# Extracting an elusive sigma

#### GaryJH

##### New Member

I have a tubular vertical screw-elevator, a new invention!
I would like to make some conclusions regarding the Repeatability of its flow rate at any set speed of rotation. (similar conveyors quote 1 - 5% )

The Definition of Repeatability is :
Repeatability, a statistical measure of the variability of feeder discharge at a given setpoint, is traditionally based on 30 one-minute samples and is expressed in terms of +X% of set rate at a 2 Sigma or 95.5% confidence level.

Fine : I have done this calculation on raw data of flowrate and found four repeatability %'s/(run time)

vis 1.3%(100sec) 1.7%(75 sec) 3.8%(55 secs) 3.9%(60 sec) at different speeds.
(Easy...or so I thought...)

eg. 6384 lb/hr, sigma = 42lb/hr Repeatability @95% (2 x 42)/ 6384 = 1.3%

However on reflection I am horrified to think that my hand-stopwatch measurement of Time, a key factor over the test runs can likely have a Sigma of 0.7sec.
This is 1.4% for a 100sec test at the 95% Confidence Level.
Worse, if I look at the 55 sec test.!!

So I have my dependant variable (FlowRate) being messed-up (statistically) by interfering variations in another crucial control variable Time, (which I will happily take a guess at knowing its sigma.)

When I try and read up on this, I get lost.... and hope there is a Simple answer. The answer may be a qualitative rather than numerical.

The two Gaussian variables (ie. time interval hand-measured, and inherent machine characteristics) could perhaps be said to interfere constructively and destructively across the data sets. I know (or can guess) the sigma of one (time) but how can I (if at all) get at the sigma of the other from my hard-won data, and hence proclaim some knowledge of the Repeatability of the intrinsic and purely machine-characterised Flow rate.

i.e. see how reliable is the machine, not how good a time-keeper I am..!!

all thoughts would be greatly appreciated! thank you.