Monotonicity

In a non-monotonic function, the slope changes its sign. The following figure shows what this means for a characteristic curve:

The output value rises at first. Then the output value falls, even though the physical quantity continues to rise. The output value is the same for two values of the physical quantity. The measurement system therefore cannot distinguish the two values of the physical quantity, because both have the same output value (see the black dashed line). This error cannot be corrected either. As with continuity, the measuring range is again restricted. This measuring instrument can only be used between its zero point and the maximum. Of course, the problem of the non-linearity of the characteristic still has to be solved in this range.

Summary

Offset and slope can be detected and corrected relatively easily. The effort for detecting and correcting non-linear characteristics is considerably higher. Non-continuous and non-monotonic ranges of the characteristic must be excluded from the measuring range. That is why good measurement technology focuses on building measurement systems that are as linear, monotonic and continuous as possible. In digital signal processing, all known errors of a measurement system are corrected.