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Breakdown processes of systems in parallel

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Random errors in analysis of population growth

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PL
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EN
The model of bacteria population growth in terms of the logistic equation is considered assuming the plate dilution technique of viable counting in the experiment and random errors in data. For example the Fisher test states that the growth equation and the standard description of the random errors are rejected. The extended analysis of errors is presented in terms of an operator which enables to separate three types of random elements: the stochastic growth of dilutions and sampling. On the basis of the triple repetition of observations the variance of dilution errors is estimated.
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Random split of the interval [0,1]

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We define two splitting procedures of the interval [0,1], one using uniformly distributed points on the chosen piece and the other splitting a piece in half. We also define two procedures for choosing the piece to be split; one chooses a piece with a probability proportional to its length and the other chooses each piece with equal probability. We analyse the probability distribution of the lengths of the pieces arising from these procedures.
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Breakdown processes of systems in series

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O podziale terytorialny Polski na części

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On the sequence of facility installation

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EN
One of the basic characteristics of queueing systems is the stochastic process {n(t),t≥0}, which is defined to be the number of units present in the system at time t. In certain cases, this process is Markovian and then its analysis is relatively simple. When the process {n(t),t≥0} is not Markovian, its "Markovization'' can be accomplished by a suitable extension of the states of the system or by the construction of a suitable imbedded Markov chain. The method of extension of the states of the system, which depends on the formation of a vector process, one of whose components is the process {n(t),t≥0}, gives the characteristics of the process {n(t),t≥0}. The method of imbedded Markov chains, which consists of investigating the process in a suitably chosen sequence of time points, yields the characteristics of the process only at the selected time points. For example, a GI/M/N system may be analyzed at the moments of time at which the units enter the system. Because of this, when the method of imbedded Markov chains is used, the interesting characteristics of continuous-time processes can be obtained only with some additional effort. (MR0467961)
EN
The recurrence formulas for the probability distribution function of the maximum length of a series of 1's in a binary 0-1 Markovian sequence are analysed and the limiting distribution estimated. The result is used to test a semi-Markov model of basketball games.
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Cumulative processes in basketball games

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We assume that the current score of a basketball game can be modeled by a bivariate cumulative process based on some marked renewal process. The basic element of a game is a cycle, which is concluded whenever a team scores. This paper deals with the joint probability distribution function of this cumulative process, the process describing the host's advantage and its expected value. The practical usefulness of the model is demonstrated by analyzing the effect of small modifications of the model parameters on the outcome of a game. The 2001 Lithuania-Latvia game is used as an example.
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Estimation of the reliability of systems

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PL
MR0549986
EN
The authors survey methods of estimating the reliability of systems under the condition that the probability distributions of survival times of some minimal critical sets of elements are not fully known. The survey includes methods with various degrees of complexity.
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