Quantile-Quantile Plot of Folded-Normal Distribution and its Applications in Reliability and Quality Modeling

When a dataset from a non-negative random variable contains zero or very small observations, the folded-normal distribution (FND) can be an appropriate model for fitting the data. Such data includes the well-known bus-motor major failure time data and quality characteristics data from manufacturing processes. The probability or quantile plot of a distribution (if it exists) is a useful tool for intuitively determining whether the distribution is appropriate for fitting a given dataset. The main purposes of this paper are to develop a quantile-quantile (QQ) plot for the FND and illustrate its appropriateness and usefulness in modeling failure time with early failure and quality characteristics data. Two real-world examples that involve five bus-motor major failure time datasets and two quality characteristics datasets are included. The results show that the bus-motor major failure time datasets can be well fitted by the FND or its special case (i.e., half-normal distribution) and the fitted models outperform the existing models in the literature in terms of model simplicity and goodness of fit. The QQ plot of the FND developed in this paper can considerably facilitate and promote the practical application of the FND.