Improved Gamma Process for Degradation Analysis Under Nonlinear Condition

2015 ◽  
Vol 22 (06) ◽  
pp. 1550030 ◽  
Author(s):  
Zhao-Yi Fan ◽  
Hua Ju ◽  
Feng-Bin Sun
Keyword(s):  
Scale Parameter ◽  
Gamma Process ◽  
Improved Method ◽  
Degradation Analysis ◽  
Degradation Models ◽  
Life Tests ◽  
Nonlinear Condition ◽  
Improved Model ◽  
Product Degradation ◽  
Process Method

Some life tests result in few or no failures. In such cases, we can, and should, consider using degradation measurements to assess reliability. In real world, product degradation is a stochastic process. Since such degradation is often seen as a monotonous process, literature widely uses Gamma Process to describe and quantify degradation. However, in these publications, scale parameter is considered constant over time and results under this assumption may have big deviation from the actual measurements under nonlinear condition. The purpose of this paper is to improve Gamma Process method to fit a broader class of degradation models. Firstly, we use MLE to estimate the parameters under the timely constant-scale-parameter assumption and analyze why the model does not fit data well. Then we propose an improved model to improve the method and use Monte Carlo simulation to verify the validity of the improved method.

An Improved Model-Free Sampling Technique Based on Bootstrap Methods

2016 ◽  
Author(s):  
Xinshui Yu ◽  
Zhaohui Yang ◽  
Kunling Song ◽  
Tianxiang Yu ◽  
Bozhi Guo
Keyword(s):  
Random Variables ◽  
Sampling Technique ◽  
Improved Method ◽  
Initial Sample ◽  
Bootstrap Methods ◽  
Local Characteristics ◽  
Model Free ◽  
Improved Model ◽  
Center Distance ◽  
Selection Of

The distribution and parameters of the random variables is an important part of conventional reliability analysis methods, such as Monte Carlo method, which should be known fist before using these methods, but it is often hard or impossible to obtain. Model-free sampling technique puts forward a method to get the distribution of the random variables, but the accuracy of the extended sample generated by it is not enough. This paper presented an improved model-free sampling technique, which is based on Bootstrap methods, to increase the accuracy of the extended sample and decrease the iteration times. In this improved model-free sampling technique, the method of the selection of initial sample points and the generation of iterative sample is improved. Meanwhile, a center distance criterion, which considers the local characteristics of the extended sample, is added to the generating criterion of dissimilarity measure. The effectiveness of this improved method is illustrated through some numerical examples.

An Improved Component-Mode Synthesis Method to Predict Vibration of Rotating Spindles and Its Application to Position Errors of Hard Disk Drives

2005 ◽  
Vol 128 (5) ◽  
pp. 568-575 ◽  
Author(s):  
Takehiko Eguchi ◽  
Teruhiro Nakamiya
Keyword(s):  
Mathematical Model ◽  
Natural Frequencies ◽  
Hard Disk ◽  
Equation Of Motion ◽  
Component Mode Synthesis ◽  
Mode Shapes ◽  
Air Bearings ◽  
Improved Method ◽  
Stationary Part ◽  
Improved Model

This paper describes an accurate mathematical model that can predict forced vibration of a rotating spindle system with a flexible stationary part. In particular, we demonstrate this new formulation on a hard disk drive (HDD) spindle to predict its position error signal (PES). This improved method is a nontrivial extension of the mathematical model by Shen and his fellow researchers, as the improved method allows the flexible stationary part to comprise multiple substructures. When applied to HDD vibration, the improved model consists not only a rotating hub, multiple rotating disks, a stationary base, and bearings (as in Shen’s model) but also an independent flexible carriage part. Moreover, the carriage part is connected to the stationary base with pivot bearings and to the disks with air bearings at the head sliders mounted on the far end of the carriage. To build the improved mathematical model, we use finite element analysis (FEA) to model the complicated geometry of the rotating hub, the stationary base and the flexible carriage. With the mode shapes, natural frequencies, and modal damping ratios obtained from FEA, we use the principle of virtual work and component-mode synthesis to derive an equation of motion. Naturally, the stiffness and damping matrices of the equation of motion depend on properties of the pivot and air bearings as well as the natural frequencies and mode shapes of the flexible base, the flexible carriage, the hub, and the disks. Under this formulation, we define PES resulting from spindle vibration as the product of the relative displacement between the head element and the disk surface and the error rejection transfer function. To verify the improved model, we measured the frequency response functions using impact hammer tests for a real HDD that had a fluid-dynamic bearing spindle, two disks, and three heads. The experimental results agreed very well with the simulation results not only in natural frequencies but also in gain and phase.

Optimum Accelerated Life Tests with a Nonconstant Scale Parameter

Technometrics ◽  
1994 ◽  
Vol 36 (1) ◽  
pp. 71 ◽  
Author(s):  
Carol A. Meeter ◽  
William Q. Meeker
Keyword(s):  
Scale Parameter ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests

scholarly journals A comparative study of the photochemistry of biphenyl adsorbed on cellulose and silicalite

2004 ◽  
Vol 6 (4) ◽  
pp. 193-198 ◽  
Author(s):  
J. P. Da Silva ◽  
L. F. Vieira Ferreira
Keyword(s):  
Ground State ◽  
Diffuse Reflectance ◽  
Solid Support ◽  
Ground State Absorption ◽  
Solid Supports ◽  
Time Resolved ◽  
Planar Configuration ◽  
Degradation Analysis ◽  
Photochemical Behaviour ◽  
Product Degradation

The photochemistry of biphenyl (BP) was studied on two model solid supports, silicalite and cellulose, using time resolved diffuse reflectance techniques and product degradation analysis. The results showed that the photochemical behaviour of BP depends on the solid support. Ground state absorption spectra indicated a near planar configuration in the ground state. BP triplet state was the only species detected on cellulose, while the radical cation(BP•+)was observed in silicalite. BP is relatively stable in both supports. Prolonged irradiations in cellulose lead to the formation of the three monohydroxybiphenyls, while in silicalite photooxidation products prevailed.

Inverse Gaussian–based model with measurement errors for degradation analysis

2019 ◽  
Vol 233 (6) ◽  
pp. 1086-1098 ◽  
Author(s):  
Xudan Chen ◽  
Guoxun Ji ◽  
Xinli Sun ◽  
Zhen Li
Keyword(s):  
Measurement Errors ◽  
Random Effect ◽  
State Space Model ◽  
Expectation Maximization Algorithm ◽  
Particle Methods ◽  
Inverse Gaussian ◽  
Estimation Algorithms ◽  
Degradation Analysis ◽  
Degradation Models ◽  
Non Gaussian

To build more credible degradation models, it is necessary to consider measurement errors in degradation analysis. This article proposes an inverse Gaussian-based state space model with measurement errors that can capture the unit-to-unit variability of the degradation rate by incorporating a random effect. Then, the lifetime distribution and alarm probabilities are derived. Under the non-Gaussian assumptions, conventional parameter estimation algorithms cannot be applied directly. Therefore, an improved expectation–maximization algorithm that is combined with particle methods is developed to estimate parameters. Finally, this article concludes with a simulation study and two case applications to demonstrate the applicability and advantages of the proposed model.

Lower Percentile Estimation of Accelerated Life Tests with Nonconstant Scale Parameter

2017 ◽  
Vol 33 (7) ◽  
pp. 1437-1446 ◽  
Author(s):  
Shanshan Lv ◽  
Zhanwen Niu ◽  
Guodong Wang ◽  
Liang Qu ◽  
Zhen He
Keyword(s):  
Scale Parameter ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Percentile Estimation ◽  
Life Tests ◽  
Lower Percentile
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