Example 7.3

A sophisticated CNC machine is being used in the shop floor and there is a critical component in the machine which regularly fails, hence you always keep few spare parts of that critical component. The average failure rate of the critical component is 5 hours. You as the shop floor manager ask you main operator to investigate the problem and he says that the break down occurs every night at a particular time which is 8.30 PM. Verify the claim made by the main operator is true or false.

Solution 7.3
From the information given the average failure rate of the machine is  failures per hour, thus , hence we will always have: , where k is constant.

Nomenclature

Machine functioning (green colour code)
Machine may or may not function (yellow colour code)
Machine failed (for this example it fails at 2030 hours) (red colour code)

What we are doing is to evaluate the probability on a time scale of 24 hours and check whether the value is equal or not, but as this is exponential, hence the statement that the value of the probability that the machine fails from where ever you measure your time is untrue, hence the claim of the operator is false.