在逐步增加II型截尾寿命数据下,本研究深入探讨了比例危险率模型的参数以及可靠性指标的贝叶斯估计与样本预测问题。首先,通过频率方法对模型参数进行了预先估计,并分析了其相关性质。随后,在平衡损失函数框架下,本文得到了可靠性指标的贝叶斯估计,同时也得出平衡损失比一般损失更加灵活的实用性结论。本文还进行了一系列数值模拟示例,其模拟结果与理论分析相一致。以上的理论研究和示例均证实了所提出的平衡损失下贝叶斯方法的实用性和有效性。This study delves into the Bayesian estimation and sample prediction issues of the proportional hazard rate model’s parameters and reliability indicators under progressive type-II censored lifetime data. Firstly, a preliminary estimation of the model parameters was conducted through frequency methods, and their related properties were analyzed. Subsequently, within the framework of the balanced loss function, this paper obtained the Bayesian estimation of the reliability indicators and also concluded that the balanced loss is more flexible and practical than the general loss. A series of numerical simulation examples were also conducted, and the simulation results were consistent with the theoretical analysis. The theoretical research and examples presented above all confirm the practicality and effectiveness of the proposed Bayesian method under balanced loss.
It is well known that the system (1 + 1) can be unequal to 2, because this system has both observation error and system error. Furthermore, we must provide our mustered service within our cool head and warm heart, where two states of nature are existing upon us. Any system is regarded as the two-dimensional variable error model. On the other hand, we consider that the fuzziness is existing in this system. Though we can usually obtain the fuzzy number from the possibility theory, it is not fuzzy but possibility, because the possibility function is as same as the likelihood function, and we can obtain the possibility measure by the maximal likelihood method (i.e. max product method proposed by Dr. Hideo Tanaka). Therefore, Fuzzy is regarded as the only one case according to Vague, which has both some state of nature in this world and another state of nature in the other world. Here, we can consider that Type 1 Vague Event in other world can be obtained by mapping and translating from Type 1 fuzzy Event in this world. We named this estimation as Type 1 Bayes-Fuzzy Estimation. When the Vague Events were abnormal (ex. under War), we need to consider that another world could exist around other world. In this case, we call it Type 2 Bayes-Fuzzy Estimation. Where Hori et al. constructed the stochastic different equation upon Type 1 Vague Events, along with the general following probabilistic introduction method from the single regression model, multi-regression model, AR model, Markov (decision) process, to the stochastic different equation. Furthermore, we showed that the system theory approach is Possibility Markov Process, and that the making decision approach is Sequential Bayes Estimation, too. After all, Type 1 Bays-Fuzzy estimation is the special case in Bayes estimation, because the pareto solutions can exist in two stochastic different equations upon Type 2 Vague Events, after we ignore one equation each other (note that this is Type 1 case), we can obtain both its system solution and its decision solution. Here
