A proposed approach for approximating lower truncated normal cumulative distribution: application to reliability of used devices

The distribution of a normally distributed hardware is changed to a lower truncated normal distribution after it has been in service for a certain period. Therefore, it is necessary to approximate this type of distribution with simple, applicable and accurate models. In the current paper, a model is proposed to represent the lower truncated normal distribution very accurately. To evaluate the model's accuracy, the truncation is used up to 50% of the original domain from left. The results show an increase in the model maximum deviation from true lower truncated normal distribution with the truncation percentage. At 50% truncation, the maximum deviation is 0.0000212. Besides being very accurate, the model is viable and simple, and it can be used manually, or with the help of a spreadsheet.