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Normal Distribution

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:

Normal Distribution PDF Equation Probability Density Function

Normal Distribution PDF Equation Reliability Function

Normal Distribution PDF Equation Hazard Rate

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.
Normal Distribution
The calculation inputs below show units of "hours," but any life metric (cycles, years, etc.) can be used as long as there is consistency among the three inputs.

Calculation Inputs:

1. Mean life (μ, hours):
2. Standard deviation (σ, hours):
3. Time period of interest (t, hours):
4. Decimal places:
5. Chart options:


Title (optional):

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  1. MIL-HDBK-338, Electronic Reliability Design Handbook.
  2. Bazovsky, Igor, Reliability Theory and Practice.
  3. O'Connor, Patrick, D. T., Practical Reliability Engineering.
  5. Khan Academy, Introduction to the Normal Distribution.
  6. Khan Academy, Normal Distribution Excel Exercise.