Probability distribution of a tolerance interval

Converts a ±3σ tolerance range into mean, standard deviation, and a probability interval at a chosen reliability.

✓ validated against legacyoriginal: /calculators/t1_2c.htm
Probability distribution of a tolerance interval — original diagram from /calculators/t1_2c.htm
Mean, μ0
Standard deviation, σ0.03
Parameter u2.33
Probability interval, min (±u·σ)-0.078
Probability interval, max (±u·σ)0.078

Method & references

  • Probability distribution derived from a ±3σ tolerance range, at a chosen reliability level.

The computation is a literal port of the original client-side JavaScript from /calculators/t1_2c.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.

Probability distribution of a tolerance interval — Engineering ABC