Optimal Simple Step-Stress Plan for Cumulative Exposure Model Using Log-Normal Distribution

2005 ◽  
Vol 54 (1) ◽  
pp. 64-68 ◽  
Author(s):  
A.A. Alhadeed ◽  
S.-S. Yang
Keyword(s):  
Normal Distribution ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Cumulative Exposure Model ◽  
Simple Step ◽  
Log Normal ◽  
Log Normal Distribution

scholarly journals Optimum Times for Step-Stress Cumulative Exposure Model Using Log-Logistic Distribution with Known Scale Parameter

2016 ◽  
Vol 38 (1) ◽  
Author(s):  
Abedel-Qader Al-Masri ◽  
Mohammed Al-Haj Ebrahem
Keyword(s):  
Scale Parameter ◽  
Asymptotic Variance ◽  
Life Time ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Cumulative Exposure Model ◽  
Simple Step ◽  
Design Stress

In this paper we assume that the life time of a test unit follows a log-logistic distribution with known scale parameter. Tables of optimum times of changing stress level for simple step-stress plans under a cumulative exposure model are obtained by minimizing the asymptotic variance of the maximum likelihood estimator of the model parameters at the design stress with respect to the change time.

Simple step-stress model for an extension of the exponential distribution with type-I censoring

2015 ◽  
Vol 32 (8) ◽  
pp. 906-920 ◽  
Author(s):  
Firoozeh Haghighi
Keyword(s):  
Exponential Distribution ◽  
Maximum Likelihood Estimates ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Type I ◽  
Stress Model ◽  
Content Type ◽  
Type I Censoring ◽  
Cumulative Exposure Model ◽  
Simple Step

Purpose – The purpose of this paper is to design a simple step-stress model under type-I censoring when the failure time has an extension of the exponential distribution. Design/methodology/approach – The scale parameter of the distribution is assumed to be a log-linear function of the stress and a cumulative exposure model is hold. The maximum likelihood estimates of the parameters, as well as the corresponding Fisher information matrix are derived. Two real examples are given to show the application of an extension of the exponential distribution in reliability studies and a numerical example is presented to illustrate the method discussed here. Findings – A simple step-stress test under cumulative exposure model and type-I censoring for an extension of the exponential distribution is presented. Originality/value – The work is original.

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

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