Reliability is a key factor for realizing safety guarantee of full autonomous robot systems. In this paper, we focus on reliability in mobile robot localization. Monte Carlo localization (MCL) is widely used for mobile robot localization. However, it is still difficult to guarantee its safety because there are no methods determining reliability for MCL estimate. This paper presents a novel localization framework that enables robust localization, reliability estimation, and quick re-localization, simultaneously. The presented method can be implemented using similar estimation manner to that of MCL. The method can increase localization robustness to environment changes by estimating known and unknown obstacles while performing localization; however, localization failure of course occurs by unanticipated errors. The method also includes a reliability estimation function that enables us to know whether localization has failed. Additionally, the method can seamlessly integrate a global localization method via importance sampling. Consequently, quick re-localization from failures can be realized while mitigating noisy influence of global localization. Through three types of experiments, we show that reliable MCL that performs robust localization, self-failure detection, and quick failure recovery can be realized.