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G Mohtashami R Borzadaran - One of the best experts on this subject based on the ideXlab platform.
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some results on upper bounds for the variance of functions of the Residual Life random variables
Journal of Computational and Applied Mathematics, 2017Co-Authors: Faranak Goodarzi, Mohammad Amini, G Mohtashami R BorzadaranAbstract:As a measure of maximum dispersion from the mean, upper bounds on variance have applications in all areas of theoretical and applied mathematical sciences. In this paper, we obtain an upper bound for the variance of a function of the Residual Life random variable Xt. Since one of the most important types of system structures is the parallel structure, we give an upper bound for the variance of a function of this system consisting of n identical and independent components, under the condition that, at time t, nr+1, r=1,,n of its components are still working. Here we characterize the Pareto distribution through Cauchys functional equation for mean Residual Life. It is shown that the underlying distribution function F can be recovered from the proposed mean and variance Residual Life function of the system for r=1. Moreover, we see that the variance Residual Lifetime of the components of the system is not necessarily a decreasing function of r and increasing of n for r=1, unlike their mean Residual Lifetime. As an application, the variance of XF1(p0) for all p0[0,1) is investigated and also a real data analysis is presented.
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reversed variance Residual Life function and its properties in discrete Lifetime models
International Journal of Quality & Reliability Management, 2013Co-Authors: M Khorashadizadeh, A Rezaei H Roknabadi, G Mohtashami R BorzadaranAbstract:Purpose – In reliability studies, interests in discrete failure data came relatively late in comparison to its continuous analogue. Also, discrete failure data arise in several common situations. So, in this paper the authors try to study some reliability concepts such as reversed variance and reversed mean Residual Life functions based on discrete Lifetime random variable.Design/methodology/approach – Supposed T be a non‐negative discrete random variable, then based on reversed Residual random variable Tk*=(k−T|T≤k), some useful and applicable relations and bounds are achieved.Findings – In this paper, the authors study the reversed variance Residual Life in discrete Lifetime distributions, the results of which are not similar to the continuous case. Its relationship with reversed mean Residual Life and reversed Residual coefficient of variation are obtained. Also, its monotonicity and the associated ageing classes of distributions are discussed. Some characterization results of the class of increasing r...
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variance Residual Life function based on double truncation
Metron-International Journal of Statistics, 2013Co-Authors: M Khorashadizadeh, A Rezaei H Roknabadi, G Mohtashami R BorzadaranAbstract:Since, most of the real observations in industrial and reliability studies, are left, right or doubly truncated data, studying the reliability concepts of the components of a system or a device based on conditional random variables, are important and usual. One of the important and applicable reliability concepts, that recently has gathered the attention of the researchers, is the variance Residual Life. In this paper, we try to study some of the reliability properties of the variance Residual Life based on doubly truncated data. Its monotonicity properties and relations with doubly truncated mean Residual Life and doubly truncated Residual coefficient of variation are discussed. Furthermore, the lower (upper) bound for it under some conditions is obtained. We also discuss and find the similar results for discrete random ageing which its differences with the continuous case, are noticeable. Finally, some examples due to this subject are mentioned.
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variance Residual Life function in discrete random ageing
Metron-International Journal of Statistics, 2010Co-Authors: M Khorashadizadeh, A Rezaei H Roknabadi, G Mohtashami R BorzadaranAbstract:The random variable X t = X − t¦X ≥ t, which is called the Residual Life random variable, has gathered the attention of most researchers in reliability. The mean and the variance of this variable in continuous distribution have been studied by several authors. But, in discrete case, only in recent years, some studies have been done for the mean of this variable. In this paper, we define and study the properties of variance of T k = T − k¦T ≥ k where T is a discrete random variable. Besides similar results for discrete and continuous Lifetime distributions, relationships with its mean, monotonicity and the associated ageing classes of distributions are obtained for discrete cases. Furthermore, some characterization results about the class of increasing (decreasing) variance Residual Life distributions based on mean Residual Life and Residual coefficient of variation, are presented and the lower and upper bound for them are achieved.
Nagi Gebraeel - One of the best experts on this subject based on the ideXlab platform.
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prognostic degradation models for computing and updating Residual Life distributions in a time varying environment
IEEE Transactions on Reliability, 2008Co-Authors: Nagi GebraeelAbstract:This paper presents a degradation modeling framework for computing condition-based Residual Life distributions of partially degraded systems and/or components functioning under time-varying environmental and/or operational conditions. Our approach is to mathematically model degradation-based signals from a population of components using stochastic models that combine three main sources of information: real-time degradation characteristics of component obtained by observing the component's in-situ degradation signal, the degradation characteristics of the component's population, and the real-time status of the environmental conditions under which the component is operating. Prior degradation information is used to estimate the model coefficients. The resulting generalized stochastic degradation model is then used to predict an initial Residual Life distribution for the component being monitored. In-situ degradation signals, along with real-time information related to the environmental conditions, are then used to update the Residual Life distributions in real-time. Because these updated distributions capture current health information and the latest environmental conditions, they provide precise Lifetime estimates. The performance of the proposed models is evaluated using real world vibration-based degradation signals from a rotating machinery application.
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a neural network degradation model for computing and updating Residual Life distributions
IEEE Transactions on Automation Science and Engineering, 2008Co-Authors: Nagi Gebraeel, Mark LawleyAbstract:The ability to accurately estimate the Residual Life of partially degraded components is arguably the most challenging problem in prognostic condition monitoring. This paper focuses on the development of a neural network-based degradation model that utilizes condition-based sensory signals to compute and continuously update Residual Life distributions of partially degraded components. Initial predicted failure times are estimated through trained neural networks using real-time sensory signals. These estimates are used to derive a prior failure time distribution for the component that is being monitored. Subsequent failure time estimates are then utilized to update the prior distributions using a Bayesian approach. The proposed methodology is tested using real world vibration-based degradation signals from rolling contact thrust bearings. The proposed methodology performed favorably when compared to other reliability-based and statistical-based benchmarks.
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sensory updated Residual Life distributions for components with exponential degradation patterns
IEEE Transactions on Automation Science and Engineering, 2006Co-Authors: Nagi GebraeelAbstract:Research on interpreting data communicated by smart sensors and distributed sensor networks, and utilizing these data streams in making critical decisions stands to provide significant advancements across a wide range of application domains such as maintenance management. In this paper, a stochastic degradation modeling framework is developed for computing and continuously updating Residual Life distributions of partially degraded components. The proposed degradation methodology combines population-specific degradation characteristics with component-specific sensory data acquired through condition monitoring in order to compute and continuously update remaining Life distributions of partially degraded components. Two sensory updating procedures are developed and validated using real-world vibration-based degradation information acquired from rolling element thrust bearings. The results are compared with two benchmark policies and illustrate the benefits of the sensory updated degradation models proposed in this paper. Note for Practitioners-The proposed degradation-based prognostic methodology provides a comprehensive assessment of the current and future degradation states of partially degraded components by combining population-specific degradation or reliability information with real-time sensory health monitoring data. It is specifically beneficial for cases where degradation occurs in a cumulative manner and the degradation signal can be approximated by an exponential functional form. To implement this methodology, it is necessary: 1) to identify the physical phenomena associated with the evolution of the degradation process (spalling and wear herein); 2) choose the appropriate condition monitoring technology to monitor this phenomena (accelerometers); 3) identify a characteristic pattern in the sensory information to help develop a degradation signal (exponential growth); and 4) identify a failure threshold associated with the degradation signal. The first step in implementing this prognostic methodology is to obtain prior information related to stochastic parameters f the exponential model. This may require fitting some sample degradation signals with an exponential functional form and noting the values of the exponential parameters, or using subjective prior distributions. The second step is to acquire sensory information and begin updating the prior distribution. The updating frequency will dictate which expressions are used to compute the posterior distributions. Once the posterior means, variances, and correlation are computed, the truncated CDF of the Residual Life can be evaluated using (10) and (11). Note that the truncation is necessary to preclude negative values of the remaining Life. Practitioners can implement this methodology using a simple spreadsheet. Since the Residual Life distributions are skewed, it is reasonable to utilize the median as a measure of the central tendency and, hence, an alternative estimate for the expected value of the remaining Life
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Residual Life distributions from component degradation signals a bayesian approach
Iie Transactions, 2005Co-Authors: Nagi Gebraeel, Mark Lawley, Jennifer K RyanAbstract:Real-time condition monitoring is becoming an important tool in maintenance decision-making. Condition monitoring is the process of collecting real-time sensor information from a functioning device in order to reason about the health of the device. To make effective use of condition information, it is useful to characterize a device degradation signal, a quantity computed from condition information that captures the current state of the device and provides information on how that condition is likely to evolve in the future. If properly modeled, the degradation signal can be used to compute a Residual-Life distribution for the device being monitored, which can then be used in decision models. In this work, we develop Bayesian updating methods that use real-time condition monitoring information to update the stochastic parameters of exponential degradation models. We use these degradation models to develop a closed-form Residual-Life distribution for the monitored device. Finally, we apply these degradation...
M Khorashadizadeh - One of the best experts on this subject based on the ideXlab platform.
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reversed variance Residual Life function and its properties in discrete Lifetime models
International Journal of Quality & Reliability Management, 2013Co-Authors: M Khorashadizadeh, A Rezaei H Roknabadi, G Mohtashami R BorzadaranAbstract:Purpose – In reliability studies, interests in discrete failure data came relatively late in comparison to its continuous analogue. Also, discrete failure data arise in several common situations. So, in this paper the authors try to study some reliability concepts such as reversed variance and reversed mean Residual Life functions based on discrete Lifetime random variable.Design/methodology/approach – Supposed T be a non‐negative discrete random variable, then based on reversed Residual random variable Tk*=(k−T|T≤k), some useful and applicable relations and bounds are achieved.Findings – In this paper, the authors study the reversed variance Residual Life in discrete Lifetime distributions, the results of which are not similar to the continuous case. Its relationship with reversed mean Residual Life and reversed Residual coefficient of variation are obtained. Also, its monotonicity and the associated ageing classes of distributions are discussed. Some characterization results of the class of increasing r...
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variance Residual Life function based on double truncation
Metron-International Journal of Statistics, 2013Co-Authors: M Khorashadizadeh, A Rezaei H Roknabadi, G Mohtashami R BorzadaranAbstract:Since, most of the real observations in industrial and reliability studies, are left, right or doubly truncated data, studying the reliability concepts of the components of a system or a device based on conditional random variables, are important and usual. One of the important and applicable reliability concepts, that recently has gathered the attention of the researchers, is the variance Residual Life. In this paper, we try to study some of the reliability properties of the variance Residual Life based on doubly truncated data. Its monotonicity properties and relations with doubly truncated mean Residual Life and doubly truncated Residual coefficient of variation are discussed. Furthermore, the lower (upper) bound for it under some conditions is obtained. We also discuss and find the similar results for discrete random ageing which its differences with the continuous case, are noticeable. Finally, some examples due to this subject are mentioned.
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variance Residual Life function in discrete random ageing
Metron-International Journal of Statistics, 2010Co-Authors: M Khorashadizadeh, A Rezaei H Roknabadi, G Mohtashami R BorzadaranAbstract:The random variable X t = X − t¦X ≥ t, which is called the Residual Life random variable, has gathered the attention of most researchers in reliability. The mean and the variance of this variable in continuous distribution have been studied by several authors. But, in discrete case, only in recent years, some studies have been done for the mean of this variable. In this paper, we define and study the properties of variance of T k = T − k¦T ≥ k where T is a discrete random variable. Besides similar results for discrete and continuous Lifetime distributions, relationships with its mean, monotonicity and the associated ageing classes of distributions are obtained for discrete cases. Furthermore, some characterization results about the class of increasing (decreasing) variance Residual Life distributions based on mean Residual Life and Residual coefficient of variation, are presented and the lower and upper bound for them are achieved.
R N Rattihalli - One of the best experts on this subject based on the ideXlab platform.
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nonparametric estimation of a bivariate mean Residual Life function
Journal of the American Statistical Association, 2002Co-Authors: H V Kulkarni, R N RattihalliAbstract:In many statistical studies involving failure data, mean Residual Life function is of prime importance. The bivariate mean Residual Life function has received relatively less attention in the literature. In this article we use a simple nonparametric estimator for a bivariate mean Residual Life function. The estimator is shown to be uniformly strongly consistent and, on proper normalization, converges weakly to a zero-mean bivariate Gaussian process. Numerical studies demonstrate that the estimator performs well even for moderate sample sizes. Results are applied to a real dataset related to cancer recurrence. A few supporting results in connection with weak convergence proved in Appendix C may be of independent interest.
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characterization of bivariate mean Residual Life function
IEEE Transactions on Reliability, 1996Co-Authors: H V Kulkarni, R N RattihalliAbstract:This paper gives a counter example to invalidate a claim of Nair and Nair (1989) regarding a characterization of bivariate mean Residual-Life function (BMRLF). The authors characterize BMRLF of an absolutely continuous Life-time distribution and, based on the form of the BMRLF, introduce probability models for bivariate Life-time data.
M. Kayid - One of the best experts on this subject based on the ideXlab platform.
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A Nonparametric Estimator of Bivariate Quantile Residual Life Model with Application to Tumor Recurrence Data Set
Journal of Classification, 2020Co-Authors: M. Kayid, M. Shafaei Noughabi, A. M. AbouammohAbstract:Recently, Shafaei and Kayid (Statistical Papers, 2017) introduced and studied the bivariate quantile Residual Life model. It has been shown that two suitable bivariate quantile Residual Life functions characterize the underlying distribution uniquely. In the current investigation, we first propose a nonparametric estimator of this new model. The estimator is strongly consistent and, on proper normalization, asymptotically follows a bivariate Gaussian process. An extensive simulation study has been conducted to discuss the behavior of the estimator. Finally, to illustrate the applications, a real data set related to a tumor recurrence trial is presented and discussed.
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bivariate quantile Residual Life a characterization theorem and statistical properties
Statistical Papers, 2019Co-Authors: Shafaei M Noughabi, M. KayidAbstract:The concept of $$\alpha $$ -quantile Residual Life measure plays an important role in statistics, reliability and Life testing. In this investigation, the bivariate $$\alpha $$ -quantile Residual Life measure has been proposed and studied. It has been shown that two suitable bivariate quantile Residual Life characterize the underlying distribution uniquely. Moreover, some concerned statistical and reliability properties have been proven
