# Math Help - How to use probability to determine impact of change in inspection interval?

1. ## How to use probability to determine impact of change in inspection interval?

Hi,

I'm new to this forum so if i'm in the wrong place, please tell me ok?

I have a problem that i can describe but i can define the problem statement in terms of probability. I'm not even sure whether probability can be used to solve the problem in the first place. Anyway, here goes..

I'm currently inspecting an aircraft component for corrosion and cracks every 200hrly. These are random failures. I have inspected 50 aircraft for the past 1000hrs for each aircraft i.e. thats makes for 5 inspections done so far per aircraft. I have found zero defects thus far. I now want to extend the interval for the same inspection from 200hrly to 400hrly. I know that at the back of my head, that by doing so, i increase the probability of not detecting any cracks and corrosion, because i'm checking the component less often. BUT i also know that the data thus far tells me that the reliability of the component is good i.e. no cracks and corrosion so far. How can i use probability to say how much less likely am i able to detect cracks and corrosion, when i extend the interval?

Thanks!

Ethan Ng

2. Originally Posted by EthanNg
Hi,

I'm new to this forum so if i'm in the wrong place, please tell me ok?

I have a problem that i can describe but i can define the problem statement in terms of probability. I'm not even sure whether probability can be used to solve the problem in the first place. Anyway, here goes..

I'm currently inspecting an aircraft component for corrosion and cracks every 200hrly. These are random failures. I have inspected 50 aircraft for the past 1000hrs for each aircraft i.e. thats makes for 5 inspections done so far per aircraft. I have found zero defects thus far. I now want to extend the interval for the same inspection from 200hrly to 400hrly. I know that at the back of my head, that by doing so, i increase the probability of not detecting any cracks and corrosion, because i'm checking the component less often. BUT i also know that the data thus far tells me that the reliability of the component is good i.e. no cracks and corrosion so far. How can i use probability to say how much less likely am i able to detect cracks and corrosion, when i extend the interval?

Thanks!

Ethan Ng
1. If this is a real problem (we are talking about inspecting real aircraft) then don't ask here but get paid for professional advice.

2. One approach to this problem is to assume that failures are random in time with a mean time between failure of $t_0$ which we assume apriori is uniformly distributed between 1 and 100000 hours. Now we have a problem in Bayesian statistics to compute the posterior distribution of the mean time between failure given your data, and from that everything else we are interested in

CB

Ethan Ng

4. Originally Posted by EthanNg