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Statistical models and analysis of cumulated damage processes
Volf, Petr
The contribution deals with a stochastic process which cumulates random increments at random moments. We derive its martingale - compensator decomposition and then we propose the estimator of characteristics of distribution of increments. An application deals with the process of growing damage of a technical device leading to a break of device when cumulated damage exceeds a certain level. We also discuss the problem of prediction of the cumulative process behaviour.
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Random field model and statistical quality control
Linka, A. ; Volf, Petr
A digitalized image of textile material is analyzed with the help of a Gauss-Markov random field model. The parameters of the field are statistically estimated. The method comparing the values of parameters in different data samples and checking the stability of model is proposed and used as a tool for statistical detection of material nonhomogeneity. Simultaneously, the MCMC procedure is used for the simulation of the corresponding random field representation.
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