In (1973) Littlewood and Verrall proposed a model which perhaps the best-known Bayesian software reliability model. For this model, the distribution of failure times was assumed to be exponential, with the failure rate distributed as a gamma distribution in the prior.In this paper, under the assumption of Weibull failure time distribution and φ is a random variable which has gamma distribution we will illustrate that the times till failure of the N faults are independent random variables having a common three parameter Burr type XII distribution.This general and flexible formula can produce Pareto distribution of second kind and a special case of Burr type XII distribution as special cases. Also, in this paper, several reliability measures of this general formula will be obtained. The mathematical equations that will help to obtain the parameters estimates for maximum likelihood, nonlinear least squares, weighted nonlinear least squares estimation methods will be found. In the final sections, simulated and real world data applications are conducted to validate our general suggested formula.
Prof. Dr. Bilal BİLGİN