Reliability Assessment of Highly Reliable Samples Using the Tolerance Limits and the Weibull’s Law

Among the most relevant issues of reliability is the assessment of the reliability of complex technical systems with a small number of observations. In practice, a situation often arises when an estimate of satisfactory accuracy can be obtained only at the end of tests or operation, when it loses its relevance. Then it is better to use methods of processing a small amount of data collected during preliminary tests, to obtain some estimates of reliability indicators, than to postpone the acceptance of more accurate estimates until a time when more reliable statistical material has been accumulated. The paper proposes an approach to the solution of the problem of constructing an estimate of the time of uptime using the theory of β-expected limits. The paper proposes to apply the theory of tolerance limits to determine the reliability of highly reliable samples of complex technical systems when using a failure model in the form of the Weibull distribution law. The choice of the Weibull distribution is due to its universality of use in the analysis of the reliability of mechanical, electronic and other systems. The paper provides examples of the use of the proposed methodology for calculating reliability indicators with a small number of failures. The lower tolerance limits of earnings per failure that correspond to the given level of probability are found. The obtained results are sufficient for making managerial decisions regarding the determination of reliability in the conditions discussed above.