyzing time-to-hospital-release data to treat early recovery as a meaningful event as well. Our extension of the type of analyses leads to ten ranking lists. We conclude that 20 out of 30 factors are deemed to be reliably associated to faster-death or faster-recovery. Considering correlation among factors and evidenced by stepwise variable selection in random survival forest, 10 ~ 15 factors seem to be able to achieve the optimal prognosis performance. Our final list of risk factors contain calcium, white blood cell and neutrophils count, urea and creatine, d -dimer, red cell distribution widths, age, ferritin, glucose, lactate dehydrogenase, lymphocyte, basophils, anemia related factors (hemoglobin, hematocrit, mean corpuscular hemoglobin concentration), sodium, potassium, eosinophils, and aspartate aminotransferase. [Display omitted] • An "intra-data" meta analysis is carried out by using prediction performance, being multi-variable, and utilizing time-to-release information. • About 20 blood test factors are associated with COVID-19 severity (or mildness) and mortality, consistent with other reports. [ABSTRACT FROM AUTHOR]

In this paper we propose a class of flexible weight functions for use in comparison of two cumulative incidence functions. The proposed weights allow the users to focus their comparison on an early or a late time period post treatment or to treat all time points with equal emphasis. These weight functions can be used to compare two cumulative incidence functions via their risk difference, their relative risk, or their odds ratio. The proposed method has been implemented in the R-CIFsmry package which is readily available for download and is easy to use as illustrated in the example. [ABSTRACT FROM AUTHOR]

Abstract: The nonparametric predictive inference (NPI) approach for competing risks data has recently been presented, in particular addressing the question due to which of the competing risks the next unit will fail, and also considering the effects of unobserved, re-defined, unknown or removed competing risks. In this paper, we introduce how the NPI approach can be used to deal with situations where units are not all at risk from all competing risks. This may typically occur if one combines information from multiple samples, which can, e.g. be related to further aspects of units that define the samples or groups to which the units belong or to different applications where the circumstances under which the units operate can vary. We study the effect of combining the additional information from these multiple samples, so effectively borrowing information on specific competing risks from other units, on the inferences. Such combination of information can be relevant to competing risks scenarios in a variety of application areas, including engineering and medical studies. [Copyright &y& Elsevier]

Existing maintenance optimization models for single-component repairable systems are extensively studied. However, maintenance optimization in multicomponent reparable systems (MCRS) is still a challenging problem, especially when dealing with stochastic dependent (s -dependent) competing risks between components. This paper develops a novel reliability-centered maintenance optimization model for MCRS operating under s -dependent competing risks. The s -dependency is captured by the joint reliability function constructed using Copula method and unknown parameters are estimated by maximum likelihood estimations (MLE). Maintenance strategies are carried out both at components and system levels. At components level, a preventive maintenance (PM) is performed whenever the reliability of the MCRS reaches a given threshold. PM actions are imperfect and modeled using the hybrid hazard rate approach. At system level, the whole system is preventively replaced after a certain number of PM cycles. The objective of the proposed maintenance strategies is to determine the optimal reliability threshold together with the optimal number of PM cycles that minimize the total expected maintenance cost rate in the infinite time horizon. The optimality conditions of the resulting maintenance optimization problem are formally discussed via two propositions. A case study that investigates a ball screw mechanism with multiple components is provided to validate the proposed approaches. • A novel model for maintenance optimization in multicomponent system is proposed. • Both s -dependent competing risks and imperfect maintenance are accounted for. • Maintenance strategies are conducted both at system and component levels. • Optimization conditions for the proposed model are discussed mathematically. • The hybrid hazard rate model is extended from single to multicomponent system. [ABSTRACT FROM AUTHOR]

Abstract: It is of interest that researchers study competing risks in which subjects may fail from any one of k causes. Comparing any two competing risks with covariate effects is very important in medical studies. In this paper, we develop tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels under the additive risk model by a weighted difference of estimates of cumulative cause-specific hazard rates. Motivated by McKeague et al. (2001), we construct simultaneous confidence bands for the difference of two conditional cumulative incidence functions as a useful graphical tool. In addition, we conduct a simulation study, and the simulation result shows that the proposed procedure has a good finite sample performance. A melanoma data set in clinical trial is used for the purpose of illustration. [Copyright &y& Elsevier]

Abstract: This paper aims to empirically investigate the impact of a vast array of public policies on wireline broadband penetration through a novel and unique dataset covering 30 OECD countries, over the period 1995–2010. Estimation results show that, while both supply- and demand-side policies have a positive effect on broadband penetration, their relative impact depends on the actual stage of broadband diffusion. When an advanced stage is reached, only demand-side policies appear to generate a positive and increasing effect. The analysis also finds that broadband adoption rates increase with the share of the service sector in the economy, with the number of mobile subscriptions and with the degree of market competition. This study thus allows to attain a more refined understanding of past experiences of broadband stimulation that may provide new insights for a selective policy design to promote both the development of traditional broadband and the rollout of next generation networks. [Copyright &y& Elsevier]

Abstract: ZERO TO THREE: National Center for Infants, Toddlers, and Families developed the Court Teams for Maltreated Infants and Toddlers initiative to accelerate the time to permanency for young children in the child welfare system. This paper considers how the Court Teams children exit the child welfare system. Court Teams children from the four initial sites (n=298) are compared to a group of similar cases from the National Survey of Child and Adolescent Well-Being (NSCAW) (n=511). Propensity score weights are combined with a competing risks analysis to isolate program effect on types of foster care exits. Findings indicate that Court Teams cases experience a different pattern of exits from the foster care system. Reunification is the most common type of exit for Court Teams cases (38%) while adoption is the most prevalent for the comparison group (41%). Descriptive data suggest that Court Teams children exit the foster care system faster regardless of the type of exit. The competing risks analysis shows that Court Teams children are significantly more likely to exit foster care for reunification, relative custodianship, and non-relative legal guardianship rather than stay in foster care. [Copyright &y& Elsevier]

Abstract: Competing risks data usually arises in studies in which the death or failure of an individual or an item may be classified into one of k ≥2 mutually exclusive causes. In this paper a simple competing risks distribution is proposed as a possible alternative to the Exponential or Weibull distributions usually considered in lifetime data analysis. We consider the case when the competing risks have a Lindley distribution. Also, we assume that the competing events are uncorrelated and that each subject can experience only one type of event at any particular time. [Copyright &y& Elsevier]

Abstract: The cumulative incidence function is commonly reported in studies with competing risks. The aim of this paper is to compute the treatment-specific cumulative incidence functions, adjusting for potentially imbalanced prognostic factors among treatment groups. The underlying regression model considered in this study is the proportional hazards model for a subdistribution function . We propose estimating the direct adjusted cumulative incidences for each treatment using the pooled samples as the reference population. We develop two SAS macros for estimating the direct adjusted cumulative incidence function for each treatment based on two regression models. One model assumes the constant subdistribution hazard ratios between the treatments and the alternative model allows each treatment to have its own baseline subdistribution hazard function. The macros compute the standard errors for the direct adjusted cumulative incidence estimates, as well as the standard errors for the differences of adjusted cumulative incidence functions between any two treatments. Based on the macros’ output, one can assess treatment effects at predetermined time points. A real bone marrow transplant data example illustrates the practical utility of the SAS macros. [ABSTRACT FROM AUTHOR]

Abstract: Competing risks are frequently encountered in the analysis of survival data. Different methods of analysis can be used in estimated and comparing cumulative incidence functions provided enough information is available as to the times and causes of failure. Algorithms written in R have been developed to handle this type of data. In this paper we propose an R add-on function to the cmprsk package. This function is specifically oriented towards the non-parametric analysis of competing risk data and which provides analyses of three commonly used methods all in one program. We illustrate the use of this function with two examples in oncology and compare the estimates with those provided on the cmprsk and survival package. [ABSTRACT FROM AUTHOR]

Abstract: Statistical inference for the parameters in three competing risks models is considered in this paper. It is assumed that there are more than two causes of failure. The maximum likelihood procedure is used to derive point and asymptotic confidence interval estimates of the unknown parameters. The risks due to each cause of failure are investigated. Two sets of data are analyzed in order to (1) illustrate how the model can be applied and (2) test the hypothesis that the causes of failure follow the Chen distribution rather than the exponential distribution, or the Weibull distribution. [Copyright &y& Elsevier]

Abstract: The recent growth in the number of electrical and electronic devices is viewed as one the priority waste streams in European Union waste management policy. This paper presents the findings of a survey to study domestic habits with respect to Waste Electrical and Electronic Equipment (WEEE) in Spain. A specific problem when performing this estimation arises from the fact that consumers quite often store old appliances at home when they are no longer used. Focusing on four different types of appliance, survival analysis (SA) is used to study both the usage span and the reasons for no longer using each device. The time that the discarded products were kept at home before being disposed of was studied using competing risks (CR) analysis. The results of the analysis provide information on the distribution of the studied variables for the different outcomes as well as the influence exerted by the socio-demographic variables considered. Relations between these characteristics and the storage time of the appliances before disposal emerge based on survey data. For instance, the CR model finds that the storage time of the some appliances (i.e. refrigerator) is related to these social-demographics factors. However, other appliances (i.e. microwave oven) are less influenced by these factors. The attitude and motivation of the respondents to the survey as regards the End-of-Life of appliances were also analysed. A majority of respondents do not store discarded appliances at home. The first reason for storing appliances at home is the possibility of it being useful in the future and the second that the respondents did not know what to do with them. [Copyright &y& Elsevier]

Abstract: In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow the Conway–Maxwell Poisson distribution. This model includes as special cases some of the well-known cure rate models discussed in the literature. Next, we discuss the maximum likelihood estimation of the parameters of this cure rate survival model. Finally, we illustrate the usefulness of this model by applying it to a real cutaneous melanoma data. [Copyright &y& Elsevier]

Abstract: Semiparametric Bayesian models are nowadays a popular tool in event history analysis. An important area of research concerns the investigation of frequentist properties of posterior inference. In this paper, we propose novel semiparametric Bayesian models for the analysis of competing risks data and investigate the Bernstein–von Mises theorem for differentiable functionals of model parameters. The model is specified by expressing the cause-specific hazard as the product of the conditional probability of a failure type and the overall hazard rate. We take the conditional probability as a smooth function of time and leave the cumulative overall hazard unspecified. A prior distribution is defined on the joint parameter space, which includes a beta process prior for the cumulative overall hazard. We first develop the large-sample properties of maximum likelihood estimators by giving simple sufficient conditions for them to hold. Then, we show that, under the chosen priors, the posterior distribution for any differentiable functional of interest is asymptotically equivalent to the sampling distribution derived from maximum likelihood estimation. A simulation study is provided to illustrate the coverage properties of credible intervals on cumulative incidence functions. [Copyright &y& Elsevier]

Abstract: In a rapidly changing environment, competition among enterprises has a tendency towards competing between supply chain systems instead of competing between individual companies. Traditional scheduling models which only address the sequence of jobs to be processed at the production stage under some criteria are no longer suitable and should be extended to cope with the distribution stage after production. Emphasizing on the coordination and integration among various members of a supply chain has become one of the vital strategies for the modern manufacturers to gain competitive advantages. This paper studies the NP-hard problem of the two-stage scheduling in which jobs are processed by two parallel machines and delivered to a customer with the objective of minimizing the makespan . The proposed heuristic algorithm is shown to have a worst-case ratio of 63/40, except for two particular cases. [Copyright &y& Elsevier]