Standard specifications for the shop-welding of certain structural assemblies indicate that welds with internal flaws g...
Standard specifications for the shop-welding of certain structural assemblies indicate that welds with internal flaws greater than a critical volume cannot be permitted in order to guarantee adequate strength. An expensive x-ray inspection system is presently being used to inspect all welds. The test is considered to be absolutely accurate, and history shows that 15 percent of all welds are found flawed and therefore need to be re-welded The fabricator is considering introducing a new, less-expensive, but not perfectly reliable ultrasonic inspection device. If a flaw is present, the device will indicate the flaw with probability of 0.85 and erroneously pass the weld with probability 0.15. If no flaw is present, the device will pass the specimen with probability 0.90 and incorrectly indicate a critical flaw with probability 0.10. The use of the x-ray system costs $3.00 per weld. The cost of the new method is $1.00. If a weld needs to be re-weld the cost is $10.00, but if a flawed weld leaves the shop the cost is $35.00. If a weld is found to be flawed and gets redone, assume that the x-ray test will be used to re-check the quality before it leaves the shop. Answer the following: a. What is the probability of finding a flawed weld using the ultrasonic device? [5 marks] b. Set-up a decision tree that considers all options in order to find the minimum expected cost. Use the decision tree to find the minimum expected cost. You must calculate all probabilities of the decision tree. [15 marks]
Standard specifications for the shop-welding of certain structural assemblies indicate that welds with internal flaws greater than a critical volume cannot be permitted in order to guarantee adequate strength. An expensive x-ray inspection system is presently being used to inspect all welds. The test is considered to be absolutely accurate, and history shows that 15 percent of all welds are found flawed and therefore need to be re-welded The fabricator is considering introducing a new, less-expensive, but not perfectly reliable ultrasonic inspection device. If a flaw is present, the device will indicate the flaw with probability of 0.85 and erroneously pass the weld with probability 0.15. If no flaw is present, the device will pass the specimen with probability 0.90 and incorrectly indicate a critical flaw with probability 0.10. The use of the x-ray system costs $3.00 per weld. The cost of the new method is $1.00. If a weld needs to be re-weld the cost is $10.00, but if a flawed weld leaves the shop the cost is $35.00. If a weld is found to be flawed and gets redone, assume that the x-ray test will be used to re-check the quality before it leaves the shop. Answer the following: a. What is the probability of finding a flawed weld using the ultrasonic device? [5 marks] b. Set-up a decision tree that considers all options in order to find the minimum expected cost. Use the decision tree to find the minimum expected cost. You must calculate all probabilities of the decision tree. [15 marks]