# equip. failure

#### Outlier

##### TS Contributor
A widget fails each month for six months. A fix is then installed.

How many months of no failures would need to go by before I can be 95% confident that the problem is fixed?

How is this calculated?

I wrote a paper on this and cannot find it for the life of me.

#### BGM

##### TS Contributor
Are you going to test
$$H_0: p = \frac {1} {6}$$ vs $$H_1: p = 0$$

with the number of months of no failure $$\sim Geometric(p)$$ ?

#### Outlier

##### TS Contributor
I used a binomial distribution. Maybe that was incorrect. I'll have to find that paper.

#### Link

##### Ninja say what!?!
Could it have been a poisson distribution with a rate parameter? I ask because you stated that there was 1 event/month.

#### Outlier

##### TS Contributor
How would you all recommend I do this?

#### Link

##### Ninja say what!?!
Following a Poisson distribution: $$Pr(N_{t}=k)=f(k;\lambda t)=\frac{(\lambda t)^{k}e^{-\lambda t}}{k!}, where \; \lambda =1$$
$$f(0;\lambda *1)=0.37$$
$$f(0;\lambda *2) =0.14$$
$$f(0;\lambda *3)=0.05$$

So three months.