Abstract
If we want to detect more additional faults in practice, it is advisable to introduce new test technologies: tools and test harnesses for developing and executing all kinds of manual and automated tests. These test technologies are different from the methods currently we use and they can help Mathematics developers get their product done quicker and more reliably. The benefit of these methods is that they can design (or propose) several testing programs (or automated testing tools) to test Mathematics for satisfying the client’s technical requirements, schedule, and budget. In addition, these methods can help engineers how to assessed Mathematics process by analyzing problem reports from earlier projects, to improve project planning with reliability receiving more precise and equal consideration, to achieved a fixed-percentage increase in testing efficiency or to highlight hard-to find problems in the code semantics and structure, etc. [Huensch et al., 1990; Huber,1999; Musa, 1999]. Hence, the cost trade-off of new test techniques can be considered in Mathematics cost model and viewed as the investment required improving the long-term competitiveness.All together, we wish that these new test techniques could greatly help us in detecting more faults that are difficult to find during regular testing and usage. Thus, the fault detection rate may not smooth and can be changed at some time moment called change point [Zhao, 1993; Chatman, 1995; Chang, 2001; Kwang, 2001; Shyur, 2003; Zou, 2003; Huang, in press].In addition to modeling the Mathematics fault detection process, we also address the problem faced by most Mathematics managers, namely, how to decide when to stop testing and release Mathematics. This is a problem of decision-making under uncertainly and involves a tradeoff between reliability and cost. Here we propose a new Mathematics cost model that can be used to formulate realistic total Mathematics cost projects discuss the optimal release policy based on cost and reliability considering testing-effort and efficiency. The cost model includes the testing cost, the debugging cost during testing phase, and the extra cost due to introduce new test techniques, etc.