Std deviation with multiple lot sizes

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    I am trying to calculate the std devition of some of our assembly times but in many instances I only have 2 or 3 pc lot averages and am tring to find a good solution..
    For example I might have 5 data points that represent a single unit, 3 data points that represent an average of a lot of 2 units (six total units) and 2 data points that represent the average of 3 units (six total units) representing 17 built units.
    I considered just counting the averages as a single points, getting 10 points, but that understates the multi-unit lots in the mean. 
    I also tried using the lot averages mutiple times to get 17 points.  This gives me the correct mean, but I am now understating the standard deviation because I am introducing multiple points with the same value; a lot of 3 might have one high value, one low value and one mid value, but the reported average is in the middle.
    Does anyone have any suggestions on how to compensate for this?



    Go to Gemba!  Sounds like you need to physically observe the assembly process.  If you are batch building, you can observe individual element times.  From these individual element times, you can determine (roughly) the time for each unit.  If it is sequential build, you need to record individual element times and total cycle time per unit.  Either way, you get the data you need to look at the deviation of the process.  You cannot simply take the lot times and determine a deviation that makes sense.  Mathematically you can do it, but it has no basis in reality.  For that, you must go to gemba.
    BTW, take copious notes and understand the factors driving cycle time differences.  You will need to observe quite a number of assembly events, maybe without visibly recording anything in order to gain the trust of the operators.  If you just show up and start taking time study data, you’ll likely get results not representative of actual production.  Even after working with one mold-change team for about a month, before time studying them, I had one tech say, “I don’t know why we’re working so hard.  We know it’s only you.”  The point is your presence will influence the results so take that into consideration.

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