Reserch on optimal truncated sequential test without substitution

In order to reduce the testing costs for products with high reliability and long-life testing characteristics, the optimal truncated sequential tests of exponential distribution without substitution are studied in this paper. The theory of optimal truncated sequential test without substitution is established. The calculation formulas for essential statistical features, such as the operating characteristic curve and expected natural calendar testing time of the test plans, are derived. A sample space sorting method is established to address the optimal truncated sequential tests. Through comparison with the test plans provided by the international standard IEC61124, the results show that, with strict control over type I and type II error probabilities, the new test plans proposed here can save nearly 80% of synthesis expected natural calendar testing time. Moreover, in comparison with the optimal truncated sequential tests with substitution, the results show that, the new test plans can reduce nearly 70% of the synthesis expected natural calendar testing time. The new test plans proposed in this paper significantly decrease the synthesis expected natural calendar testing time, thereby substantially reducing the testing costs for products with high reliability and long-life testing characteristics.