Measuring Software Reliability: A Trend Using Machine Learning Techniques

Abstract

It has become inevitable for every software developer to understand, to follow that how and why software fails, and to express reliability in quantitative terms. This has led to a proliferation of software reliability models to estimate and predict reliability. The basic approach is to model past failure data to predict future behavior. Most of the models have three major components: assumptions, factors and a mathematical function, usually high order exponential or logarithmic used to relate factors to reliability. Software reliability models are used to forecast the curve of failure rate by statistical evidence available during testing phase. They also can indicate about the extra time required to carry out the test procedure in order to meet the specifications and deliver desired functionality with minimum number of defects. Therefore there are challenges whether, autonomous or machine learning techniques like other predictive methods could be able to forecast the reliability measures for a specific software application. This chapter contemplates reliability issue through a generic Machine Learning paradigm while referring the most common aspects of Support Vector Machine scenario. Couples of customized simulation and experimental results have been presented to support the proposed reliability measures and strategies.

Keywords

Appendix: Sample Snap Code for Machine Learning Classifier Used by Software Fault Data Set of Billing System

• ## A Test Classifier

• x < – rnorm(100, mean = 5)

• probplot(x)

• ## the same with horizontal tickmarks at the y-axis

• opar < – par(“las”)

• par(las = 1)

• probplot(x)

• ## this should show the lack of fit at the tails

• probplot(x, “qunif”)

• ## for increasing degrees of freedom the t-distribution converges to rbridge ## normal

• probplot(x, qt, df = 1) probplot(x, qt, df = 3) probplot(x, qt, df = 10) probplot(x, qt, df = 100) ## manually add the line through the quartiles

• p < – probplot(x, line = FALSE)

• lines(p, col = “green”, lty = 2, lwd = 2)

• ## Make the line at prob = 0.5 red

• lines(p, h = 0.5, col = “red”)

• ### The following use the estimated distribution given by the green

• ### line:

• ## What is the probability that x is smaller than 7?

• lines(p, v = 7, bend = TRUE, col = “blue”)

• ## Median and 90lines(p, h = 0.5, col = “red”, lwd = 3, bend = TRUE)

• lines(p, h = c(0.05, 0.95), col = “red”, lwd = 2, lty = 3, bend = TRUE)

• par(opar)

• attach(Sample data Set)

• ## classification mode

• # default with factor response:

• model < – svm(Species ~., data = iris)

• # alternatively the traditional interface:

• x < – subset(iris, select = −Species)

• y < – Species

• model < – svm(x, y)

• print(model)

• summary(model)

• # test with train data

• pred < – predict(model, x)

• # (same as:)

• pred < – fitted(model)

• # Check accuracy:

• table(pred, y)

• # compute decision values and probabilities:

• pred < – predict(model, x, decision.values = TRUE)

• attr(pred, “decision.values”)[1:4,]

• # visualize (classes by color, SV by crosses):

• plot(cmdscale(dist(iris,[−5])),

• col = as.integer(iris,[5]),

• pch = c(“o”, “ + ”)[1:150 tune 53

• ## try regression mode on two dimensions

• # create data

• x < – seq (0.1, 5, by = 0.05)

• y < – log(x) + rnorm(x, sd = 0.2)

• # estimate model and predict input values

• m < – svm(x, y)

• new < –predict(m, x)

• # visualize

• plot(x, y)

• points(x, log(x), col = 2)

• points(x, new, col = 4)

• ## density-estimation

• # create 2-dim. normal with rho = 0:

• X < –data.frame(a = rnorm(1000), b = rnorm(1000))

• attach(X)

• # traditional way:

• m < – svm(X, gamma = 0.1)

• # formula interface:

• m < – svm(~., data = X, gamma = 0.1)

• # or:

• m < – svm(~ a + b, gamma = 0.1)

• # test:

• newdata < – data.frame(a = c(0, 4), b = c(0, 4))

• predict (m, newdata)

• # visualize:

• plot(X, col = 1:1000 points(newdata, pch = “ + ”, col = 2, cex = 5)

• # weights: (example not particularly sensible)

• i2 < – iris

• levels(i2$Species)[3] < – “versicolor”

• summary(i2$Species)

• wts < – 100 /table(i2$Species)

• wts

• m < – svm(Species ~., data = i2, class.weights = wts)