The modified Gompertz reliability growth model

An S-shaped reliability growth curve is used to describe a reliability growth trend with a lower rate of debugging and growth at the early stage and a higher rate later on as better fixes are found and successfully implemented. In some situations, it is unreasonable to set a high growth rate of improvement during the early stages of development for complex systems because of the difficulty of identifying the sources and causes of the failures, hence requiring the use of S-shaped reliability growth curves. One of the models now in use is the Gompertz model. From several data sets, it was seen that, in general, reliability growth data with an S-shaped trend could not be described well by the conventional Gompertz model, because this model has a fixed value of reliability at its inflection point. Therefore, only a small fraction of reliability growth data sets, following an S-shaped reliability growth curve, could be fitted to it. The modified Gompertz model that is presented in this paper overcomes this shortcoming by using a fourth parameter, which shifts it vertically, thus accommodating S-shaped growth data sets. The resulting model is much more flexible than it's predecessor, especially for fitting data with S-shaped trends.<>