Control Chart Builder

Control limits are not specification limits

Control limits are calculated from the process. They describe what the process does. Specification limits come from the customer, the drawing or the contract, and describe what it is supposed to do. The two have no arithmetic relationship.

Never plot specification limits on a control chart. A control chart asks whether the process is stable; a specification asks whether parts are acceptable. Putting both on one chart invites the reader to adjust a stable process because a point approached a specification, which is tampering and makes the process worse.

A process can be perfectly in control and produce nothing but scrap. It can also be wildly out of control while every part happens to fall inside specification.

Signals other than a point outside the limits

A single point beyond three sigma is the obvious signal and the only one most people look for. The run rules catch the rest: eight consecutive points on one side of the center line, six in a row steadily rising or falling, two of three beyond two sigma on the same side, and four of five beyond one sigma on the same side.

Each of these is improbable enough under normal variation to be worth investigating. Eight points below the center line with every point inside the limits is a process that has shifted, and a chart read only for excursions will miss it entirely.

Recalculating the limits

Limits are recalculated when the process genuinely changes — a new machine, a new material, a deliberate adjustment. They are not recalculated because points keep falling outside them, which is the chart doing its job.

Limits carried forward from a study run three years ago describe a process that may no longer exist. Half the charts on a shop floor are comparing today against a version of the process nobody remembers.

Choosing the chart

X-bar and R for measured data in small subgroups, which is the common case. Individuals and moving range where subgrouping is not possible because parts arrive one at a time.

For counts and classifications: p and np charts for proportions and numbers defective, c and u charts for defects per unit. Using a measurement chart on attribute data, or the reverse, produces limits that do not mean what they appear to.

Moving average and moving range (MAMR)

When readings come one at a time and the shifts that matter are small, a chart of individuals reacts slowly. A moving average of span w plots the mean of the latest w readings, so its limits are narrower by about the square root of w and a small, sustained shift shows sooner. The moving range of the same w readings is plotted beneath it, and the limits use A₂, D₃ and D₄ for a subgroup of size w.

Each moving average shares w − 1 readings with the one before it, so neighboring points are correlated. Runs and trends on a moving average chart are expected rather than meaningful, which is why the calculator tests only for points beyond the limits on this chart.

Short-run charts

A cell that runs several part numbers in small batches never collects enough of any one part for its own chart. Short-run charts put every part on one chart by plotting each reading against its own part’s nominal.

• Deviation from nominal (DNOM). Plot x − nominal. Simple, and correct when every part number varies about as much as the others. The calculator compares the average ranges of the parts and warns when one is more than twice another.
• Standardized. Divide each part’s deviation by that part’s own average range (subgroups), or its own σ estimated from the moving range (individuals). Parts that vary differently can then share one chart, with limits of ±A₂ (subgroups) or ±3 (individuals).

Enter one nominal for each subgroup, in order. Subgroups with the same nominal are treated as the same part number, so the standardized chart needs at least two subgroups of each.

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