On a software reliability model by Koch and Spreij

In a very concise paper, Koch and Spreij have proposed a software reliability model which generalized Jelinski-Moranda's one. The basic assumption is that the failure intensity is proportional to the residual number of failures, but the initial number of failures is not known. In fact, this paper contained original ideas which were rediscovered by others some time later usually in a Bayesian modelling framework. Their paper will be revisited here. Specifically the results supporting the discussion on various specific models by Koch and Spreij [Koch, G., Spreij, P., 1983. Software reliability as an application of martingale & filtering theory. IEEE Trans. Reliab. 32, 342-345] are stated and proved.