Typical is not a limit

The number

Datasheets list three kinds of value side by side: minimum, typical and maximum. The typical value is a central value of the units the maker characterized, usually a mean or a median, with no stated spread and often no production test behind it. The limits are what the maker tests against, on every unit or on a sample from each lot under a sampling plan such as ISO 2859-1.

The datasheet of the fictional NB-532-3-B filter, Rev B, lists the center wavelength as typical 532.0 nm, minimum 531.0 nm and maximum 533.0 nm, and states that typical values are not tested on every unit.

What it means

If the population is normal with mean $\mu$ and standard deviation $\sigma$, the share of parts inside the lower and upper limits $L$ and $U$, and the process capability index, are

With the mean at 532.0 nm and $\sigma$ = 0.4 nm, the ±1 nm limits sit 2.5σ from the mean: 98.8 % of parts fall inside and $C_{pk}$ is 0.83. At $\sigma$ = 0.5 nm the share falls to 95.4 %. A mean 0.3 nm off center with the same 0.4 nm spread gives 95.9 %, and a typical value printed from an earlier characterization would not show the move.

The calculator evaluates erf with the rational approximation 7.1.26 of Abramowitz and Stegun (1964), whose error is below 1.5 × 10⁻⁷.

Compute it

Where it misleads

A typical value says nothing about spread. Two lots with the same typical can differ by half in σ, and the share inside ±1 nm then moves from 99.7 % at σ = 0.333 nm to 95.4 % at σ = 0.5 nm.

A limit is not one kind of promise either. A limit tested on every unit removes the parts outside it, so the delivered distribution is truncated at the limits. A limit verified on a lot sample bounds the lot statistically, not each part. A limit set by design and never measured is a design target.

The normal model on this page is an illustration. Real distributions are often skewed, bimodal across coating runs or truncated by sorting, and the share inside the limits then comes from the measured distribution, with capability indices interpreted as in Montgomery (2019).

What to specify

• Tested minimum and maximum limits at stated conditions: temperature, angle of incidence, beam and bias.
• The test policy: every unit, a sampling plan with its acceptance level, or design value only.
• The measured distribution or the capability index when yield at the limits matters, with the number of units and lots behind it.
• Typical values as context, never as an acceptance criterion.

References

• Abramowitz, M. and Stegun, I. A., eds. (1964). Handbook of Mathematical Functions. National Bureau of Standards, Applied Mathematics Series 55, eq. 7.1.26.
• ISO 2859-1:1999. Sampling procedures for inspection by attributes, Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection. International Organization for Standardization, Geneva.
• Montgomery, D. C. (2019). Introduction to Statistical Quality Control, 8th ed. Wiley, Hoboken.