A proposed approach for approximating lower truncated normal cumulative distribution based on Hamaker’s Model

In various workplaces, reliability engineers face many cases where the normal distribution is truncated from the lower side. For example, the distribution of used devices is a truncated distribution. Moreover, the distribution of products after screening and removing the unfit products is truncated distribution. Although there are many mathematical models and algorithms to approximate normal cumulative distribution, there is a limited number of approximations for truncated normal distributions. This paper proposes a new accurate approximation for the lower truncated normal distribution. The proposed model is simple and easy to implement. Numerical experiments show that the model accuracy, represented by the maximum absolute deviation from the true values, is about 0.00124 for the entire definition domain [Z_L : ∞], where Z_L is the point at truncation, and it takes values up to zero (i.e., Z_L [–∞: 0]). The proposed model can be used for quick manual calculations, especially if the intention is to avoid purchasing an expensive specialised program/software.