Conditional Mean Residual Life Research Articles

Reliability estimation of a system subject to condition monitoring with two dependent failure modes

ABSTRACTA new competing risk model is proposed to calculate the Conditional Mean Residual Life (CMRL) and Conditional Reliability Function (CRF) of a system subject to two dependent failure modes, namely, degradation failure and catastrophic failure. The degradation process can be represented by a three-state continuous-time stochastic process having a healthy state, a warning state, and a failure state. The system is subject to condition monitoring at regular sampling times that provides partial information about the system is working state and only the failure state is observable. To model the dependency between two failure modes, it is assumed that the joint distribution of the time to catastrophic failure and sojourn time in the healthy state follow Marshal–Olkin bivariate exponential distributions. The Expectation–Maximization algorithm is developed to estimate the model's parameters and the explicit formulas for the CRF and CMRL are derived in terms of the posterior probability that the system is in the warning state. A comparison with a previously published model is provided to illustrate the effectiveness of the proposed model using real data.

Nonparametric estimation of the conditional mean residual life function with censored data

The conditional mean residual life (MRL) function is the expected remaining lifetime of a system given survival past a particular time point and the values of a set of predictor variables. This function is a valuable tool in reliability and actuarial studies when the right tail of the distribution is of interest, and can be more informative than the survivor function. In this paper, we identify theoretical limitations of some semi-parametric conditional MRL models, and propose two nonparametric methods of estimating the conditional MRL function. Asymptotic properties such as consistency and normality of our proposed estimators are established. We investigate via simulation study the empirical properties of the proposed estimators, including bootstrap pointwise confidence intervals. Using Monte Carlo simulations we compare the proposed nonparametric estimators to two popular semi-parametric methods of analysis, for varying types of data. The proposed estimators are demonstrated on the Veteran's Administration lung cancer trial.

Discrete Models Characterized by Bivariate Conditional Mean Residual Life

The concept of the univariate mean residual life (mrl) function is generalized to the bivariate case in the discrete set up and its properties are studied. This bivariate mrl is utilized to characterize bivariate distributions by its functional form .

On some association measures in bivariate distributions and their relationships

In this paper, we study three time-dependent measures of association, viz. the odds ratio, conditional mean residual life and the conditional probability. We examine conditions under which these measures exceed unity. We also obtain a class of distributions for which the components of the hazard gradient (mean residual lives) are proportional. Finally, some examples are provided to illustrate the results.

Conditional mean residual life functions

In this paper a conditional mean residual life in the context of reliability theory is introduced. The properties of the conditional mean residual life are studied. Various characterizations by the conditional mean residual life are proposed.

An approach to the retention problem based on claim experience

In the present note it is shown that for a statistical treatment of the retention probelm it is sufficient and, moreover, highly advantageous to consider the conditional mean residual life function.

Sensitivity of the (Q, R) inventory model to penalty cost parameter

AbstractThis paper treats an approximate continuous review inventory model with backlogging of excess demand and stochastic leadtime. The major result derived is that the behavior of the optimal order size with respect to the shortage cost parameter is determined solely by the “conditional mean residual life” function corresponding to the leadtime demand distribution. Some minor results and illustrative examples are also included.