## 4 Case Study: Application of the Modified FMEA-DEA for the RFID System
### Measurement of the Efficiency of the FMs by DEA (Steps 2.1-2.4)  
The outcomes of the modified FMEA and the synthetization procedure served as inputs/outputs of the DEA model explained in Section 3.3.1. The efficiencies of DMUs (FMs) were found using PIM DEA version 3.2; the application of the steps of stage two explained in Section 3.3.2 yielded the results in Appendix C, as summarized in Figure 5.  
The ranks of the failure modes in the modified FMEA and the FMEA-DEA methods are contrasted in Figure 6. After the application of the DEA and the incorporation of time and cost, most FM ranks seemingly changed. Consequently, we obtained three categories of FMs: those with increased priority, those with decreased priority, and the few FMs that retained their position. For instance, \(FM_{2}\) had minimal priority in the FMEA method, but when efficiency was incorporated together with cost and time, its priority rank switched from 43 to 9. This FM concerns the settings that can be adjusted in a short duration of time with the minimum dispensed, whilst not fixing it would lead to improper or even non-functioning of the system. At the same time, the failure mode \(FM_{22}\), which is related to the positioning of the tag, was initially ranked last and moved into eighth by winning 33 ranks. Similarly, \(FM_{5}\), caused by corrosion, won 33 ranks; this can be avoided by effectively choosing the tag. Meanwhile, the failure mode \(FM_{34}\) moved down by 34 ranks, which was related to the age of the tag and the non-reception of the signals due to environmental disturbances. This FM occurs infrequently because the life cycle of the tags is usually sufficient for the destined application. Moreover, attempting to deal with the space between the tag and the reader would be very costly and is often uncontrollable.  
Table 5 presents some of the FMs that became high-ranking against others that lost ranks, in addition to suggested replacements; obviously, other combinations are possible. As an example, we can use reduced time and cost to solve failure modes 2, 5, and 22 instead of \(FM_{34}\). Furthermore, the summation of their RPNs is 32.479. This is more than the RPN of \(FM_{34}\), which is equal to 22.52. Another example is \(FM_{35}\), which is related to the signal transmission between the tag and the reader caused by wave disturbance. This dropped to the 28 th rank by losing 25 positions with an RPN equal to 31.563; solving this FM requires USD 101 and 95 min. Thus, we can solve \(FM_{31}\) and \(FM_{17}\) in less time (\(50+42.5=70.5\) min) and at a cheaper cost (USD 35.25 + USD 35.25 = USD 70.5), with higher resulting RPN (\(15.84+24=39.84\)). This is because \(FM_{31}\) is related to the reader setting, which is easy and important, and \(FM_{17}\) occurs when different tags have the same EPC number and can be  
Figure 5: Measurement of the Efficiency of the FMs by DEA and final ranks.  
eliminated solely by quickly checking the tag numbers before using them in applications or projects.  
In light of what has been stated previously, we can conclude that the most efficient FMs concern the transfer of data, source of energy, settings, and choice of tags (memory, humidity, life cycle, temperature), as well as the settling of the transponder and the base station.