Five 2-parameter Variants of Folded-normal Distribution and Their Application in Reliability Modeling

The well-known bus-motor major failure data have attracted many studies, and the earlier modeling attempts find that common 2-parameter distribution models cannot provide good fittings to the data. A recent study shows that the folded normal distribution (FND) and half-normal distribution (HND) provide better fitting to the bus-motor failure data than the existing models in the literature in terms of model simplicity and goodness of fit. There are many variants of the FND in the literature. The purpose of this paper is to examine whether there are the variants that can provide better fittings to the data than the FND. Five 2-parameter variants (i.e., generalization and inverse generalization of the HND, power HND, epsilon HND and quasi-normal distribution) are examined. The results show that the generalization of the HND and power HND really outperform the FND for fitting the bus-motor failure data. Further, it is found that the inverse generalization of the HND is appropriate for modeling failure data with a failure-free interval. This is illustrated through analyzing a bearing fatigue life dataset. The results of the paper considerably promote the practical application of these variants in reliability modeling.