When a designer wishes to meet a specific error budget, it is desirable to have a single specification that places a limit on errors from all sources.
Although gain and offset errors can be trimmed externally, trimming increases costs and sometimes reduces reliability.
When a designer wishes to meet a specific error budget, it is desirable to have a single specification that places a limit on errors from all sources.
Total Unadjusted Error (TUE) is a comprehensive static (d.c.) specification that includes linearity errors, gain error, and offset error and serves the above needs.
TUE is the worst-case deviation from the ideal device transfer curve, assuming ideal the end points.

TUE is a static specification. That is, it is useful for applications with d.c. or slowly moving input signals. Such applications include, for example, digitizing the outputs of weigh scales and of temperature and pressure sensors.
You won’t find this specification on all ADC products; it is of value only when the total error specification is less than one or two LSB, so it is generally not found on data sheets of converters with higher resolution than eight-bits.
The ADCS7478 and the ADC081S101, for example, are both specified at ±0.3 LSB Total Unadjusted Error while the 10- and 12-bit devices in these families do not have a TUE specification.
The ADC10738 and the ADC12138 families of ADCs are exceptions in that these are 10-bit and 12-bit ADCs with a TUE specification.
If the total unadjusted error is much larger than about 1 or 2 LSB, it makes more sense to specify separate data sheet limits for each of the component errors (Offset Error, Gain Error and INL).Otherwise, a device with ±½ LSB linearity and ±3 LSB full-scale error might be classified simply as an ADC with "3 LSB linearity" and the user wouldn’t know that the device could provide excellent performance in applications that require linearity but don’t need offset or full-scale accuracy.