I have a dataset of sensor values and machine breakdowns. Based on the sensor values I try to build an early recognition of upcoming breakdowns (classic predictive maintenance task). I've been analyzing the given data for quite some time now and with several methods and came to the assumption that there is no connection between the sensor values and the machine breakdowns.
Therefore, now I want to show more formally that there indeed is no connection. Is there a (common) way to do this?
If I fit a stochastic process* on the sensor values and get normally distributed residuals**, does this prove that the sensor values are of no predictive power regarding the breakdowns?
Many thanks in advance!
*(e.g. random walk with mean reversion, moving average or autoregressive process)
**(for both cases: close to a breakdown and far away from the next breakdown)