A shaft diameter on the drawing
A turning cell makes shafts. The drawing gives the bearing seat as 48.00 ± 0.10 mm. Every operator who measures the diameter needs to know one thing straight away: is this part good or not? The answer comes from two numbers, the lower specification limit (LSL) of 47.90 mm and the upper specification limit (USL) of 48.10 mm.
Specification limits are also called tolerance limits. The distance between them, USL - LSL, is the tolerance. In this example the tolerance is 0.20 mm.
Where the limits come from
Tolerance limits describe the requirement, not the process. They are set by design engineering, usually based on function: how the shaft fits in its bearing, how two parts assemble, what the customer has specified. They are written on the drawing or in a specification, and they should only change through a formal change to that document.
A limit can be written in two ways:
- Absolute: LSL = 47.90 mm and USL = 48.10 mm.
- Relative to a nominal value: 48.00 mm with a lower deviation of -0.10 and an upper deviation of +0.10.
Both mean the same thing. Relative limits are common on drawings, while software and statistics usually work with the absolute values. Tolerances do not have to be symmetric: 48.00 +0.05/-0.15 gives LSL = 47.85 and USL = 48.05. Some characteristics have only one limit, for example a maximum roughness or a minimum hardness. They are called one-sided.
Accepted or rejected
For a single part, the logic is simple. If LSL ≤ value ≤ USL, the part meets the requirement. If not, it is nonconforming and must be handled according to your procedure: quarantined, sorted, reworked or scrapped.
In the figure all values but the last are inside the limits. The last one is above the USL and the part is rejected. Notice that the values before it were already climbing. The tolerance limits did not react to that: every one of those parts was accepted.
What the limits cannot tell you
This is the most common misunderstanding about tolerance limits. Because they decide acceptance, it is tempting to use them to steer the process too: leave the machine alone while parts are within tolerance, adjust when one is not. That approach has two weaknesses.
First, it reacts late. By the time a value crosses a limit, a nonconforming part has already been made, and perhaps many more if parts are only checked now and then.
Second, it says nothing about the cause. A part close to the USL may be normal variation in a process that is centred badly, or the first sign of a worn tool. The tolerance limits cannot tell the two apart.
That is the job of control limits, which are calculated from the process’s own data. Tolerance limits answer “is this part good?” Control limits answer “is the process behaving as it normally does?”
Tolerance and capability
The tolerance is also the yardstick for process capability. Indices like Cp and Cpk compare the width of the tolerance with the spread of the process. A process whose spread uses only a small part of the tolerance has room for normal variation and small shifts. A process whose spread fills the tolerance will produce rejects even when nothing is wrong with it.
Measurement near the limits
A measured value is never exact. Near a limit, measurement variation can make a good part look bad or a bad part look good. If many values sit close to the limits, it is worth knowing how large the measurement system’s contribution is, which is what measurement system analysis investigates.
In short
LSL and USL define what an acceptable part is. Use them to decide about parts, use control limits to decide about the process, and use capability to judge whether the process can meet the tolerance in the long run.
