Table 3. Description of Cost with One Inspection Compared to Inspection with Re-Inspection of Initially Rejected Parts
Results of Only One Inspection Case 1
Inspection Cost
Internal Defect Cost External Defect Cost Total Cost
Inspection Cost
Internal Defect Cost External Defect Cost Total Cost
$500 $260 $300
$1,060
$565 $149 $555
$1,269
Case 2 $500 $65
$300 $865
Results of Initial Plus Reinspection Case 1
Case 2 $565 $37
$555 $1,157
Case 3 $500 $260 $75
$835
Case 3 $565 $149 $139 $853
Case 4 $500 $260 $750
$1,510
Case 4 $565 $149
$1,388 $2,102
rejection of a good part, also known as a false alarm. Te miss rate (m) is defined as the number of defective parts accepted divided by the total number of inspected, actually defective parts. Te false alarm rate (f ) is defined as the number of acceptable parts rejected divided by the total number of actually good parts inspected. Te model of inspection assumes the deci- sion to accept or reject a part is not swayed by the decisions made on prior parts or knowledge of the lot quality ahead of time. Te study also assumed sufficient references existed to abso- lutely define good from bad parts. Schorn offers this example: Sup- pose a tub of 1,000 castings is to be inspected and it is known that 10% of those castings are nonconforming. Te inspector operates with a miss rate of 15% (m = 0.15) and a false alarm rate of 5% (f = 0.05). Te expected results are found in Table 1. Te percentage of parts that are actually conforming and sent on to the customer is 855 of the 870 that were judged to be good parts, or 98.28% of the total inspected parts. Te defect rate to the next operation has been improved from 10% bad to 1.724% bad, equivalent to 17,241 parts per million (PPM). In the example, the number of
2
castings that were rejected at inspec- tion was 130, only 85 of which were actually bad. Depending on the next operation for these rejected castings, they may be melted, reinspected or reworked in some manner. Te cost associated with false internal rejects can be substantial. Te overall effec- tiveness of the inspection depends on both types of errors (miss rate and false alarm rate) and the relative percentage of bad product in the lot. In this example, the overall effective- ness is simply the percentage of correct decisions: 94%. A subsequent round of inspection is meant to catch any parts the inspector might have missed, but it also subjects the lot to another round of false alarm
46 | MODERN CASTING November 2012
Procedure Te study began with
two errors that can be made in the process of inspection: missed bad parts and the
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