Average of standard deviation as repeat accuracy for five measurement series

Hi there,
I hope you can help me with the following question.
I measured the power input and output of a storage and retrieval vehicle with 1,000 single measuring points. I repeated the measurement five times with the same measure method and same time steps. The result is five measurement series with 1,000 measuring points. Now I calculated the standard deviation of the five values of every single measurement point. Is it now on statistical/mathematical aspects permitted to calculate the mean of every 1,000 standard deviations? Is there a value „average of standard deviations“?
My purpose is to validate my measuring method with one value (repeat accuracy). My calculated value is fine for the moment, but I need (and can’t find) a statement in the literature that my procedure was fine. I also calculated the confidence interval (student's t-distribution) and plotted it on MATLAB.
Can anyone help me please? Thank you.