Compare the allowed tolerance band with the process's centre and spread, without mistaking five good parts for proof of capability.
The drawing sets the limits; the process produces the spread
The drawing sets the limits; the process produces the spread
A tolerance band is the permitted interval from the lower size limit to the upper size limit. Process spread describes how much the manufactured values vary. Changing a machine setting may shift the centre; it does not necessarily reduce the spread.
A capable process consistently fits its variation within the required limits with useful margin. A narrow spread near a limit can still produce rejects if the process drifts. A wide spread cannot be fixed simply by moving its average to the middle.
Illustrative spreads, not probability curves or measured capability results. Both rows use the same size axis.
Consider five invented readings: 24.98, 24.99, 25.00, 25.01 and 25.02 mm, with limits of 24.95 to 25.05 mm.
Mean: add all five readings and divide by five: 125.00 / 5 = 25.00 mm.
Range: subtract the smallest from the largest: 25.02 − 24.98 = 0.04 mm.
Midpoint of the limits: (24.95 + 25.05) / 2 = 25.00 mm. This sample mean is centred on that midpoint, and all five values are inside the limits.
Now add 0.04 mm to every reading. The mean becomes 25.04 mm and the range remains 0.04 mm, but the largest reading becomes 25.06 mm and fails. Centre and spread answer different questions.
Why a small sample range is not the full process spread
The range uses only the two extremes observed in this sample. More readings, different tools, temperature changes and later production may reveal variation not present in these five parts. Standard deviation is another measure of spread that uses every reading's distance from the mean; no standard-deviation calculation is needed for this example.
Passing parts are evidence, not proof of a capable process; Interactive; Practice
Passing parts are evidence, not proof of a capable process
Capability concerns a process over time, not a single successful part. First establish that the measurement method is suitable and the process is stable enough to describe meaningfully. Collect representative readings across the conditions the conclusion is meant to cover.
A stable process can still be too wide for the tolerance. An unstable process can happen to produce five passing parts. Neither case is resolved by averaging away the problem. Investigate a trend or sudden change using the inspection plan.
Where capability indices fit
Indices such as Cp and Cpk compare estimated process variation and its position with specification limits. Their interpretation depends on the data, stability, distribution and application requirements. A single threshold is not a universal acceptance rule, and a five-reading classroom example is not a capability study.
Capability explorer: assume a stable process with roughly normal output. μ is the process mean; σ (standard deviation) measures spread. These are chosen teaching inputs, not estimates from the five readings above. The five-readings example above explains why passing parts are evidence, not proof of a capable process.
Cp = (USL − LSL) / (6σ) compares tolerance width with spread, ignoring centring. Cpk = min(USL − μ, μ − LSL) / (3σ) uses the nearer limit. Cpk is negative when the mean lies outside the limits. LSL and USL are the lower and upper size limits.
Predict first: which case has the higher Cp? Does it also have fewer parts outside the limits?
Centring makes Cp and Cpk equal. The wide spread still puts parts beyond both limits.
Expected ppm means parts outside the limits per million under this normal model, not a measured reject count. Values are rounded; less than 1 ppm is not a guarantee of zero rejects. Requirements depend on the application; no universal pass threshold is used here.
