# Logic testing-effort function

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Logictesting-effort function

Logictesting-effort function

Insection two of the article, the authors start by reviewing the logictesting-effort function in place of the Weibull-type testing-effortconsumption function to evaluate the test effort patterns whenutilized during the software development process. The function wasutilized to obtain the future schedules/costs and calculate theresource consumption curve of a software project during its lifetime.

Thefollowing equation depicts the total testing effort consumption in atime (0,t)of the

Ata testing timetthe testing-effort expenditure is given by

Fromthe above equation, one can observe that w (t) is a smoothbell-shaped function with a left tailed side. Both the w (t) andtesting effort w (t) reach the their maximum value time

Theauthors then, use the following equation to express the mathematicalexpression of a testing-effort

Thatis,

Whenusing the boundary condition m(0) =0 {m (t) mean value function equaling to zero}to solve thedifferential equation, we obtain

m(t) =expected mean number of detected faults in a time (0,t)

w(t) =Consumptionof the current testing-effort

a= numberof initial faults

r= errordetection rate per unit testing-effort at a testing time t satisfyingr

Inthe second part of section two, the authors details the relationshipbetweenm(t)and w(t)as demonstrated in the first part of section two but using theYamada S-shaped software reliability model

f(t)is the total number of detected failures up tot

g(t)isthe total number of isolated failures up to t

Ifwe solve equations (7) and (8) using the f(0)=g(0)=0 boundary condtions we get

isthe value of the failure detection rate

isthe failure isolation rate

Whileassuing the fault detation rate and the isolation fault rateparameters, the detecte sofrawe faults of the NHPP model while usingthe delyed S-shaped grwoth curve becomes

isthe detection rate fault per unit testing-effort in a testing time t,which satisfies

Insection three of the article the authours analyze data form the studyconducted by Ohba 2003. In the study the total number of detectedfaults were 358. The value 359 is the used as additional comparitioncriterion. While using the LSE and MLE the logic testing-effortestimted paramaters are A =13.0334, N =54.8364 and = 0.226337 the table belows shows the estiamted paramters in Eq (6),when comparing the to the estimated the MSF and intial faults a ofother general SRGMs.The fuction of the testing effor reaches itsmaximum time at t = 11.3438 weeks with is closly relted to W(t) =3.10288 CPU hours and W(t) 23.5107 CPU hours.

 Model a (r or ) AE (%) MSF SRGM 394.076 0.0427223 10.06 118.29 SRGM with Rayleigh TEF 333.18 0.100415 6.93 798.49 Yamada S-Shaped Model 374.05 0.197651 4.48 368.67 Delayed S model with Logistic TEF 338.136 0.10004 5.54 242.79 Delayed S model with Rayleigh TEF 459.08 0.0273367 28.23 268.42 G-O Model 760.00 0.0322688 112.29 139.82 Inflection S-Shaped Model 389.1 0.0935493 8.69 333.53 Delayed S-Shaped Model 374.05 0.197651 4.48 368.67 Exponential Model 455.371 0.0267368 27.09 206.93

AE= Accuracy of estimation

MSF= Mean Square fitting Faults

TEF= Testing-effort function