Reference no: EM132856074
Your company specializes in the design and construction of pre-fabricated, welded, openframe, steel structures for industrial use (e.g. pre-fabricated warehouses).
From past experience about 0.4% (i.e. 4 in 1, 000) of new welds contain potentially significant flaws We will call these bad welds. If a bad weld is placed in service it may lead to a visual failure of the joint when the structure is in service. If a bad weld is placed in service, the probability that it causes a joint failure is 0.05 (i.e. 5 in 100 bad welds that are placed into service suffer a visual failure during the warrantee period). For the purposes of this problem, assume that this is the only significant mechanism for joint failure.
If a joint fails in service during the warrantee period, your warranty requires that you fix the failed joint in the field. This is a costly endeavor. The anticipated cost of the necessary in-service, remedial work for a failed joint is $12, 000 per failed joint. An ultrasonic testing device may be used to inspect each weld in the fabrication plant. This device will detect a bad weld with a probability of 0.97 (i.e. 97 out of 100 bad welds are identified by the ultrasonic testing device). Note this means that 3% (i.e. 3 out of 100) of the bad welds go undetected by the ultrasonic testing device; these cases are called false negatives. Furthermore, the ultrasonic test will also wrongly signal a bad weld in 1% of the good (not flawed) welds; these cases are called false positives. The additional cost of the ultrasonic tests is $2 per weld. A thorough X-ray analysis of a weld is an alternative test that can be carried out in the fabrication plant. Such tests are completely accurate, but they are considerably more expensive costing $10 per weld. The cost of an initial weld is $9 per weld. The cost to redo a bad weld in the fabrication plant is $15 per weld. Compute and compare the expected costs per weld (including the welding, testing, replacement, and remediation costs) under the following four candidate policies:
a) No inspection in the fabrication plant. Simply pay for the field repairs when the need arises.