Minimization of the volume of reliability tests of the machines under development taking into account the reliability functions for certain types of failures

2020 ◽  
pp. 33-36
Author(s):  
A.S. Ivanov
Keyword(s):  
Random Variables ◽  
Test Time ◽  
Scattering Parameters ◽  
Degradation Failure

A method of minimizing the volume of reliability tests for non-recoverable machines at the stage of their development by increasing the test time and using forced modes is described. Keywords tests, degradation failure, reliability, scattering parameters, random variables [email protected]

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

On the Mathematical Basis of Zelen’s Prerandomized Designs

1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann
Keyword(s):  
Clinical Trial ◽  
Normal Distribution ◽  
Random Variables ◽  
Small Samples ◽  
Selection Effects ◽  
Sample Sizes ◽  
Mathematical Basis ◽  
Additional Assumptions

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.

Stimulated Platelet Aggregation, Thromboxane B2 Formation and Platelet Sensitivity to Prostacyclin - A Critical Evaluation

1981 ◽  
Vol 45 (03) ◽  
pp. 204-207 ◽  
Author(s):  
Wolfgang Siess ◽  
Peter Roth ◽  
Peter C Weber
Keyword(s):  
Arachidonic Acid ◽  
Platelet Count ◽  
Platelet Aggregation ◽  
Reliable Method ◽  
Platelet Rich Plasma ◽  
Critical Evaluation ◽  
Vascular Diseases ◽  
Thromboxane B2 ◽  
Test Time ◽  
Stimulation Of

SummaryPlatelets have been implicated in the development of atherosclerotic and thrombotic vascular diseases. Evaluation of platelet aggregation in relation to endogenously formed compounds which affect platelet function may provide information of clinical and pharmacological relevance. We describe a method in which thromboxane B2 (TXB2) formation was analyzed following stimulation of platelet-rich plasma (PRP) with ADP, 1-epinephrine, collagen, and arachidonic acid. In addition, we determined platelet sensitivity to prostacyclin following ADP- and collagen-induced platelet aggregation. The parameters under study were found to depend on the platelet count in PRP, on the type and dose of the aggregating agent used, and on the test time after blood sampling. By standardization of these variables, a reliable method was established which can be used in clinical and pharmacological trials.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

Experimental investigation and modelling of light scattering in a-Si:H solar cells deposited on glass/ZnO:Al substrates

2002 ◽  
Vol 715 ◽  
Author(s):  
J. Krc ◽  
M. Zeman ◽  
O. Kluth ◽  
F. Smole ◽  
M. Topic
Keyword(s):  
Surface Roughness ◽  
Experimental Investigation ◽  
Solar Cells ◽  
Angular Distribution ◽  
Light Scattering ◽  
Optical Model ◽  
Distribution Functions ◽  
Interface Roughness ◽  
Scattering Parameters ◽  
Good Agreement

AbstractThe descriptive scattering parameters, haze and angular distribution functions of textured ZnO:Al transparent conductive oxides with different surface roughness are measured. An approach to determine the scattering parameters of all internal interfaces in p-i-n a-Si:H solar cells deposited on the glass/ZnO:Al substrates is presented. Using the determined scattering parameters as the input parameters of the optical model, a good agreement between the measured and simulated quantum efficiencies of the p-i-n a-Si:H solar cells with different interface roughness is achieved.

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