The company is employing three machines for the production of deck shoes. The three machines operate in a sequence from A to C and each machine completes a component on the shoes. So failure of one machine will break the entire chain of production. The individual reliability of success of each company is 0.84, 0.91 and 0.99 for machine A, B and C, respectively.
Reliability and Redundancy
The combined reliability of the entire production system is
0.84 x 0.91 x 0.99 = 0.757
The overall system reliability is very low which can be increased by means of redundancy(Heizer & Render, 2001). Redundancy is the way of backing up the individual or all components of system. In our case, each individual component can be replaced with another which will have same reliability.
Alternatives
The company can increased its overall reliabilities by means of redundancy. The company has various alternatives from backing up only one machine at a time to backing up the whole system. The results of various alternatives are (for calculation, see appendix):
Option A
If the company wishes to backup a single machine
In case machine A is backed up only, the system reliability will increase to 0.878 while machine A reliability will increase from 0.84 to 0.974.
In case machine B is backed up only, the system reliability will increase to 0.825 while machine A reliability will increase from 0.91 to 0.992.
In case machine C is backed up only, the system reliability will increase to 0.764 while machine A reliability will increase from 0.99 to 1.00
Option B
If the company wishes to back up two machines at a time,
In case of A and B, the system reliability will increase to 0.957
In case of C and B, the system reliability will increase ...