Question

The life length X of an electrical component follows an exponential distribution. There are 2 Processes by which component may be manufactured. The expected life length of the Component is 100 hrs. if process I is used to manufacture, while 150 hrs. if process II is used. The cost of manufacturing a single component byprocess I is 10 OMR , while it is 20 OMR for Process II. Moreover, if the components last less than the guaranteed life of 200 hrs., a loss of 50 OMR is to borne by the manufacturer. Which process is advantageous to manufacturer?

Answer 1

For process 1, = 100 hrs

For process 2, = 150 hrs

Now, Probability that X is less than 200 hours when manufactured from Process 1 = = 0.8647

Probability that X is less than 200 hours when manufactured from Process 2 = = 0.7364

Average Total spending on a single electrical component when manufactured from Process 1 = 10 + 0.8647*50 = 53.24 OMR

Average total spending on a single electrical component when manufactured from Process 2 = 20 + 0.7364*50 = 56.82 OMR

Thus, the process 1 is advantageous to manufacturer