Bootstrapping the change-point of a hazard rate

Pham, Tuan Dinh; Nguyen, Hung T.

doi:10.1007/bf00775818

Cited by 14 publications

(6 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Studies on critical time have a relative longer history than that of the turning point in literature. For more details of change point in the failure rate, the reader is refereed to, for example, [1], [14], [20] and [21]. Similar to what we commented on the turning point, the estimated change point usually does not have a closed analytical expression.…”

Section: Introductionmentioning

confidence: 87%

Estimating the turning points of the beta generalized exponential failure rate

Peng

2011

The Proceedings of 2011 9th International Conference on Reliability, Maintainability and Safety

View full text Add to dashboard Cite

This note concerns the interval estimation of the turning point of the failure rate based on the newly proposed beta generalized exponential distribution. The point estimate of the turning point is obtained using the maximum likelihood estimation. Since there is no closed form of the turning point of the BGE failure rate function, we propose to construct the confidence interval of the turning point using simulation methods. Two real life data sets are used to illustrate the proposed procedures.

show abstract

Section: Introductionmentioning

confidence: 87%

Estimating the turning points of the beta generalized exponential failure rate

Peng

2011

The Proceedings of 2011 9th International Conference on Reliability, Maintainability and Safety

View full text Add to dashboard Cite

show abstract

“…, X * n be independent random variables sampled conditionally from the model (2) where the parameters are replaced with α n , and τ * n be the estimator of τ obtained similar to τ n from the bootstrap sample. Then, Pham and Nguyen [13] show that the distribution of n(τ * n − τ n ) = U n (X * 1 , X * 2 , . .…”

Section: Hazard Change Point Estimationmentioning

confidence: 99%

“…The result above provides the limiting distribution of n(τ − τ ), however, it is seen that it is a highly complicated one, which requires heavy computation. Pham and Nguyen [13] propose to overcome this difficulty by considering the parametric bootstrap distribution. Writing n(τ − τ ) = U n (X 1 , X 2 , .…”

Section: Hazard Change Point Estimationmentioning

confidence: 99%

Hazard Change Point Estimation

Gürler

2014

Wiley StatsRef: Statistics Reference Online

View full text Add to dashboard Cite

In survival and reliability studies, hazard‐rate function plays an important role. Sudden changes in the hazard function may occur due to treatment effects or maintenance activities. A problem of statistical interest is the estimation of the times of the changes, as well as their sizes. In this note, we review the basic estimation methods for hazard change‐point models for complete data. Some related literature is also provided for estimation with incomplete data and hypothesis testing.

show abstract

“…Bebbington et al 20 used the empirical estimation method to obtain the change point of the HR function of the modified Weibull distribution. Pham and Nguyen 21 used a non-regular model and the bootstrapping method to find the change point. Jiang 22 proposed to use spline functions to approximate the degradation process and to find the change point.…”

Section: Introductionmentioning

confidence: 99%

Bayesian method to solve the early failure period of numerical control machine tool

Yang

Wang

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part B:

View full text Add to dashboard Cite

The hazard rate curve of the numerical control machine tool is a bathtub curve. The change point between the early failure period and the random failure period of the curve is difficult to obtain with a small data sample; thus, a Bayesian method is proposed. A method to build the prior distributions of the Weibull parameters is developed, which integrates the multi-source prior information of the target numerical control machine tool and the reference numerical control machine tool. The Markov chain Monte Carlo method is adopted to calculate the estimators of the Weibull parameters corresponding to each failure, which solves the problem of the absence of an analytical solution. The total working time of the numerical control machine tool when the estimator of the shape parameter is equal to 1 is estimated by taking the estimator of the shape parameter as the function of time. As a result, the change point and the early failure period are obtained. Comparison result shows that the result obtained through an existing change point solving method with a large dataset is close to the result generated through the proposed method with a small dataset. The change point and the early failure period obtained with the proposed method can be used to guide the early failure test and to design a rational maintenance strategy, which are of vital engineering significance.

show abstract

Bootstrapping the change-point of a hazard rate

Abstract: Change-point, consistency of bootstrap method, parametric bootstrapping,

Cited by 14 publications

References 10 publications

Estimating the turning points of the beta generalized exponential failure rate

Estimating the turning points of the beta generalized exponential failure rate

Hazard Change Point Estimation

Bayesian method to solve the early failure period of numerical control machine tool

Contact Info

Product

Resources

About