Alternative to mean and least squares methods used in processing the results of scientific and technical experiments


  • V.U. Ihnatkin
  • V.S. Dudnikov
  • T.R. Luchyshyn
  • S.V. Aleksieienko
  • O.P. Yushkevych
  • T.P. Karpova
  • T.S. Khokhlova
  • Yu.S. Khomosh
  • V.A. Tikhonov



control parameters, rational nomenclature, parameter redundancy, distribution laws, correlation


The nomenclature of controlled parameters and norms of measurement accuracy determines the reliability of control and its laboriousness. On average, the labor-intensiveness of control is about 10% of the total labor-intensiveness of manufacturing objects, and in a number of industries it is much higher (aerospace engineering). The simplest task in determining a rational nomenclature of controlled parameters of ob-jects is the exclusion of excessive parameters, while it is necessary to determine the probability that the deviations of some Х2 parameter within the specified tolerances are the same as the deviations of the Х1 parameter within its specified tolerances. At the same time, inequalities are defined that determine the smallest value of this probability. The general principle of solving this problem is the determination of conditional proba-bilities (if two parameters are considered) P Р11, Р12; , or Р21, Р22. At the same time, if the obtained values: Р11, Р12, are more likely than (or equal to) the permissible value of Rdop, then it is advisable to control only parameter Х1, and exclude Х2 from the no-menclature of parameters. If: Р21, Р22 , are greater than (or equal to) the permissible value of Rdop, then Х1 is turned off. An example of the exclusion of a redundant control parameter is given. The method can be generalized for any number of parameters, for which it is necessary to use correlation matrices or a simple enumeration of parameter combinations. A computer program has been developed that can be used if the following information is available: 1) the number of controlled parameters (n); 2) values of toler-ances (Xni, Xvi), which parameters are subject to control; 3) numerical characteristics of distributions of parameter values within the specified tolerances - the average value of and the average squared deviation σХі,; 4) types of distribution laws of parameter values; 5) data on correlations between parameters and values of pairwise correlation coefficients ( rij ); 6) the value of the probabilities of control errors Р12, Р21 (with two parameters). Calculations should be adjusted as statistical data accumulate.


Bidyuk P.I., Gozhiy O.P. Imovirnistno-statistical methods of modeling and fore-casting: Monograph. - Mykolaiv: Chornomorsky State University named after Peter Mogila, 2014. - 440 p.

Pindus N.M. Vimiruvalny experiment and review of results. - Ivano-Frankivsk: Fakel, 2010. - 248 p.

EURACHEM/CITAC Guide, Quantifying Uncertainty in Analytical Measurement, Second Edition. Laboratory of the Government Chemist, London (2000). ISBN 0-948926-15-5.

EURACHEM/CITAC Guide, Measurement uncertainty arising from sampling: A guide to methods and approaches. EURACHEM, (2007). Available from

ISO 21748:2010. Guide to the use of repeatability, reproducibility and trueness estimates in measurement uncertainty estimation. ISO, Geneva (2010).

Analytical Methods Committee. Measurement uncertainty evaluation for a non-negative measurand: an alternative to limit of detection. Accred. Qual. Assur. Vol 13, pp 29-32 (2008).

Bondarenko S.G. Fundamentals of machine-building technology: introductory guide. - Lviv: Magnolia, 2007. – 500 s.

Work processes of high technologies in mechanical engineering: textbook/ A.I. Hrabchenko, M.V. Verezub/ed. A.I. Grabchenko. - Zhytomyr: ZhDSU, 2011. - 507 p.