Time-censored Data Research Articles

Inference and optimal design of accelerated life test using the geometric process for power rayleigh distribution under time-censored data

In this paper, a new extension of the standard Rayleigh distribution called the Power Rayleigh distribution (PRD) is investigated for the accelerated life test (ALT) using the geometric process (GP) under Type-I censored data. Point estimates of the formulated model parameters are obtained via the likelihood estimation approach. In addition, interval estimates are obtained based on the asymptotic normality of the derived estimators. To evaluate the performance of the obtained estimates, a simulation study of 4, 5 and 6 levels of stress is conducted for ALT in different combinations of sample sizes and censored times. Simulation results indicated that point estimates are very close to their initial true values, have small relative errors, are robust and are efficient for estimating the model parameters. Similarly, the interval estimates have small lengths and their coverage probabilities are almost converging to their 95% nominated significance level. The estimation procedure is also improved by the approach of finding optimum values of the acceleration factor to have optimum values for the reliability function at the specified design stress level. This work confirms that PRD has the superiority to model the lifetimes in ALT using GP under any censoring scheme and can be effectively used in reliability and survival analysis.

Estimation of self-exciting point processes from time-censored data.

Self-exciting point processes, widely used to model arrival phenomena in nature and society, are often difficult to identify. The estimation becomes even more challenging when arrivals are recorded only as bin counts on a finite partition of the observation interval. In this paper, we propose the recursive identification with sample correction (RISC) algorithm for the estimation of process parameters from time-censored data. In every iteration, a synthetic sample path is generated and corrected to match the observed bin counts. Then the process parameters update and a unique iteration is performed to successively approximate the stochastic characteristics of the observed process. In terms of finite-sample approximation error, the proposed RISC framework performs favorably over extant methods, as well as compared to a naïve locally uniform sample redistribution. The results of an extensive numerical experiment indicate that the reconstruction of an intrabin history based on the conditional intensity of the process is crucial for attaining superior performance in terms of estimation error.

Estimation of step-stress life testing model using time-censoring: A Bayesian approach

Accelerated life tests (ALTs) of highly reliable products or materials are effective testing techniques to gather failure data rapidly in a limited time period. Also, partially accelerated life tests (PALTs) can enable us to achieve this goal without putting all test units under severe conditions. This article considers both frequent and Bayesian estimations of the step-stress PALTs model using time-censored data from generalized exponential distribution (GED). The maximum likelihood and Bayesian estimates of the model parameters are obtained. The posterior means and posterior variances are computed under the squared error (SE) loss function using Lindley’s procedure. The performance of the estimators is evaluated numerically for different parameter values and different sample sizes via their mean squared error (MSE). In addition, the average confidence intervals lengths (ACIL) of the model parameters are also obtained. For illustrative purposes, a simulation study is given.

Bootstrap Interval Estimation of Reliability for Numerical Controlled Machine Tools Considering the Time-censored Data

Bootstrap Interval Estimation of Reliability for Numerical Controlled Machine Tools Considering the Time-censored Data

Optimum Time-Censored Modified Ramp-Stress ALT for the Burr Type XII Distribution with Warranty: A Goal Programming Approach

Accelerated life tests (ALTs) are used to make timely assessments of the life time distribution of highly reliable materials and components. Much of the previous work on ALTs has focused on constant-stress, step-stress, ramp-stress schemes and their various combinations. In the literature ramp-stress ALTs that have been formulated can be conducted when more than one test chambers are available; installation of which may prove to be costly. Even when one test chamber is used the stress rate remains constant throughout the duration of the experiment. It is not only necessary but imperative to examine if the test specimen is able to withstand differing stress conditions with the passage of time. This paper therefore, presents an optimal design of multi-objective modified ramp-stress ALT model with weighted goal programming approach. The modified ramp-stress uses one test chamber in place of the various chambers used in simple ramp-stress ALT thus saving experimental cost. With the market being increasingly competitive the emphasis today is on goal attainment with minimum deviations. Goal programming is a method to solve multi-objective problems that has applications in varied fields of engineering and operational research. The optimal plan consists in finding out relevant experimental variables, namely, stress rate, stress rate change point and warranty period, by using goal programming on weighted sum of variance of reliability function and expected warranty cost with pre-specified mission time under normal operating conditions. The Burr type XII life distribution and time-censored data have been used for the purpose. Burr type XII life distribution has been found appropriate for accelerated life testing experiments. The method developed has been explained using a numerical example and sensitivity analysis carried out. Comparative study has also been done to highlight the merits of the proposed model.

Two modified estimators of reliability function with exponential failure model based on prior information and time-censored data

In this article, we have assumed that the observations are carried out for a period of time T, and when a unit failed, it was replaced with a new identical unit. We have considered the exponential distribution of failure, and we have proposed two estimators of reliability function ([Formula: see text]) by using time-censored data when a prior value (uncertain prior information) about the unknown parameter [Formula: see text] was previously available. The expressions for the bias, risk and relative efficiency were obtained. The investigation concerning the improvement of the proposed estimators of [Formula: see text] on the bases of the criterion of bias ratio, risk and relative efficiency under different cases showed that the proposed estimators were better than the classical estimators. The conclusions, concluding remarks and limitations were then reported.

Accelerated Life Test Plans Robust to Misspecification of the Stress—Life Relationship

This article discusses methodology for deriving the asymptotic distribution of maximum likelihood estimators of model parameters in accelerated life tests (ALTs) when the form of the stress–life relationship is misspecified. If the practitioner can describe possible departures from an assumed ALT model, often linear in the appropriately transformed accelerating variable, then the results here can be used to obtain ALT plans that provide protection against potential bias and loss in estimation efficiency. General results are derived for log location-scale distributions and time-censored data, whereas specific results are presented for the lognormal and Weibull distributions. In a practical ALT situation, the methodology is applied to derive robust test plans based on minimizing asymptotic bias, asymptotic variance, or asymptotic mean squared error. Test plans are evaluated in terms of bias, efficiency, extrapolation to use level, and expected number failing.

Planning accelerated life tests for censored two-parameter exponential distributions

We consider optimal test plans involving life distributions with failure-free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two-parameter exponential distribution and the stress-life relationship is given by the inverse power law model. Near-optimal test plans for constant-stress ALT under both failure-censoring and time-censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure-censored and time-censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near-optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal-allocation plan. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 169–186, 1999

Homogeneity tests for scale parameters of 2-parameter exponential populations under time censoring

Comparing two or more scale parameters of exponential distributions is often important in life-testing problems. This paper considers tests for the equality of several exponential scale parameters in presence of unspecified location parameters based on time-censored data. Using a conditional approach, various test statistics are derived. The Monte Carlo studies were carried out for comparing the powers of these statistics with the power of the usual likelihood ratio statistic. The power of the usual likelihood ratio test was better than those of the other tests for various combinations of mean number of failures. >