The Bayesian Analysis of Reliability of Electrical Products

The technology of the reliability theory and its application is a new technology. It has important effect to ensure and improve the quality of the products of electrical engineering. In the reliability test of the products of electrical engineering, assume F(t,¿) is the distribution function of the lifetime T of the product, where ¿ ¿ ¿ is an unknown parameter, and ¿ is the space of the parameters. Assume t₁2¿¿¿t_m, at time t_i (i=1,2,¿¿¿ ,m), n_i products are tested. If the test results are zero-failure, these data are called zero-failure data. These data are written as (t_i , n_i ) , i=1,2, ,m. In this paper, a form of prior distribution about the failure probability p_i=P{Ti } in time t_i of zero-failure data (t_i , n_i ) is developed reasonably. Basing on the prior distribution, the Bayesian estimation of pi is obtained. Then the reliability estimation of Zero-failure data is obtained. Finally, calculation is performed regarding to practical problem. It turns out that the proposed method accords with the engineering priors.