equip. failure

[Outlier]

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]

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]

I used a binomial distribution. Maybe that was incorrect. I'll have to find that paper. :confused:

[Link]

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

[Outlier]

How would you all recommend I do this?

[Link]

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.