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Acceptance sampling plan of accelerated life testing for lognormal distribution under time-censoring

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Chinese Journal of Aeronautics 2015年第3期28卷 814-821页

作者： Li Xiaoyang Gao Pengfei Sun Fuqiang Science & Technology on Reliability & Environmental Engineering Laboratory Beihang Univeristy

Abstract lognormal distribution is commonly used in engineering. It is also a life distribution of important research values. For long-life products follow this distribution, it is necessary to apply accelerated testing techniques to product demonstration. This paper describes the development of accelerated life testing sampling plans （ALSPs） for lognormal distribution under time-censoring conditions. ALSPs take both producer and consumer risks into account, and they can be designed to work whether acceleration factor （AF） is known or unknown. When AF is known, lift testing is assumed to be conducted under accelerated conditions with time-censoring. The producer and con- sumer risks are satisfied, and the size of test sample and the size of acceptance number arc opti- mized. Then sensitivity analyses are conducted. When AF is unknown, two or more predetermined levels of accelerated stress are used. The sample sizes and sample proportion allo- cated to each stress level are optimized. The acceptance constant that satisfies producer and consumer risk is obtdned by minimizing the generalized asymptotic variance of the test statistics. Finally, the properties of the two ALSPs （one for known-AF conditions and one for unknown AF conditions） are investigated to show that the proposed method is corrcct and usablc through numerical examples.

关键词： Accelerated life testing Acceleration factor Acceptance sampling lognormal distribution Producer and consumerrisks Time-censoring

The lognormal distribution and Quantum Monte Carlo Data

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Communications in Computational Physics 2014年第5期15卷 1352-1367页

作者： Mervlyn Moodley School of Chemistry and Physics Quantum Research GroupUniversity of KwaZulu-NatalWestville CampusPrivate Bag X54001Durban4000South Africa.

Quantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis cannot be based on simple Gaussian *** this extent a method is introduced to estimate these distributions and thus give better estimates to errors associated with *** method entails reconstructing the probability distribution of a set of data,with given mean and variance,that has been assumed to be lognormal prior to undergoing a blocking or renormalization *** doing so,we perform a numerical evaluation of the renormalized sum of lognormal random *** technique is applied to a simple quantum model utilizing the single-thread Monte Carlo algorithm to estimate the ground state energy or dominant eigenvalue of a Hamiltonian matrix.

关键词： lognormal distribution renormalization transformation quantum Monte Carlo.

The research of lognormal probability distribution of software defects

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The research of lognormal probability distribution of softwa...

The Perturbed Compound Poisson Risk Model with Proportional Investment

2010 International Conference on Circuit and Signal Processing (ICCSP 2010) & 2010 Second IITA International Joint Conference on Artificial Intelligence (IITA-JCAI 2010)

作者： Ouyang Xin Faculty of Information Engineering and Automation Kunming University of Science and Technology Kunming,China Shuai Chun-Yan Faculty of Electric Power Engineering Kunming University of Science and Technology Kunming,China

In recent years the distribution of software defects in software engineering was one of the most active domains,which plays an important role in the analysis of software quality,rationally allocating resources of software test,improving the efficiency of software test and making the balance of software *** paper selected representative software failure data to fit exponential distribution and lognormal distribution,and carried out Kolmogorov-Smirnov hypothesis *** a mathematical point of view,the paper proved the lognormal distribution more accurately reflected and described the software defect distribution,and provided evidence for the next step of the analysis of software defects,software testing.

关键词： software defects lognormal distribution Probability distribution exponential distribution Kolmogorov-Smirnov hypothesis testing.

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 109-128页

作者： Nai-dan Deng Chun-wei Wang Jia-en Xu School of Mathematics and Statistics Henan University of Science and TechnologyLuoyang471023China

In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case.

关键词： expected discounted dividend payments lognormal distribution proportional investment perturbed risk model sinc numerical method

Identifying the failure mechanism in accelerated life tests by two-parameter lognormal distributions

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Journal of Semiconductors 2014年第8期35卷 110-114页

作者：郭春生张燕峰万宁朱慧冯士维 College of Electronic Information and Control Engineering Beijing University of Technology

The failure mechanism stimulated by accelerated stress in the degradation may be different from that under normal conditions, which would lead to invalid accelerated life tests. To solve the problem, we study the re- lation between the Arrhenius equation and the lognormal distribution in the degradation process. Two relationships of the lognormal distribution parameters must be satisfied in the conclusion of the unaltered failure mechanism, the first is that the logarithmic standard deviations must be equivalent at different temperature levels, and the second is that the ratio of the differences between logarithmic means must be equal to the ratio of the differences between reciprocals of temperature. The logarithm of distribution lines must simultaneously have the same slope and regular interval lines. We studied the degradation of thick-film resistors in MCM by accelerated stress at four temperature levels （390, 400, 410 and 420 K）, and the result agreed well with our method.

关键词： Arrhenius model accelerated life tests failure mechanisms lognormal distribution

Probabilistic predictive model with complex remembrance

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Acta Seismologica Sinica(English Edition) 1994年第4期7卷 653-658页

作者：王键 Institute of Geophysics State Seismological Bureau Beijing China

（王键）Ｐｒｏｂａｂｉｌｉｓｔｉｃｐｒｅｄｉｃｔｉｖｅｍｏｄｅｌｗｉｔｈｃｏｍｐｌｅｘｒｅｍｅｍｂｒａｎｃｅ￥ＪｉａｎＷＡＮＧ（ＩｎｓｔｉｔｕｔｅｏｆＧｅｏｐｈｙｓｉｃｓ，ＳｔａｔｅＳｅｉｓｍｏｌｏｇｉｃａｌＢｕｒｅ... 详细信息

（王键）Ｐｒｏｂａｂｉｌｉｓｔｉｃｐｒｅｄｉｃｔｉｖｅｍｏｄｅｌｗｉｔｈｃｏｍｐｌｅｘｒｅｍｅｍｂｒａｎｃｅ￥ＪｉａｎＷＡＮＧ（ＩｎｓｔｉｔｕｔｅｏｆＧｅｏｐｈｙｓｉｃｓ，ＳｔａｔｅＳｅｉｓｍｏｌｏｇｉｃａｌＢｕｒｅａｕ，Ｂｅｉｊｉｎｇ１０００８１，...

关键词： lognormal distribution Weibull distribution Seismic Zone ACTA SEISMOLOGICA SINICA Seismic Intensity

Stochastic seismic response of multi-layered soil with random layer heights

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Earthquake Engineering and Engineering Vibration 2010年第2期9卷 213-221页

作者： M.Badaoui M.K.Berrah A.Mébarki Université Paris-Est Laboratoire Modélisation et Simulation Multi Echelle Ecole Nationale Polytechnique

This paper deals with the effect of layer height randomness on the seismic response of a layered soil. These parameters are assumed to be lognormal random variables. The analysis is carried out via Monte Carlo simulations coupled with the stiffness matrix method. A parametric study is conducted to derive the stochastic behavior of the peak ground acceleration and its response spectrum,the transfer function and the amplification factors. The input soil characteristics correspond to a site in Mexico City and the input seismic accelerations correspond to the Loma Prieta earthquake. It is found that the layer height heterogeneity causes a widening of the frequency content and a slight increase in the fundamental frequency of the soil profile,indicating that the resonance phenomenon is a concern for a large number of structures. Variation of the layer height randomness acts as a variation of the incident angle,i.e.,a decrease of the amplitude and a shift of the resonant frequencies.

关键词： random layer heights layered soil seismic acceleration lognormal distribution amplification factors Mexico City

Polydispersity effects on the magnetization of diluted ferrofluids:a lognormal analysis

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Chinese Physics B 2010年第10期19卷 534-540页

作者：王旭飞施立群 Applied Ion Beam Physics Laboratory Fudan University Key Laboratory of the Ministry of Education Institute of Modern Physics Department of Nuclear Science and Technology Fudan University

Based on a lognormal particle size distribution, this paper makes a model analysis on the polydispersity effects on the magnetization behaviour of diluted ferrofluids. Using a modified Langevin relationship for the lognormal dispersion, it first performs reduced calculations without material parameters. From the results, it is extrapolated that for the ferrofluid of lognormal polydispersion, in comparison with the corresponding monodispersion, the saturation magnetization is enhanced higher by the particle size distribution. It also indicates that in an equivalent magnetic field, the lognormally polydispersed ferrofluid is magnetically saturated faster than the corresponding monodispersion. Along the theoretical extrapolations, the polydispersity effects are evaluated for a typical ferrofluid of magnetite, with a dispersity of σ = 0.20. The results indicate that the lognormal polydispersity leads to a slight increase of the saturation magnetization, but a noticeable increase of the speed to reach the saturation value in an equivalent magnetic field.

关键词： ferrofluid polydispersity effects lognormal distribution

Exact Statistical distribution and Correlation of Human Height and Weight: Analysis and Experimental Confirmation

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Open Journal of Statistics 2022年第5期12卷 743-787页

作者： Mark P. Silverman Department of Physics Trinity College Hartford USA

The statistical relationship between human height and weight is of especial importance to clinical medicine, epidemiology, and the biology of human development. Yet, after more than a century of anthropometric measurements and analyses, there has been no consensus on this relationship. The purpose of this article is to provide a definitive statistical distribution function from which all desired statistics (probabilities, moments, and correlation functions) can be determined. The statistical analysis reported in this article provides strong evidence that height and weight in a diverse population of healthy adults constitute correlated bivariate lognormal random variables. This conclusion is supported by a battery of independent tests comparing empirical values of 1) probability density patterns, 2) linear and higher order correlation coefficients, 3) statistical and hyperstatistics moments up to 6th order, and 4) distance correlation (dCor) values to corresponding theoretical quantities: 1) predicted by the lognormal distribution and 2) simulated by use of appropriate random number generators. Furthermore, calculation of the conditional expectation of weight, given height, yields a theoretical power law that specifies conditions under which body mass index (BMI) can be a valid proxy of obesity. The consistency of the empirical data from a large, diverse anthropometric survey partitioned by gender with the predictions of a correlated bivariate lognormal distribution was found to be so extensive and close as to suggest that this outcome is not coincidental or approximate, but may be a consequence of some underlying biophysical mechanism.

关键词： Correlation of Height and Weight distribution of Height and Weight Body Mass Index lognormal distribution Distance Correlation (dCor) Hyperstatistics