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SRGM (Software Reliability and Growth Model) is an important mathematical tool for modeling and predicting the reliability improvement process in software testing stages (Ahmad, Bokhari, Quadri & Khan, 2008; Dohi, Matsuoka & Osaki, 2002; Zhang, Meng & Wan, 2016). Accurately modeling software reliability and predicting its possible trends are essential to determine the reliability of the entire product (Yamada, 2014;Okamura, Etani & Dohi, 2011; Okamura & Dohi, 2014; Zhang, Meng, Kao, Lü, Liu, Wan, Jiang, Cui & Liu, 2014). The description of SRGM is mainly implemented by establishing a mathematical model describing the testing process and obtaining the expression for the number of failures m(t) of cumulative testing. The study only from m(t), which is used to describe SRGM, is implemented from the perspective of reliability. At the same time, the test cost needs to be considered, that is, the TE (testing effort) needs to be considered. It is closely related to cost (Zhang, Meng, Kao, Lü, Liu, Wan, Jiang, Cui & Liu, 2014). TE describes the consumption of test resources, which can be represented by TEF (testing effort function). The release of software must consider not only the reliability requirements but also the cost factor (Zhang, Cui, Liu, Meng & Fu, 2014; Huang & Lyu, 2005). That is, the software release must consider the comprehensive standard of “cost-reliability”. Therefore, TE has become an important branch of SRGM research and has achieved a series of results.
Counting from the G-O model (Ahmad, Khan & Rafi, 2010) in the late 1970s, SRGM research has spanned two centuries, with a research history of nearly 40 years. Hundreds of related models have been proposed. These results have enriched the connotation of the research, but at the same time, they have also brought difficulties to the evaluation and selection of SRGM. At present, the performance of SRGM is mainly evaluated from the perspective of fitting and prediction, that is, the fit of m(t) to the real historical failure data and the prediction of future failures. For example, in the evaluation of the fitting between the model and historical data, MSE, variation, MEOP, TS, RMS-PE, BMMRE and R-square (Goel & Okumoto, 1979) are often used as metric choices. Among them, the closer the R-square standard is to 1, the better, but other standards are the different (the smaller these standards, the better); RE is used as the model's evaluation standard for future data prediction. The closer the RE is to 0, the better prediction. However, in fact, on different data sets, it is still difficult to find a model that performs well in the abovementioned fitting and prediction standards. In addition, it is difficult and nonquantitative to intuitively and singly judge the performance of the models from the level of these values.