2,386 research outputs found
Failure Inference and Optimization for Step Stress Model Based on Bivariate Wiener Model
In this paper, we consider the situation under a life test, in which the
failure time of the test units are not related deterministically to an
observable stochastic time varying covariate. In such a case, the joint
distribution of failure time and a marker value would be useful for modeling
the step stress life test. The problem of accelerating such an experiment is
considered as the main aim of this paper. We present a step stress accelerated
model based on a bivariate Wiener process with one component as the latent
(unobservable) degradation process, which determines the failure times and the
other as a marker process, the degradation values of which are recorded at
times of failure. Parametric inference based on the proposed model is discussed
and the optimization procedure for obtaining the optimal time for changing the
stress level is presented. The optimization criterion is to minimize the
approximate variance of the maximum likelihood estimator of a percentile of the
products' lifetime distribution
Threshold Regression for Survival Analysis: Modeling Event Times by a Stochastic Process Reaching a Boundary
Many researchers have investigated first hitting times as models for survival
data. First hitting times arise naturally in many types of stochastic
processes, ranging from Wiener processes to Markov chains. In a survival
context, the state of the underlying process represents the strength of an item
or the health of an individual. The item fails or the individual experiences a
clinical endpoint when the process reaches an adverse threshold state for the
first time. The time scale can be calendar time or some other operational
measure of degradation or disease progression. In many applications, the
process is latent (i.e., unobservable). Threshold regression refers to
first-hitting-time models with regression structures that accommodate covariate
data. The parameters of the process, threshold state and time scale may depend
on the covariates. This paper reviews aspects of this topic and discusses
fruitful avenues for future research.Comment: Published at http://dx.doi.org/10.1214/088342306000000330 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Reliability Estimation of Rotary Lip Seal in Aircraft Utility System Based on Time-Varying Dependence Degradation Model and Its Experimental Validation
With several attractive properties, rotary lip seals are widely used in aircraft utility system, and their reliability estimation has drawn more and more attention. This work proposes a reliability estimation approach based on time-varying dependence analysis. The dependence between the two performance indicators of rotary lip seals, namely leakage rate and friction torque, is modeled by time-varying copula function with polynomial to denote the time-varying parameters, and an efficient copula selection approach is utilized to select the optimal copula function. Parameter estimation is carried out based on a Bayesian method and the reliability during the whole lifetime is calculated based on a Monte Carlo method. Degradation test for rotary lip seal is conducted and the proposed model is validated by test data. The optimal copula function and optimal order of polynomial are determined based on test data. Results show that this model is effective in estimating the reliability of rotary lip seals and can achieve a better goodness of fit
Statistical Degradation Models for Electronics
With increasing presence of electronics in modern systems and in every-day products, their reliability is inextricably dependent on that of their electronics. We develop reliability models for failure-time prediction under small failure-time samples and information on individual degradation history. The development of the model extends the work of Whitmore et al. 1998, to incorporate two new data-structures common to reliability testing. Reliability models traditionally use lifetime information to evaluate the reliability of a device or system. To analyze small failure-time samples within dynamic environments where failure mechanisms are unknown, there is a need for models that make use of auxiliary reliability information. In this thesis we present models suitable for reliability data, where degradation variables are latent and can be tracked by related observable variables we call markers.
We provide an engineering justification for our model and develop parametric and predictive inference equations for a data-structure that includes terminal observations of the degradation variable and longitudinal marker measurements. We compare maximum likelihood estimation and prediction results obtained by Whitmore et. al. 1998 and show improvement in inference under small sample sizes. We introduce modeling of variable failure thresholds within the framework of bivariate degradation models and discuss ways of incorporating covariates.
In the second part of the thesis we investigate anomaly detection through a Bayesian support vector machine and discuss its place in degradation modeling. We compute posterior class probabilities for time-indexed covariate observations, which we use as measures of degradation. Lastly, we present a multistate model used to model a recurrent event process and failure-times. We compute the expected time to failure using counting process theory and investigate the effect of the event process on the expected failure-time estimates
LED Lighting System Reliability Modeling and Inference via Random Effects Gamma Process and Copula Function
Light emitting diode (LED) lamp has attracted increasing interest in the field of lighting systems due to its low energy and long lifetime. For different functions (i.e., illumination and color), it may have two or more performance characteristics. When the multiple performance characteristics are dependent, it creates a challenging problem to accurately analyze the system reliability. In this paper, we assume that the system has two performance characteristics, and each performance characteristic is governed by a random effects Gamma process where the random effects can capture the unit to unit differences. The dependency of performance characteristics is described by a Frank copula function. Via the copula function, the reliability assessment model is proposed. Considering the model is so complicated and analytically intractable, the Markov chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about actual LED lamps data is given to demonstrate the usefulness and validity of the proposed model and method
Reliability Estimation of Reciprocating Seals Based on Multivariate Dependence Analysis and It\u27s Experimental Validation
Accurate reliability estimation for reciprocating seals is of great significance due to their wide use in numerous engineering applications. This work proposes a reliability estimation method for reciprocating seals based on multivariate dependence analysis of different performance indicators. Degradation behavior corresponding to each performance indicator is first described by the Wiener process. Dependence among different performance indicators is then captured using D-vine copula, and a weight-based copula selection method is utilized to determine the optimal bivariate copula for each dependence relationship. A two-stage Bayesian method is used to estimate the parameters in the proposed model. Finally, a reciprocating seal degradation test is conducted, and the proposed reliability estimation approach is validated by test data. Results show that the proposed model is accurate and effective in estimating the reliability of reciprocating seals
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