Start-up demonstration tests with sparse connection

•Three start-up demonstration tests with sparse connection are introduced.•The traditional start-up demonstration tests are special cases of these new tests.•Probabilistic indexes are given for these new tests by using finite Markov chain.•Numerical examples exhibit improvement in test efficiency of these new tests.•The analyses are fit for all start-up demonstration tests with sparse connection.

Based on the concept of sparse connection, three start-up demonstration tests with sparse connection are introduced which are called CSTF with sparse d1, TSCF with sparse d2 and CSCF with sparse d3 and d4. The traditional start-up demonstration tests such as CSTF, TSCF and CSCF are special cases of these new tests. Furthermore, the new tests exhibit obvious improvement in test efficiency. In this paper, by using the finite Markov chain imbedding approach, several probabilistic indexes are given for these new start-up demonstration tests based on the assumption that the tests are i.i.d. case. The analyses are also extended to independent and non-identical and Markov dependent cases. In addition, procedures are provided in order to determine the optimal parameters needed in a demonstration test for selecting the products to meet the reliability requirement. Three comparison analyses are finally presented in order to illustrate the high efficiency of these new start-up demonstration tests and the effectiveness of this method.