To combat channel fading, cooperative communication achieves spatial diversity for the transmission between source and destination through the help of relay. However, if the relay behaves abnormally or maliciously and the destination is not aware, the diversity gain of the cooperative system will be significantly reduced, which degrades system performance. In our thesis, we consider an one-relay decode and forward cooperative network, and we assume that the relay may misbehave with a certain probability. If the relay is malicious, it will garble transmission signal, resulting in severe damage to cooperative system. In this work, we discuss three kinds of malicious behavior detection. More specifically, we adopt sequential detection to detect the behavior of relay. If tracing symbols are inserted among the source message, the destination detects malicious after extracting the received tracing symbols. We adopt log-likelihood ratio test to examine these tracing symbols, and then determine the behavior of relay. If the source does not transmit tracing symbols, the destination detects misbehavior according to the received data signal. Furthermore, we employ sequential detection to reduce detection time for a given probabilities of false alarm and miss detection. Through simulation results, for a certain target on probability of errors, our proposed methods can effectively reduce numbers of observations. On the other works, the destination can effectively detect misbehavior of relay, and eliminating the damage causes by malicious relay without requiring large numbers of observations.

System testing is very time-consuming and costly, especially for complex high-cost and high-reliability systems. For this reason, the number of failures needed for the developmental phase of system testing should be relatively small in general. To assess the reliability growth of a repairable system, the generalized confidence interval and the modified signed log-likelihood ratio test for the scale parameter of the power-law process are studied concerning incomplete failure data. Specifically, some recorded failure times in the early developmental phase of system testing cannot be observed; this circumstance is essential to establish a warranty period or determine a maintenance phase for repairable systems. For the proposed generalized confidence interval, we have found that this method is not biased estimates which can be seen from the coverage probabilities obtained from this method being close to the nominal level 0.95 for all levels of γ and β. When the performance of the proposed method and the existing method are compared and validated regarding average widths, the simulation results show that the proposed method is superior to another method due to shorter average widths when the predetermined number of failures is small. For the proposed modified signed log-likelihood ratio test, we have found that this test performs well in controlling type I errors for complete failure data, and it has desirable powers for all parameters configurations even for the small number of failures. For incomplete failure data, the proposed modified signed log-likelihood ratio test is preferable to the signed log-likelihood ratio test in most situations in terms of controlling type I errors. Moreover, the proposed test also performs well when the missing ratio is up to 30% and n > 10. In terms of empirical powers, the proposed modified signed log-likelihood ratio test is superior to another test for most situations. In conclusion, it is quite clear that the proposed methods, the generalized confidence interval, and the modified signed log-likelihood ratio test, are practically useful to save business costs and time during the developmental phase of system testing since the only small number of failures is required to test systems, and it yields precise results.