Final answer:
The overall reliability of a procurement setup with three vendors, each having a reliability of 0.95, is calculated by taking 1 minus the cube of their individual failure rates (0.05). This results in an overall reliability of 99.9875%.
Step-by-step explanation:
The question is asking about the overall reliability that a retailer achieves by using three vendors, each with a reliability of 0.95, to manage supply chain disruption. To calculate the overall reliability when sourcing from multiple vendors, you can multiply the probability of failure for each vendor and subtract the result from 1 (since reliability plus failure rate equals 100%).
The probability of failure for one vendor with 0.95 reliability is 0.05 (1 - 0.95). Assuming the failures are independent events, the combined probability of failure from all three vendors is 0.05 × 0.05 × 0.05 (0.05³), which is 0.000125.
The overall reliability of the system is then 1 - 0.000125, which equals 0.999875 or 99.9875%.