[Closed] Help me combine two numbers..

I'm quickly thinking 63%

In my experience, **** all

63% if they are independent of each other

69?

If they are truly independent then 63% over a long enough period of time. But due to the nature of randomness the distribution of downtime is unlikely to be even, so in a given week the percentage of downtime could be much higher or lower.

What was your guess, and what do your colleagues say?

63% if they are independent of each other

Yes. And I approve of your precision & brevity, sir.

Depends whether they are/should be in operation for the same amount of time. What are you measuring your percentages on, occasions of failure, time spent up v time spent down? If something is down for an hour but could do an operation 6 times in that hour whereas the other is down for an hour and could do an operation 12 times in an hour, then you need to decide whether they have both been down for 50% of the downtime, or one has been down 66% of the downtime.

Depends on whether you're measuring apples or pears.

At any given time, I think it's 63%. So that's the chance of them being up when you start testing. But whether they will stay up until the test is complete depends how long the test takes.

Is the probability unit of availability week or day? It doesn’t matter, but you can have fun with the calculation regarding not failing during the week.

In reality you are combining two poisson distributed random variables. The distribution will be interesting.

Right cool. Many thanks. I reckoned 63 but the boss was having none of it. He insisted it was 60%

Thanks

63% if they are independent of each other

Username checks out

7090%?

i'd spend more time trying to get those availability numbers up closer to 100% rather than spending time arguing over a few %

63% mathematically, but i'd use 60% in an argument to get someone to pull their finger out

If you use the Stercore Poloniae Transformation algorithm you get 62.9999%

(hopefully) not hi-jacking, just being completely thick here, but how did you guys work out 63% from 70 / 90% availability?

Just curious and trying to learn tbh

For two independent outcomes, the chance that both outcomes are true is the multiplication of the two chances.

In this case the testing system needs both parts to be available, the two availabilities are 0.7 and 0.9, and so multiplying these together gives 0.63 or 63%.

It's just 70% of 90%, or 90% of 70%. Statistically 63% works out, but statistics aren't real life and if you need hard and fast numbers then you can actually only guarantee 60% of the week will be available for testing. What if the 10% downtime of one falls entirely within the 70% uptime of the other? It's unlikely if we're talking truly random distribution of failures but it's not impossible, and would you like to be the one who promised 63% test capacity on the one week you only get 60%?

Is that 90% and 70% across a 5 day working week or a 7 day week and will you be testing 5 or 7 days? If downtime calculations are across 7 days and you're only using it 5 days then your 37% downtime of 2.59 days could occur in one or two chunks on working days which actually gives you a downtime of 51%. That is obviously a worse case scenario.

Edit: I think my maths are correct but it is early in the morning and I haven't had any tea or coffee.

42

Can I go against the curve here so you can take me down in flames.

There's a 30% chance of one system being unavailable and 10% chance of the other being unavailable.

0.3 x 0.1 = 0.03.

So a 3% chance of them being unavailable, meaning 97% uptime.

So by that logic add in another system with 70% uptime and you have pretty much guaranteed uptime across all three systems... Not sure about that

0.3*0.1*0.3=0.009 so 99.1% uptime? We should add in some more dependancies.

There's 3% chance that both are unavailable, so 97% that at least one is up, but the OP needs then both to be working.

@potatohead

We have two main components in our test system, both of which need to be up for testing to happen

You're calc would be appropriate if you were for example talking about a plane with two engines, each of which has a 90% success rate there's a 10% chance of an engine failure and a 1% chance of both failing at the same time - but if you can still fly with one out then you've got a 99% of a successful flight. If you need both to be working...... it drops to 81% (still preferable to Ryanair though)

if you need hard and fast numbers then you can actually only guarantee 60%

Statistically, I don't think you can guarantee any availably. There's a very small probability (if I was better at statistics I might try to calculate it) that both systems won't be up at the same time at any point in the week. But I'm curious, as the OP's boss also mentioned 60% - how did you calculate that?

52% or 48%, I don't know which.

Can I go against the curve here so you can take me down in flames.

There’s a 30% chance of one system being unavailable and 10% chance of the other being unavailable.

0.3 x 0.1 = 0.03.

So a 3% chance of them being unavailable, meaning 97% uptime.

Are you a salesman?

With the 63% if your boss says 60 ask for his working you know just so you know his methodology 😉

This does assume you can operate and maintain them independently too.

Not a salesman - just an optimist.

It does raise an important point though. If both systems could be down at same time 3% of the time then this needs to be factored into the original figure of 63%, which is only looking at one or other.

By my calculations this would bring it closer to 65% rather than 63%, which is better!!

At this point I feel like I need to build a model to show this....

Go for it-would be genuinely interest in the most mathematically correct answer. I accept 63% is the obvious answer, but that is too simplistic;

EDIT For example;

In the best case scenario, the system with 90% is only down at the same time as the system with 70% availability. In this case, you would have 70% usage.

Worst case, they are never down as the same time. This would be 60% availability.

I will but not on a Saturday night I have standards! (it's the day job anyway)
And yes the answer may be simplistic but without more data we can't have a more accurate valid answer. Also op drom me a message if you want this proved properly my rates are very good 😉

If both systems could be down at same time 3% of the time then this needs to be factored into the original figure of 63%, which is only looking at one or other.

No, because 63% is the time they are both up. What happens in the other 37% doesn't change that.
For info, the rest of the probabilities are 3% both down, 7% just the more reliable one down and 27% just the less reliable down. Those are statistical probabilities, ie, what you'd get if you averaged the availability over a lot of weeks, not what will happen any particular week.