The normal distribution can be used to model the reliability of items that experience wearout failures. Given a mean life, μ and standard deviation, σ, the reliability can be determined at a specific point in time (t).
The normal distribution probability density function, reliability function and hazard rate are given by:
Probability Density Function
For example, given a mean life of a light bulb of μ=900 hours, with a standard deviation of σ=300 hours, the reliability at the t=700 hour point is 0.75, as represented by the green shaded area in the picture below.