Assumptions Used by PNZ Model
- The phenomenon of Fault removal is modeled by using the Non-Homogeneous-Poisson-Process.
- The software is subjected to failures during the execution which is caused due to faults remaining in the software.
- The introduction rate is a linear function time-dependent overall fault content function.
- An S-shaped curve is formed by the Fault removal rate that can be used to understand the learning process of software testers.
- Due to Fault generation, faults can be introduced in the software during the process of debugging.
- The fault detection rate function is non-decreasing time-dependent with an inflection S-shaped model.
- The PNZ model assumes that faults can be classified based on their severity, and the severity of a fault affects the time it takes for the fault to be detected and removed from the software.
- The model assumes that the number of faults introduced into the software is proportional to the size of the software code and that the introduction rate can be estimated using historical data or expert judgment.
- The model assumes that the fault removal process is influenced by factors such as the expertise and experience of the testers, the quality of testing tools and techniques used, and the complexity of the software being tested.
- The model assumes that the fault detection rate is influenced by the testing effort invested, which can be measured in terms of the number of test cases executed, or the time spent on testing.
- The model assumes that the software development process is iterative and that each iteration involves testing and debugging activities that contribute to the overall fault content of the software.
- The model assumes that the fault content of the software can be reduced to an acceptable level by applying appropriate testing and debugging practices and that the residual faults remaining in the software can be managed through ongoing maintenance and support activities.
Theorem:
Assume that the time-dependent fault content function and error detection rate are, respectively, [Tex]$$ a(t)=a(1+\alpha t)$$ $$ b(t)=\frac{b}{1+\beta e^{-bt}}$$ [/Tex]where a = a(0) is the parameter for the total number of initial faults that exist in the software before testing, and [Tex]{\frac{b}{1+\beta } } [/Tex]is the initial per fault visibility or failure intensity. The mean value function of the equation [Tex]{\frac{\partial m(t)}{\partial t} }=b(t)[a(t)-m(t)] [/Tex]is given by [Tex]$$m(t)=\frac{a}{1+\beta e^{-bt}}\left ([1-e^{-bt}]\left [1-\frac{\alpha }{\beta } \right ]+\alpha t \right )$$ [/Tex]This model is known as the PNZ model. In other words, the PNZ model incorporates the imperfect debugging phenomenon by assuming that faults can be introduced during the debugging phase at a constant rate of alpha fault per detected fault. Therefore, the fault content rate function, a(t), is a linear function of the testing time. The model also assumes that the fault detection rate function, b(t), is a nondecreasing S-shaped curve, which may capture the “learning” process of the software testers.
Pham-Nordmann-Zhang Model (PNZ model) – Software Engineering
Pham Nordmann Zhang (PNZ) model is used to evaluate the reliability prediction of a component-based system or software and fault tolerance structures techniques.PNZ is considered to be one of the best models, which is based on the nonhomogeneous Poisson process(NHPP). Our goal is to produce a reliability prediction tool using PNZ models based on reliability predictions and careful analysis of the sensitivity of various models. Therefore, PNZ enables us to analyze how much the reliability of a software system can be improved by using fault tolerance structures techniques which are later discussed in this section.