Question

An item comes off an assembly line every minute and has a p=0.001 chance of being defective. The line will be stopped if there are two or more defects within 500 minutes. What is the probability the line will be stopped within the first 1000 minutes after a start up?

Answer 1

We use Poisson distribution

Let X be the number of defects per 500 minutes

with

The line will stop if there are two or more defects in first 500 minutes

Or less than 2 defects in first 500 minutes and more than 2 defects in second 500 minutes

= 1-0.9097 = 0.0902

Probability that the line will stop within 1000 minutes

=P(there are two or more defects in first 500 minutes ) + P( less than 2 defects in first 500 minutes and more than 2 defects in second 500 minutes )

= 0.0902 +0.0902*0.9097 = 0.1723