Power measurements and Confidence Interval

Recently I assessed the power consumption of a particular server rack to determine if we had sufficient power capacity remaining to support additional server installation.

Note: For my intent and purposes, the names and values have been obscured and changed to maintain confidentiality.

The power capacity of the rack was 2.5 kW, while the average measure power consumption was 2.16 kW.

This suggested that the remaining capacity = 2.5 - 2.16 = 0.34 kW

But making decision based on a single aggregated point seems risky. So I calculated the confidence interval range instead.

What is Confidence Interval

The confidence interval is the value range where the mean of the population can be found based on the sample data collected.

Mathematically,

`CI = bar x pm z s/sqrt(n)`

where

`CI = "confidence interval"`
`bar x = "sample mean"`
`z = "confidence level value, e.g. 95%"`
`s = "sample standard deviation"`
`n = "sample size"`

You can be 95% sure that the Population Mean `mu` is in that range. Note: The population mean `mu != bar x` sample mean.

In Excel, CONFIDENCE.T formula is used to calculate the confidence interval.

Graphically confidence interval can be understood like this:

How does Confidence Interval Help

So if I sampled 10 power readings and get the average of 2.16 kW, I would be inclined to think I still have a capacity of 0.34 kW. 

However this 2.16 kW is only the sample's average. What would be the possible "true" average? With Excel I can use CONFIDENCE.T on the sampled data. And this gave me a confidence range 1.85 - 2.47 kW.

We can compare between using average and using confidence interval with the graph below.

In the average approach, we are led to believe we have a remaining capacity of 0.34 kW.

Taking the confidence interval approach, the "true" average could be higher or lower. If we take the Upper Limit, to err on the side of caution, then the remaining capacity is 0.03 kW.

Improving our confidence

There are two ways we can improve our assurance with the range. One method is to decrease `alpha` in CONFIDENCE.T from 0.05 to 0.01. This would increase our confidence to 99%. But you will notice that the range gets even larger.

A better method to increase the accuracy is by taking more samples `n`. This maintains our confidence level but narrows the interval.

I hope this helps you when you are considering power measurements from you server racks. Go measure and calculate with confidence in your DC-DEN!