Fault diagnosability is the basis of fault diagnosis. Fault diagnosability evaluation refers to whether there is enough measurable information in the system to support the rapid and reliable detection of a fault. However, due to unavoidable measurement errors in a system, a quantitative evaluation index of system fault diagnosability is inadequate. In order to overcome the adverse effects of measurement errors, improve the accuracy of the quantitative evaluation of fault diagnosability, and improve the safety level of the system, a method for a permissible area analysis of measurement errors for a quantitative evaluation of fault diagnosability is proposed in this paper. Firstly, in order for the residuals obey normal distribution, a design method of the permissible area of measurement errors based on the Kullback–Leibler divergence (KLD) is given. Secondly, two key problems in calculating the KLD are solved by sparse kernel density estimation and the Monte Carlo method. Finally, the feasibility and validity of the method are analyzed through a case study.
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