FP (Frequency Partition)

Last updated on Apr 7, 2023

Frequency Partitioning (FP) is a technique used in software testing to improve the efficiency and effectiveness of testing. This approach involves dividing the input domain of a system under test into different frequency bands based on the probability of the inputs occurring. The aim is to allocate more testing effort to the higher frequency bands and less effort to the lower frequency bands.

The input domain of a software system consists of all possible inputs that can be given to the system. In general, the input domain can be infinite or very large, making it impractical to test all possible inputs. Therefore, we need to select a subset of the input domain for testing. However, selecting this subset randomly can lead to a suboptimal distribution of testing effort. This is because some inputs are more likely to occur than others, and these inputs should be given more attention during testing.

Frequency partitioning is a statistical technique that addresses this issue by dividing the input domain into different frequency bands. Each band contains inputs that are expected to occur with a certain probability. By allocating more testing effort to the higher frequency bands and less effort to the lower frequency bands, we can achieve a better distribution of testing effort.

The first step in frequency partitioning is to identify the input parameters of the system under test. An input parameter is a variable that can take on different values and affects the behavior of the system. For example, in a system that calculates the price of a product, the input parameters could be the cost of the product, the tax rate, and the discount rate.

Once the input parameters have been identified, we need to determine the probability distribution of each parameter. This can be done using historical data or expert knowledge. For example, we may know that the cost of the product follows a normal distribution with a mean of $50 and a standard deviation of $10.

Next, we divide the input domain into different frequency bands based on the probability distribution of each parameter. The number of frequency bands and the size of each band depend on the specific characteristics of the system under test. In general, we want to allocate more testing effort to the higher frequency bands and less effort to the lower frequency bands.

For example, suppose we have a system that calculates the price of a product based on the cost of the product, the tax rate, and the discount rate. We know that the cost of the product follows a normal distribution with a mean of $50 and a standard deviation of $10. We can divide the input domain into three frequency bands as follows:

Low frequency band: cost < $40 or cost > $60
Medium frequency band: $40 <= cost < $60
High frequency band: $50 <= cost < $60

We can allocate more testing effort to the high frequency band because inputs in this band are more likely to occur. We can allocate less testing effort to the low frequency band because inputs in this band are less likely to occur.

Once we have divided the input domain into different frequency bands, we can develop a testing strategy that allocates testing effort to each band based on its probability of occurrence. We can use different testing techniques for each band, depending on the characteristics of the inputs in that band.

For example, for inputs in the high frequency band, we may use exhaustive testing or boundary testing to ensure that we cover all possible values of the input parameter. For inputs in the medium frequency band, we may use random testing or equivalence class partitioning to ensure that we cover a representative sample of values. For inputs in the low frequency band, we may use exploratory testing or pairwise testing to ensure that we cover a diverse set of values.

The effectiveness of frequency partitioning depends on the accuracy of the probability distribution of the input parameters. If the probability distribution is inaccurate, the testing effort may be misallocated, leading to suboptimal testing results. Therefore, it is important to gather accurate data and use expert knowledge to estimate the probability distribution of the input parameters.

In addition, frequency partitioning should be used in conjunction with other testing techniques, such as boundary testing, equivalence class partitioning, and random testing, to ensure that all possible inputs are covered. Frequency partitioning should not be used as the sole testing technique, but rather as a complementary technique that helps to allocate testing effort more efficiently.

There are several benefits to using frequency partitioning in software testing. First, it helps to allocate testing effort more efficiently by focusing on inputs that are more likely to occur. This can save time and resources by reducing the number of inputs that need to be tested. Second, it helps to ensure that the most critical inputs are tested thoroughly. Third, it can improve the reliability and accuracy of the software by identifying and fixing defects in critical inputs.

However, there are also some limitations to using frequency partitioning. First, it requires accurate data and expert knowledge to estimate the probability distribution of the input parameters. If the data is inaccurate or the knowledge is insufficient, the testing effort may be misallocated, leading to suboptimal results. Second, it may not be applicable to all types of systems, especially those with complex and dynamic input domains. Finally, it may be difficult to determine the appropriate number of frequency bands and the size of each band.

In conclusion, frequency partitioning is a powerful technique that can help to improve the efficiency and effectiveness of software testing. It involves dividing the input domain of a system into different frequency bands based on the probability of the inputs occurring, and allocating more testing effort to the higher frequency bands and less effort to the lower frequency bands. This technique can save time and resources by focusing on critical inputs, improve the reliability and accuracy of the software, and ensure that all possible inputs are covered. However, it requires accurate data and expert knowledge to estimate the probability distribution of the input parameters and may not be applicable to all types of systems. Therefore, it should be used in conjunction with other testing techniques to ensure that all possible inputs are covered.