A new reliability growth model: Its mathematical comparison to the Duane model

The Duane reliability growth model has been traditionally used to model electronic systems undergoing development testing. This paper proposes a new reliability growth model derived from variance stabilisation transformation theory which surpasses the Duane model in typical reliability growth situations. This new model is simpler to plot and fits the data more closely than the Duane model whenever the Duane slope is less than 0.5. This paper explores the mathematical relationships between these two models; and shows that at a Duane slope of 0.5, both models are mathematically equivalent in their capacity to fit the observed data. The instantaneous MTBF of the new model is also developed and compared to that of Duane. As the new model is influenced by the later failures, compared to early failures for the Duane model, it has the further advantage of leading to reduced test times for achieving a specified instantaneous MTBF. As the reliability of electronic systems increases, this has positive implications for testing.