Change in Good Rate: 10 widgets, 9 good; find formula for

[UDcc123]

Please note that this is not a school problem, but rather a question that came up at my work. I thought it was quite interesting and hope someone here can help us out:

- Let's say we have 10 widgets, 9 of which are good. This gives us a 90% good rate
- If we pull away 5 of the good widgets, we are left with 4 good widgets out of 5 total = 80% good rate
- By pulling away 5 of the 9 good widgets, we pulled out 55% of the good widgets

- My question is: What formula would you use to say if you go from a 90% good rate to an 80% good rate, you lost 55% of your goods?

- Other examples:

- 750 good / 1000 total (75% good)...lose 500 good units (2/3 of all goods), and end up with 250 good / 500 total (50% good). What formula to use to get 2/3 as an answer when your good rate goes from 75% to 50%
- 900 good / 1000 total (90% good)...lose 800 good units (8/9 of all goods), and end up with 100 good / 200 total (50% good). What formula to use to get 8/9 as an answer when your good rate goes from 90% to 50%

Also, please note that our samples are at different points in time, so using the raw numbers is a bit complicated. As an example: When I am trying to figure out what % of goods I lose when going from 75% to 50%, my ratios are: 750/1000 to 200/400.

Thanks

 

[mmm4444bot]

Let a = initial good rate

Let b = subsequent good rate

Let n = percent of initial good removed

n = (a - b)/(a - a*b)

EG1

a = 75%

b = 50%

n = (0.75 - 0.50)/(0.75 - 0.75*0.50) = 0.6666…

n = 2/3

EG2

a = 90%

b = 50%

n = (0.90 - 0.50)/(0.90 - 0.90*0.50) = 0.8888…

n = 8/9

 

[UDcc123]

Re: Change in Good Rate

wonderful...thank you