equip. failure

Outlier

TS Contributor
#1
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
#2
Are you going to test
\( H_0: p = \frac {1} {6} \) vs \( H_1: p = 0 \)

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

Link

Ninja say what!?!
#4
Could it have been a poisson distribution with a rate parameter? I ask because you stated that there was 1 event/month.
 

Link

Ninja say what!?!
#6
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.