Help required! Percentages and SLA

[tr4v15]

Really need help from someone on how to work out a target for work...

We currently have to answer 95% of emails within 4 hours

I need to know a formula that will allow me to work out how many emails it will take to restore our Service Level back to 95% at any given moment should it drop below the 95% target

Figures I have at my disposal are:

Current Service Level in %
Total amount of emails received
Total amount of emails that have failed the 4 Hour response

Please help

 

[tkhunny]

Your difficulty is in resetting. Do you reset every day? Every week? Every three hours? It makes a difference, since 95% is meaningful only after a reset.

Let's say it's daily. Every morning, you have processed zero (0) emails.

At some point, you have processed 1000 emails, but managed only 900 within four hours. This is 900/1000 = 90%

This leaves you an algebra problem. The important part is to notice that bad emails go in the denominator and good emails go in the numerator and the denominator.

Example of bad email. We had 900/1000, after one bad one, we have 900/1001 <== See how it made it only to the denominator?
Example of good email. We had 900/1000, after one good one, we have 901/1001 <== See how it made it only to both numerator and denominator?

Solve this: \(\displaystyle \frac{900+n}{1000+n} = 0.95\)

More generally, given the informatino you have provided:

P = Current Service Level in %
R = Total amount of emails received
F = Total amount of emails that have failed the 4 Hour response

It should be obvious that \(\displaystyle P = \frac{R-F}{R}\). This makes your goal \(\displaystyle \frac{R - F + n}{R+n} = 0.95\)

Solving for n gives 20F - R

In my 1000-example, R = 1000, F = 100 and 20F - R = 2000 - 1000 = 1000. Checking (900+1000)/(1000+1000) = 1900/2000 = 0.95.

Of course, this works ONLY until you have one mroe failure. You must be PERFECT in order to achieve 95% as suggested.