Residual Operating Fatigue Lifetime—Estimation of Distribution Function

Estimation of distribution functions has many real-world applications. We study kernel estimation of a distribution function when the density function has compact support. We show that, for densities taking value zero at the endpoints of the support, the kernel distribution estimator does not need boundary correction. Otherwise, boundary correction is necessary. In this paper, we propose a boundary distribution kernel estimator which is free of boundary problem and provides non-negative and non-decreasing distribution estimates between zero and one. Extensive simulation results show that boundary distribution kernel estimator provides better distribution estimates than the existing boundary correction methods. For practical application of the proposed methods, a data-dependent method for choosing the bandwidth is also proposed.

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Reliability Evaluation of Structural Ceramics Under Multiaxial Stress State

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education ◽

10.1115/98-gt-595 ◽

1998 ◽

Cited By ~ 1

Author(s):

Takashi Ono ◽

Masaki Kaji ◽

Michiaki Nishimura

Keyword(s):

Experimental Data ◽

Distribution Function ◽

Stress State ◽

Fracture Probability ◽

Test Method ◽

Structural Ceramics ◽

Multiaxial Stress ◽

Fatigue Lifetime ◽

Empirical Parameter ◽

Multiaxial Stress State

Strength and fatigue lifetime of structural ceramics under multiaxial stress state have been estimated and compared with experimental data. Biaxial strength tests were done by an anticlastic bending test method at room temperature. Biaxial fatigue tests were done by anticlastic bending and also ring-on-ring test method at 1200°C in air. Fracture probability and lifetime were predicted on the basis of a Weibull multiaxial distribution function and subcritical crack growth, using the results of stress analyses by the finite element method. Modified maximum hoop stress theory including an empirical parameter, T, was applied to the equivalent normal stress in the multiaxial distribution function. The empirical parameter T represents a shear stress sensitivity to mixed-mode fracture due to a grain interlocking effect. It has been confirmed that the predicted fracture probability and the fatigue lifetime agrees well with the experimental data if grain interlocking effects are taking into account.

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Estimation of distribution function for control valve stiction estimation

Journal of Process Control ◽

10.1016/j.jprocont.2011.06.008 ◽

2011 ◽

Vol 21 (8) ◽

pp. 1208-1216 ◽

Cited By ~ 20

Author(s):

Fei Qi ◽

Biao Huang

Keyword(s):

Distribution Function ◽

Control Valve ◽

Estimation Of Distribution ◽

Valve Stiction

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Impact of TDDB Distribution Function on Lifetime Estimation in Ultra-Thin Gate Oxides

10.7567/ssdm.2000.b-6-5 ◽

2000 ◽

Author(s):

Hideki Satake ◽

Akira Toriumi

Keyword(s):

Distribution Function ◽

Lifetime Estimation ◽

Gate Oxides

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An inverse-probability-weighted approach to the estimation of distribution function with middle-censored data

Journal of Statistical Planning and Inference ◽

10.1016/j.jspi.2010.01.009 ◽

2010 ◽

Vol 140 (7) ◽

pp. 1844-1851 ◽

Cited By ~ 1

Author(s):

Pao-sheng Shen

Keyword(s):

Distribution Function ◽

Censored Data ◽

Inverse Probability ◽

Estimation Of Distribution ◽

Inverse Probability Weighted

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Recursions and limit theorems for the strength and lifetime distributions of a fibrous composite

Journal of Applied Probability ◽

10.1017/s0021900200030680 ◽

1987 ◽

Vol 24 (01) ◽

pp. 137-159 ◽

Cited By ~ 3

Author(s):

Chia-Chyuan Kuo ◽

S. Leigh Phoenix

Keyword(s):

Distribution Function ◽

Limit Theorem ◽

Fibrous Composite ◽

Probability Model ◽

Failure Process ◽

Static Strength ◽

Fatigue Lifetime ◽

Lifetime Distributions ◽

The Matrix ◽

A New Technique

A composite material is a parallel arrangement of stiff brittle fibers in a flexible matrix. Under load fibers fail, and the loads of failed fibers are locally redistributed onto nearby survivors through the matrix. In this paper we develop a new technique for computing the probability of failure under a previously studied model of the failure process. A recursion and limit theorem are obtained which apply separately to static strength and fatigue lifetime depending on the composite loading and the probability model for the failure of individual fibers under their own loads. The limit theorem yields an approximation for the distribution function for composite lifetime which is of the form 1 – [1 – W(t)] mn where W(t) is a characteristic distribution function and mn is the composite volume, reflecting a size effect. A similar result holds also for static strength. In both cases such a result was conjectured several years ago. This limit theorem is obtained from the recursion upon applying a key theorem in the theory of the renewal equation. In the proofs three technical conditions arise which must be verified in specific applications. In the case of static strength these conditions are quite easy to verify, but in the case of fatigue lifetime the verification is generally difficult, and entails considerable numerical computation.

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