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14869 Yellow Water Lane, Jacksonville, FL. 32234
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We provide fuel injector bench flow testing and ultrasonic cleaning for most of the  thousands of fuel injectors used in early model engines, and newer engines.


This page is a technical resource page that will provide an explanation of the statistical term "standard deviation", and why standard deviation analysis of injector flow rates are important when evaluating injector performance.


Webster's Third New International Unabridged Dictionary ( weighing in at 13 lbs, 6 ozs.) defines "standard deviation" as ......  "the square root of the average of the squares of the deviations from the mean".


That's a bit difficult to understand, but in lay terms, it may be easier to "loosely" be considered as an average of an average.  The term average (the statistical term is mean) easily understood.   It is a group of numbers, added together, and that total divided by the total numbers that were added together.  As an example...add the numbers 2, 4, 6, 8, and 10.  The total is 30.  The numbers in the group are 5.  30 divided by 5 is 6.  The average (aka mean) is 6.


Standard deviation analysis then looks at those numbers (the numbers that were added together, how many numbers were added together, as well as their average) and determines how spread apart (or how close together) the group of numbers are from the average.   Without ( and unnecessarily) going into the formula, the standard deviation for the above set of numbers is 2.82.  Again loosely speaking,  2.82 is an average of how spread out the numbers are from initial average of 6.  Technically, the standard deviation is as per the prior cited Webster definition.


Now before any of you "purist mathmaticians" correct my explanation...remember...I'm attempting to put this in terms that may be more easily comprehended, and yet still provide enough information for anyone to research standard deviation as they may desire.


So, moving on, why is standard deviation analysis important when examining fuel injector flow rates?  


The simple answer is...the less the standard deviation of the flow rate is from the average flow rate, the engine will have better HP, better fuel economy, and better performance.  A standard deviation of 0 (zero) would mean there is no deviation and all the numbers would be the same.


Elementary logic would make us conclude that if every engine cylinder receives...say 100cc of fuel (regardless of the number of engine cylinders) then the fuel/air ratio delivered to each and every cylinder, is equal, and all other things considered, (ignition being correct, O2 sensors ok, plugs good, emission system is good, etc), then the engine performance is as good as it will get.  Life is good.


But, if the injectors are not flowing the exact same amount, how much of a difference in flow rate is acceptable, and what are those parameters?  That's where we use standard deviation.


The following information is widely accepted as the industry criteria for acceptable flow rate standard deviation for petrol engines.


0 to 1 cc injector flow rate standard deviation  ...   for racing or track engines.

1 to 3 cc injector flow rate standard deviation  ...   for a daily driver, or occasional driven engine.

3 cc or above injector flow standard deviation ...   unsuitable and requires correction.


The engine fueling ECU cannot correct fueling to each injector separately.  In "closed loop" mode, the ECU is receiving voltage signals from the O2 sensor(s), and the ECU adjusts fueling (increasing or decreasing injector pulse width) to each engine bank, (and therefore to each group of injectors) until the presence of O2 in the exhaust is (hopefully) at the correct level.  We explain this further on our page HERE


Here are two examples.....


A)  Six injectors and each injector has a flow rate of 150 cc.  The average flow rate is 150 cc, and the standard deviation is 0 cc.  (zero).  A perfect set, and ready to put in your race engine.


B)  Six injectors...four have a flow rate of 150 cc, one has a flow rate of 135 cc, and one has a flow rate of 155 cc.  The average flow rate is 148.33 cc, and the standard deviation is 6.236 cc.  In this situation, the recommendation would (at a minimum) to replace the 135 cc flow rate injector with an injector that most closely matches 150 cc.  We can reasonably assume this particular group of injectors should flow at 150 cc because the "mode" is 150 cc.  The mode is the number (the flow rate in our situation) that appears most frequently in the set tested.  So we get a substitute for the 135 cc injector (the worst of the lot) and the sub has a flow rate of 149 cc.  The average is now 150.66 cc, and the standard deviation has reduced to 1.97 cc, and is now within specs for a daily/occasional driver.


It is important to recognize, that one injector (or more) with low flow(s) , or one or more injectors with overly high flow(s) , will skew the standard deviation.  Such that when doing any analysis on injector flow rates, we will look at the average (mean) flow rate, the mode (the number of injectors with the same flow rate), the highest injector flow rate, the lowest injector flow rate, and the standard deviation for the set.  With that data in hand, we can recommend solutions for any replacement injectors necessary to put a set back to spec.  We do not rely on only one condition, rather we examine the accumulated data, to make our recommendations.  


If you have a dead or fouled spark plug in your vehicle, would you leave it in, or would you clean it, and regap, or replace it? Apply the same logic to your injectors.


We hope this tech page helps you. The standard deviation analysis is included in your injector servicing, pre testing (before ultrasonic cleaning) as well as post testing (after ultrasonic cleaning).


SD Faircloth

This page last updated Thursday, 11/16/2017.


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