Bayesian Approach To A Constant Stress Accelerated Life Test Based On Gibbs Sampling Under Log-Normal Distrbution

Accelerated life test is a kind of life test to shorten the test period through strengthening the test stress. In these tests, the reliability of common products can be evaluate quickly, and the reason of failure can also be checked out very soon, so that it is possible to evaluate the reliability of high reliable and long life products. In 70's, accelerated life test came into our country, which immediately inspired the interests of the scientists engaged in engineer and statistics, who using this method in electronic machinery and instrument on one side, and begin researching on the other side. In these twenty years, they have accumulated lots of experience about accelerated life test, and put forth some new models and data processing methods in accelerated life test, which largely increased the theory and method in this field. There are a lot of accelerated life tests, of which the three kinds below are usual in use. 1. Constant stress accelerated life test. In this kind of test, we select a team of accelerated stress level firstly, such as, which are all higher than the regular stress level, where. And secondly, we part a quantity of samples into k teams, and the life test is carried out based on the same accelerated stress lever until there appears a quantity of each team. 2. Step stress accelerated life test. In this kind of test, we also select a team of accelerated stress level firstly, such as, which are all higher than regular stress level. We begin the test with a quantity of products based on the same stress with level. After some time, such as hours, we increase the stress level to, and carry out the test with the products without failure based on the same stress level of, we carry out the test until there appear quantity samples in failure, again and again. 3. Progressive stress accelerated life test. The test procedure is similar with step-stress test in most, and the difference is that the stress level will increase continuously with time, and the simplest one is that the level will increase linearly with time. In this kind of test, the stress change fast and the failure come fast too, particularly, so that equipment to control the change of stress level and to track the failure of products are required, without whom, the test can't be carried out in practice. These three accelerated life tests above have all been in use in our county, about which, there are many successful examples, and the constant stress test is the most in use. The reason is that the constant stress test can be easily carried out and the method of data processing is more successful. Even though the time requires in this test is not the shortest, it can also be shortened timely than other life tests. Our scientists have formulated criteria about this kind of test, with the number of GB2689.1~4-81. The difficulty in statistical inference using Bayesian approach is calculating the posterior margin distribution, in most situations, it is very difficult to do so and even the formula can not be got. Even though we have got it, the result would be very complex, difficult to put into practice and spread.