Compound-Poisson software reliability model

The probability density estimation of the number of software failures in the event of clustering or clumping of the software failures is considered. A discrete compound Poisson (CP) prediction model is proposed for the random variable X_rem, which is the remaining number of software failures. The compounding distributions, which are assumed to govern the failure sizes at Poisson arrivals, are respectively taken to be geometric when failures are forgetful and logarithmic-series when failures are contagious. The expected value (μ) of X_rem is calculated as a function of the time-dependent Poisson and compounding distribution based on the failures experienced. Also, the variance/mean parameter for the remaining number of failures, q_rem, is best estimated by q_past from the failures already experienced. Then, one obtains the PDF of the remaining number of failures estimated by CP(μ,q). CP is found to be superior to Poisson where clumping of failures exists. Its predictive validity is comparable to the Musa-Okumoto log-Poisson model in certain cases