Plan of tests with addition. Efficient estimate of dependability indicators

The Aim of the paper consists in improving the efficiency of dependability indicator estimation for the plan of tests with addition, i.e. probability of no-failure and mean time to failure. Due to economic considerations, determinative dependability tests of highly dependable and costly products involve minimal numbers of products, expecting failure-free testing or testing with one failure, thus minimizing the number of tested products. The latter case is most interesting. By selecting specific values of the acceptance number Q and number of tested products, the tester performs a preliminary estimation of the dependability indicator, while selecting Q = 1 the tester minimizes the risks caused by an unlikely random failure. However, as the value Q grows, the number of tested products does so as well, which makes the testing costly. Therefore, the reduction of the number of products tested for dependability is the firstpriory problem and, in this context, economic planning of testing with addition is becoming increasingly important. We will consider binomial tests (original sample) with addition of one product (oversampling) to testing in case of failure of any of the initially submitted products. Testing ends when all submitted products have been tested with any outcome (original sampling and oversampling). Hereinafter it is understood that the testing time is identical for all products. Testing with the acceptance number of failures greater than zero (Q > 0) conducted with addition allows reducing the number of tested products through successful testing of the original sample. Methods. Efficient estimation is based on the integral approach formulated in many papers. The integral approach is based on the formulation of the rule of efficient estimate selection specified on the vertical sum of absolute (or relative) biases of estimates selected out of a certain set based on the distribution law parameter, where n is the number of products initially submitted to testing. The criterion of selection of an efficient estimate of the probability of failure (or PNF) at a set of estimates is based on the total square of absolute (or relative) biases of the mathematical expectation of estimates from probability of failure p for all possible values of p, n. Conclusions. The paper examines the probability of no-failure estimates for the plan of tests with addition. For the case of n > 3, the estimates and composite estimate are more efficient in comparison with estimate . The composite estimate of the probability of no-failure should be used in failure-free tests. For the case of n > 3, testing with the acceptance number of failures greater than zero (Q > 0) conducted with addition allows reducing the number of tested products through successful testing of the original sample. The composite estimate of the mean time to failure is bias-efficient among the proposed mean time to failure estimates. The obtained composite estimates and are of practical significance in the context of failure-free testing with addition .