A SPECIAL CASE OF FINDING EFFECTIVE ESTIMATES 

Mikhailov Viktor Sergeevich, lead engineer, Central Research Institute of Chemistry and Mechanics named after D. I. Mendeleev (115487, 16а Nagatinskaya street, Moscow, Russia), E-mail: Mvs1956@list.ru
Yurkov Nikolay Kondratievich, doctor of technical sciences, professor, the honoured worker of science of the Russian Federation, head of sub-department of radio equipment design and production, Penza State University (440026, 40 Krasnaya street, Penza, Russia), E-mail: yurkov_NK@mail.ru 

519.248:62-192 

10.21685/2307-4205-2019-2-12 

Background. Over the past few years, a lot of work has been done to improve the effectiveness of evaluations of reliability indicators for various test plans, with particular attention being paid to failing tests. In these papers, the estimates obtained were compared in terms of effectiveness. In addition to the estimates for trouble-free tests, there were certain requirements for the result of evaluating the reliability index: to be monotonous with an increase in the number of failures and different from zero and one. It seemed that the estimates obtained could not be significantly improved. However, in some cases it is not. The aim of the work is to increase the efficiency of estimates of the probability of failure-free operation for a binomial test plan in the case of tests that did not give failures.
Materials and methods. The study of effective estimates is based on an integral approach based on the construction of a selection rule (criterion) for an effective estimate of θ ̂ ₀ (n; r) given on the sum of the values of absolute (or relative) displacements of estimates θ (n; r) selected sets, on the parameter of the distribution law, where n is the number of products initially put up for testing.
Results and conclusions. 1. As a result of the research, it was possible to obtain: estimates p ̃ and v ̃ are more effective than previously proposed ones; assessment effective on a fairly wide class of estimates and more effective in comparison with the previously proposed. 2. The obtained estimates of p ̃ and v ̃, which are close to the effective one, and the estimate Tˆ₁ , effective on a fairly wide class of estimates, are proposed for use for reliable tests carried out according to the binomial plan. 3. For a binomial plan and a test plan with recovery and limited test time, estimates of the probability of failure-free operation, estimates Tˆ₁ and Tˆ₀₁ are approximately equal to each other when failures did not occur during the test, which was to be expected. The choice of what grades to use in this case remains with the tester. 

the Bernoulli scheme; test plan; point estimation; the probability of failure; probability of failure-free operation; effective of assessment