Plan of tests with addition

It is common practice to estimate the values of dependability indicators (point estimation). Normally, the probability of no-failure (PNF) is used as the dependability indicator. Due to economic reasons, determinative dependability tests of highly dependable and costly products involve minimal numbers of products, expecting failure-free testing (acceptance number Q = 0) or testing with one failure (Q = 1), thus minimizing the number of tested products. The latter case is most interesting. By selecting specific values of the acceptance number and number of tested products, the tester performs a preliminary estimation of the planned PNF, 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. That is why the reduction of the number of products tested for dependability is of paramount importance. Preparation of the plan of tests with addition. 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. The Aim of the paper consists in preparing and examining PNF estimates for the plan of tests with addition. Methods of research of dependability indicator estimates. Efficient estimation is based on the integral approach formulated in [6, 8-10]. The integrative 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, in our case, n is the number of products initially submitted to testing. Criterion of selection of efficient estimation for PNF. 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) bias of the mathematical expectation of estimates E Ѳ (n,k,m) from probability of failure p for all possible values of p, n. Conclusions. PNF estimates for the plan of tests with addition was prepared and examined. For the case n > 3, the PNF estimate P (n,k,m) =1– p (n,k,m)=1–(k+m)/(n+k) in comparison with the implicit estimate V (n,k,m) =1– v (n,k,m) is bias efficient. 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. Estimates p₂, w₂ and w₃, and are unbiassed and, as a consequence, bias efficient for the cases n = 2 and n = 3 respectively.

Bernoulli scheme, test plan, point estimation, probability of no-failure, efficient estimate, mean time to failure

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