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This paper gives an overview of parameter estimation and system identification for quantum input–output systems by continuous observation of the output field. We present recent results on the quantum Fisher information of the output with respect to unknown dynamical parameters. We discuss the structure of continuous-time measurements as solutions of the quantum Zakai equation, and their relationship to parameter estimation methods. Proceeding beyond parameter estimation, the paper also gives an overview of the emerging topic of quantum system identification for black-box modelling of quantum systems by continuous observation of a travelling wave probe, for the case of ergodic quantum input–output systems and linear quantum systems. Empirical methods for such black-box modelling are also discussed. [ABSTRACT FROM AUTHOR]

In reliability engineering or medical studies, failure of units or individuals may occurring due to several failure modes which is known by competing risks model. In this paper, we have adopted a competing risks model under consideration that, the failure time has generalized inverted exponential distribution (GIED) and the failure modes are independent and partially observed. Under type-II progressive censoring scheme (type-II PCS), the experiment is designed as a quite popular scheme for collecting data specially, for a highly reliable product. The point estimates of the model parameters are formulated under classical approach (maximum likelihood and bootstrap) and Bayesian approach with respect to the symmetric squared error loss function. Also, the approximate confidence intervals under a large sample theory, bootstrap technique's and Markov chain Monte Carlo method (MCMC) are constructed. The estimators are assessed and compared with building the simulation study. Analysis a set of type-II PCS competing risks mortality data for illustration purpose. [ABSTRACT FROM AUTHOR]

The problem of testing the product units under stress higher than normal stress conditions is widely used in reliability analysis specially, in a high reliable products to saving time and cost which is known by accelerated life tests (ALTs) model. In this paper, we are adopted partially constant-stress ALTs model for product units have generalized inverted exponential (GIE) lifetime. And, the test is running under progressive Type-II censoring scheme. The model parameters are estimated with maximum likelihood and Bayes methods. The corresponding asymptotic confidence intervals as well as credible intervals are also constructed. The theoretical results are assessed and compared through Monte Carlo simulation study. The numerical data set is analyzed under the proposed model for illustrative purpose. Finally, we reported some comments about numerical computation. [ABSTRACT FROM AUTHOR]