TITLE

Optimum Burn-in Time for a Bathtub Shaped Failure Distribution

AUTHOR(S)
Bebbington, Mark; Lai, Chin-Diew; Zitikis, Ricardas
PUB. DATE
March 2007
SOURCE
Methodology & Computing in Applied Probability;Mar2007, Vol. 9 Issue 1, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
An important problem in reliability is to define and estimate the optimal burn-in time. For bathtub shaped failure-rate lifetime distributions, the optimal burn-in time is frequently defined as the point where the corresponding mean residual life function achieves its maximum. For this point, we construct an empirical estimator and develop the corresponding statistical inferential theory. Theoretical results are accompanied with simulation studies and applications to real data. Furthermore, we develop a statistical inferential theory for the difference between the minimum point of the corresponding failure rate function and the aforementioned maximum point of the mean residual life function. The difference measures the length of the time interval after the optimal burn-in time during which the failure rate function continues to decrease and thus the burn-in process can be stopped.
ACCESSION #
24242881

 

Related Articles

  • Stability of characterization of Weibull distribution. Romanas, Yanushkevichius; Olga, Yanushkevichiene // Statistical Papers;Jul2005, Vol. 46 Issue 3, p459 

    If assumptions of the theorem are satisfied not exactly but only approximately, then may we state that the conclusion of the theorem is also fulfilled approximately? Theorems, in which the problems of this kind are considered, are called stability theorems. The present paper presents some...

  • Proposed Estimators of the shape, location and scale Parameters of the Weibull Distribution. Zouaoui, Chikr el-Mezouar // International Journal of Statistics & Systems;2007, Vol. 2 Issue 2, p157 

    The shape, location and scale parameters of the weibull distribution are estimated by the using the method of moments, new estimators are proposed. We compare them with Cran estimators, using simulation.

  • Large deviation theory for non-regular location shift family. Hayashi, Masahito // Annals of the Institute of Statistical Mathematics;Aug2011, Vol. 63 Issue 4, p689 

    We apply non-regular extensions of the large deviation theory to non-regular location shift families. Our calculation contains the location shift families generated by Beta distribution, Weibull distribution, and Gamma distribution. We point out the optimal estimator depends on the choice of our...

  • ESTIMATION OF THE PARAMETERS OF MIXED EXPONENTIATED WEIBULL AND EXPONENTIATED EXPONENTIAL FROM CENSORED TYPE I SAMPLES. Rashwan, Nasr Ibrahim // Advances & Applications in Statistics;2015, Vol. 47 Issue 1, p1 

    Mixture of life distributions occur when two different causes of failure are present. The aim of this paper is to introduce a method of mixing model of exponentiated Weibull and exponentiated exponential (EWEE) distributions. The mixture model has a number of parameters which include shape and...

  • Modified Maximum Likelihood Prediction for Type II Censored Data under the Weibull Distribution. Jyun-You Chiang // International Journal of Intelligent Technologies & Applied Stat;2010, Vol. 3 Issue 1, p17 

    The paper develops three new modified maximum likelihood predictors (MMLPs) to predict unobserved order statistics from Weibull samples with type II censoring. A Monte Carlo simulation study is conducted to evaluate the performance of the proposed prediction method. When the sample size is...

  • Nested Renewal Processes with Special Erlangian Densities. Bendell, A.; Scott, N. H. // Operations Research;Nov/Dec84, Vol. 32 Issue 6, p1345 

    We consider the class of nested renewal processes in which all densities are Special Erlangian. We first derive explicit expressions for the transient and steady-state distributions of the accumulated number of shocks and for their mean and variance. We also consider situations with infrequent...

  • A robust stage-discharge rating curve model based on critical flow from a reservoir. Petersen-Øverleir, Asgeir // Nordic Hydrology;2006, Vol. 37 Issue 3, p217 

    Hydrometric gauging stations are often sited in reservoirs such as lakes and river pools since they possess favourable features for streamflow determination. By applying the equations which govern critical flow from a reservoir along with a spline representation of the known geometric...

  • Erratum to: A Wald-type variance estimation for the nonparametric distribution estimators for doubly censored data. Sugimoto, Tomoyuki // Annals of the Institute of Statistical Mathematics;Aug2011, Vol. 63 Issue 4, p671 

    No abstract available.

  • Estimation of the Extreme Value Type I Distribution by the Method of LQ-Moments. Shabri, Ani; Jemain, Abdul Aziz // Journal of Mathematics & Statistics;2009, Vol. 5 Issue 4, p298 

    Problem statement: The study evaluated the effectiveness of the various quantile estimators of the LQ-moments method for estimating parameters of the Extreme Value Type 1 (EV1) distribution. Approach: The performances of the LQ-moments were analyzed and compared against a widely used method of...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics