【正文】 probability of the percentage of reachability ? / 2 events being p is ??? / 2 f? ,? ( p)dp . By adjusting the values of ? and ?, we can change the form of test profiles, as shown in Figure 3. D. Test Profile Model based onDmax Dmax is an integer value within 0 and Q, where Q is the relationship between the GUI test profiles and the fault detection in GUI testing. We show the procedure using the test profile model with a single parameter ?, as model (1), (3) and (6). Other model can also be applied on this procedure. We first study what values the parameter ? can set. A set of values of ? are then determined. For each of the value of ?, n test suites are generated following the distribution of TP(?). These test cases are executed on the m faulty versions of the GUI AUT. The average number of defected faults with respect length of the shortest path between the farthest two events in to each test profile TP(?) is collected (., N F (? ) ). At last, the bination of all the EFGs and the IT of the AUT (refer to Section ). At most time, Q is a much larger than the Dmax. Similar with model (1) and (2), we can approximately follow a Poisson distribution of Dmax to select test cases, as the following test profile model: TP(?) = { ?Dmax=k, ?k?1e??/(k?1)!?, k = 1,2,… ,Q}. (6) Note that when we use this test profile model, the value of ??should be set to much smaller than Q, to keep the probability of DmaxQ very small. The uniform distributions of Dmax can also used as test profiles in GUI testing, as the following model: TP = { ?Dmax=k, 1/Q?, k = 1,2,…, Q}. (7) E. Test Profile Model based on N(w) N(w) describes in the execution of a test case, how many events will be applied on the window w. We define the following test profile model based on this characteristic: TP = { ? ni, wi?, k = 1,2,… ,R}. (8) where R is the number of windows contained in the GUIs of the AUT, and wi is the ith window of the AUT. By setting different values to n1, n2, …, nR, we can adjust the test effect on each window. IV. GUI TEST PROFILE AND FAULT DETECTION We have presented eight models of GUI test profiles in the previous section. In this section, we first introduce how to study the relationship between test profiles and fault detection. Then, a control scheme is proposed to improve the test efficiency of GUI testing. A. Studying the Relationship between Test Profile and Fault Detection Suppose the test profile is modeled as TP(S), where S is the set of the parameters of the test profile model TP. Specifically, S = {?} if model (1), (3), or (6) is used, S = {?,?} is model (5) is used, S = ? if model (2), (3), or (7) is used, and S = {n1, n2,…, nR} if model (8) is used. Figure 4 shows the procedure of empirically studying the we fit the data set {(?, N F (? ) ), for ?=1,2,… ,M} on a proper function f which have a set of parameters a1, a2,… In future, many experiments should be conducted following this procedure to study the form of f. N F (1) N F (2) N F (M ) Figure 4 Study the relationship between the test profiles and the fault detection in GUI testing B. Improve Testing Efficiency by Online Adjusting Test Profile In our previous work reported in [1], we proposed a dynamic partitioning method for GUI testing following the idea of software cyberics. The method online adjusting the partitions of test cases, and the test cases in the partitions that are more likely to detect faults are used preferentially. It is an indirect method of online adjusting the test profile. Experiment results showed it is an effective way of improve the efficiency of GUI testing. Based on the models of test profile in this paper, we will propose a direct way of online adjusting the test profile. A GUI application may contain many faults. Commonly, a large test suite will be used to test it. Let’s study the following scenario. At the beginning, testers know little about the test suite and the application under test. Then they may randomly execute test cases. After some test executions, the testers can learn something about the test suite, for example, the test case with certain characteristics should be used more frequently in264 order to improve defect detection. With the knowledge, they can change the test execution strategy to improve the efficiency of testing. In the above process of software testing, the knowledge learned from the previous test executions are used to optimize the test profile. Can this process be automated? Based on the relationship between test profile and fault detection, we propose the automated GUI testing scheme shown in Figure 5 that may be able to detect more faults in testing. Figure 5 A Poisson distribution of L as a test profile At the beginning of testing, when have no prior knowledge about the test suite or the application under test. An initial test profile (a nonuniform test profile with initial parameters) is used to select/generate test cases. These test cases are then executed on the AUT. The execution result z, ., whether a fault is detected, are then recoded. After certain number of test cases executed, some knowledge can be obtained from the history data. Then the test profile is online adjusted by the controller. The controller is based on the relationship between the test profiles and fault detection obtained in Figure 4, ., f. It tries to approximate the test profile to the one that can maximize f(?