1. A system analysis device comprising: a memory storing instructions; and one or more processors configured to execute the instructions to: generate, based on time series of a plurality of metrics in a system in a learning period, a correlation model that includes a correlation between metrics; calculate learning reliability of the correlation, based on a behavior of a time series of each of metrics relevant to the correlation included in the correlation model, in the learning period; detect, by using the correlation whose learning reliability is equal to or more than a predetermined reliability threshold, correlation destruction between metrics relevant to the correlation; perform a fault analysis based on the detected correlation destruction; and output a result of the fault analysis.