Question

The life length x of an electrical component follows and 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 by process i is rs. 10 /- while it is rs. 20 /- for process ii. moreover, if the components last less than the guaranteed life of 200 hrs., a loss of rs. 50/- is to borne by the manufacturer. which process is advantageous to manufacturer ?

Answer 1

Let P1P1, P2P2 be our processes and f1f1, f2f2their respective densities. Let PlPl be the probability of loss. Then Pl;f1=∫2000λ1e−λ1xdxPl;f1=∫0200λ1e−λ1xdx. Similarly, Pl;f2=∫2000λ2e−λ2xdxPl;f2=∫0200λ2e−λ2xdx, where λ1=1/100λ1=1/100 and λ2=1/150λ2=1/150. Also average cost for P1=10+50×Pl;f1P1=10+50×Pl;f1. Similarly, average cost for P2=20+50×Pl;f2P2=20+50×Pl;f2. You need to compare average cost not just probabilities.