Probability and quality control

#1
Hi all,

I am simulating a process in Arena software. One part of the process has a delay of a normal distribution of mean 4 minutes with a deviation of 1.

The parts leaving this process have a 10% probability of failing inspection. What I want to do is decrease this probability of failure by increasing the mean time of the process, but I can't seem to work out any correlation between the process time and the failure probability.

Is it as simple as saying that a doubling of the process time i.e. up to 8 minutes, would halve the failure probability down to 5% or do I need to be looking elsewhere with this?

Many thanks in advance.
 
#2
The parts leaving this process have a 10% probability of failing inspection. What I want to do is decrease this probability of failure by increasing the mean time of the process, but I can't seem to work out any correlation between the process time and the failure probability.

(Emphasis added.)
That’s the nub of the problem. There is no obvious way to relate the process time to the failure rate. Indeed, the two may be entirely unrelated. For example, the failures could be the result of inherent flaws and/or weaknesses in the raw input materials, and no amount of slowing down the process will fix that. Or, the process machinery itself may be incipiently faulty. In short, any number of possible factors other than the process time could be the main culprit that causes failures.