Calculating Percentage of Errors

Date: 03/21/2002 at 20:57:28
From: Rod McComas
Subject: Calculating % of errors

What is a good formula for calculating % of errors when you have items 
to be picked off a shelf every day? You pick one item a day and check 
it against the order. You wish to assign a percentage to the error in 
wrong items and/or number of items. At the end of the month you wish 
to calculate the combined percentage correct, percentage of incorrect 
items, and percentage of incorrect quantities.  

I looked at (100%/number of items picked) * number incorrect (100/50)
* 50 = 100% and doing an average at the end of the month.  %/number of 
audited pickings. Interested in any better ideas!

Rod McComas

Date: 03/22/2002 at 13:02:21
From: Doctor Douglas
Subject: Re: Calculating % of errors

Hi, Rod,

Thanks for submitting your question to the Math Forum.

Here's the way I would do it. First, on a given day find the number of 
items N on the audited order.See how many line items are filled 
incorrectly, and call this number W. Then

  percentage errors in filling items would be P = (100) x (W/N)

This number will be only the percentage "wrong" on that day. Of course 
the numbers N and W will change from day to day. You can choose two 
numbers Y and Z for distinguishing between wrong items and wrong
quantities: Y and Z, since any error in filling will either be a 
problem in what kind of item (Y), or the quantity (Z). Obviously 
W >= Y and W >= Z, although it's not necessarily true that W = Y + Z, 
since a wrong line item could be *simultaneously* an error in type and 
quantity. We keep track of all the numbers (i.e. number of line items 
is N1,N2,...,N30 in a month of thirty days).

Then, at the end of the month, you add up all the numbers N, W, Y, and 
Z from all days in that month, and you can compute the same ratios:

  (100) x [W1+W2+...+W30] / [N1+N2+...+N30]   percentage "wrong"
  (100) x [Y1+Y2+...+Y30] / [N1+N2+...+N30]   percentage "wrong kind"
  (100) x [Z1+Z2+...+Z30] / [N1+N2+...+N30]   percentage "wrong qty"

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/