| In this dissertation, we address two basic aspects of statistical inference on the reliability of series system, namely hypothesis testing and interval estimation. Both two-component and multi-component series system are discussed. Due to the complexity of the underling probability distribution, we follow the conditional approach. For the general multi-component series system, unlike the two-component case, we cannot have closed expressions for the MLEs of the model parameters under the null hypothesis, which hinders the development of the traditional likelihood ratio test method. To avoid this problem, we have found approximate MLEs of the model parameters under the null (and alternative) hypothesis, which are then used to derive an approximate likelihood ratio statistic. Using the approximate likelihood ratio statistic, we then find conditional test procedures which are consistent with those for the two component case. Finally, from the acceptance regions we obtain confidence intervals for system reliability. |
