Estimates of Rayleigh distribution parameters in statistical methods of quality control

Abstract

The paper considers the problem of estimating of a two-parameter generalization of Rayleigh distribution and finding distributions of estimates. This problem arose from the needs of statistical sampling inspection of dimensions obtained in the production process with certain features of the part basing and cylindrical surface processing. Parameter estimates are found using order statistics. Computational procedures are constructed in the Matlab environment, which make it possible to construct distributions of estimates in the form of tables. The correctness of the calculations was verified using stochastic simulation and the construction of empirical distribution functions of estimates. The results obtained can be used to build operational characteristics of control plans and select control plans with the required producer’s and customer’s risks, as well as to build control charts for statistical control of the manufacturing process.