Question

You are involved with managing a factory that produces long sheets of weed matting. Every so often the machine will introduce a defect into the weed matting - you want to know if the distribution of these defects over some fixed length of matting is well described by a Poisson distribution. a. The machine is known to get less reliable as it gets closer to the time for it to be serviced. Do you think the Poisson would be a good model, what assumption might be violated?

Answer 1

the Poisson distribution may not be the best model for describing the distribution of defects over the fixed length of matting. The assumption of a Poisson distribution is that events occur independently at a constant average rate. However, in this case, the machine’s reliability decreases as it gets closer to the time for servicing. This violates the assumption of a constant average rate, as the occurrence of defects may be affected by the machine’s deteriorating performance. Therefore, a Poisson distribution may not accurately capture the changing reliability of the machine and the distribution of defects in this scenario.