Is this the correct methodology for comparing rates of speed?

August 26, 2006 1:42 PM

Is this the correct methodology for comparing rates of speed?

Let's say Miss Jane has a job in which she performs the same task all day. In the morning she gets three or four batches containing between 9 and 23 items that she has to process. We want to know how long it takes to do each batch and compare the speeds throughout the day, but it's tricky because the numbers vary.

I have a chart that looks like this that Jane fills in as she goes along:
batch number - number of items - total minutes per batch

for example
batch #1 - 18 items - 105 minutes to complete

then i use the formula # of items / time = speed, and get a series of decimals. the higher the decimal, the faster she went. then you can put these onto a graph and see if she is getting faster or slower over time.

my question is:
is this a valid and standard way of calculating this?
would i be able to show these numbers to a math person and have them get what i did?
am i leaving out anything important?
is there a better way to do this?

thank you!

posted by amethysts to grab bag (9 comments total)

Your model assumes one 18-item batch should take the same amount of time as eighteen 1-item batches. Is that true?
posted by cillit bang at 1:56 PM on August 26, 2006

Well, that's technically correct. Although it might be more proper to say rate rather then speed. The point cillit bang brings up is a good one, though.
posted by delmoi at 2:06 PM on August 26, 2006

1) Yes
2) Yes
3) As cillit bang says, you might need to adjust it for the potential overhead of having lots of small batches compared to one big batch
4) This seems like a very standard way to do it
posted by spark at 2:07 PM on August 26, 2006

yeah, lots of small batches or one big batch would be about the same.

as you can see i haven't had to think about this stuff since i was in high school math.
posted by amethysts at 2:15 PM on August 26, 2006

I think what spark meant by "overhead" (point 3) was that maybe there are some unavoidable startup tasks that take the same time with every batch (setting up the work space, filling out the header on the form, whatever).

If this were true, then your method would make it look like Miss Jane went much slower when doing small batches than large. So if she has a large batch to start, then a small batch, it will look like her efficiency is going down during the day... when really she might be taking the exact same amount of time per item in each batch.

To fix this, you could try to subtract out the "overhead" time from each batch. I'm not sure how that would work for your specific case though.
posted by LobsterMitten at 3:46 PM on August 26, 2006

Er... clearer with an example.
Suppose there are 5 minutes of startup tasks for every batch. Suppose she does two batches:
Batch 1... 50 items... 55 minutes
Batch 2... 5 items... 10 minutes

In each case it's taking her one minute per item.

But compare the rates of these batches using your method:
Batch 1... 50/55 = rate of 1.1
Batch 2... 5/10 = rate of 0.2

It looks like her efficiency is lower in the second batch. But in fact she's taking the same amount of time per item. So if there is this overhead, your method will misrepresent her efficiency if some batches are really big and some are really small.
posted by LobsterMitten at 3:52 PM on August 26, 2006

Er, where I said 1.1 it should be 0.9, and where I said 0.2 it should be 0.5. That'll teach me to look at the screen with my stupid eye.
posted by LobsterMitten at 3:57 PM on August 26, 2006

yeah, lots of small batches or one big batch would be about the same.

well, at least while you're taking your measurements, there is going to be some overhead since you mention that:

I have a chart that looks like this that Jane fills in as she goes along:
batch #1 - 18 items - 105 minutes to complete
posted by juv3nal at 7:23 PM on August 26, 2006

those are good points. but what i forgot to mention was that the startup tasks are all done at the same time, in the beginning. she gets all the batches and gets them all ready to go all at once, puts them in a pile, and then starts in. so all that prep time is considered separately. the time it takes to grab the next batch is negligable.

additionally, the stretching, peeing, coffee-getting, etc. plus when she writes down her start and finish times, isn't figured in. the only thing that's being recorded is the time she started the batch and the time she finished it. this is because if she is getting through the batches at a good pace, she can afford to take this time. but how can we know if she's going at a good pace? aha i know a way.. etc.

therefore from your suggestions i think i am A-OK.
(but please feel free to add if you want to)
posted by amethysts at 10:20 PM on August 26, 2006