# Allocation Problems at Unit Level Testing

## Abstract

As mentioned in previous chapter reliability, scheduled delivery and cost are the three main quality attributes for almost all software. By determining the release time of the software optimally taking into consideration the various constraints and aspects of the software enables to best achieve these objectives. Many a time in the software release time problems we have seen keeping the cost minimization objective alone may leave us with a solution that the reliability achieved is low. On the other hand reliability maximization objective alone may require large budget. The two objectives simultaneously are conflicting and demand bounds on budget and achievable reliability. The release time problem by no means controls the consumption of the testing resources. The total software-testing cost as well as reliability depends largely on the consumption of the testing resources during the testing process.

## Keywords

Allocation Problem Module Testing Software Module Testing Effort Resource Allocation Problem## Notation

*p*r {.}Probability

- {
*N*(*t*),*t*≥ 0} Counting process representing the cumulative number of software faults detected in the time interval [0, t]

*m*(*t*)Mean value function in the NHPP model,

*m*(0) = 0*m*_{f}(*t*)Mean value function of the failure process in the NHPP model,

*m*_{ f }(0) = 0*m*_{r}(*t*)Mean value function of the removal process in the NHPP model,

*m*_{ r }(0) = 0*w*(*t*),*W*(*t*)Current testing-resource expenditures at testing time

*t*for (*w*_{ i }(*t*),*W*_{ i }(*t*)) software (module i) and its integral form, i.e., \( W(t) = \int_{0}^{t} {w(x)dx} ;\quad W_{i} (t) = \int_{0}^{t} {w_{i} (x)dx} , \)*a*(*a*_{i})Expected initial fault content in software (module

*i*), a > 0*b*(*b*_{i})Constant fault detection/removal rate per remaining faults in software (module

*i*) 0 <*b*<1*i*Subscript for each software-module number

*i*= 1, 2, …,*N**v*_{i}Weighted importance for each software module,

*v*_{ i }> 0*z*_{i},*Z*The number of software faults remaining in each software module and the whole system

*W*The specified total testing-resource expenditures before module testing,

*W*> 0*R*(*s*)Software reliability which means that no software failures occur during the time interval (0,

*s*](*s*≥ 0) after the testing process*γ*Constant parameter related to the failure rate,

*γ*> 0*R*_{0}Objective value of the software reliability, 0 <

*R*_{0}< 1- *
Superscript that denotes the optimal solution of the test resource allocation problem

*A*_{i}*v*_{ i }*a*_{ i }*b*_{ i }(detectability of module*i*)*L*,*λ*Lagrangian, Lagrange multiplier

*λ*

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