u Chart: Hold the Gain When Inspection Size Keeps Changing

The u chart monitors the rate of defects per unit when the inspection area varies between subgroups. That is the whole job. You count defects, you count the units you inspected, and the chart plots the ratio.

The variable part matters. Many counting charts assume you inspect the same number of items every time. Real work rarely cooperates. One day you check eighty orders. The next day ninety five. The u chart handles that by recalculating the control limits for each point according to how much was inspected.

In RDMAICS, this is a Control phase tool. By the time you reach Control, you have already found the cause and changed the process. The question is no longer what is wrong. The question is whether the new level of performance holds when the project team stops watching.

Use a u chart when three conditions are true. You are counting defects rather than defective items. A single unit can carry more than one defect. And the number of units inspected changes from subgroup to subgroup.

Typical settings include order checking, document review, inspection of batches that arrive in different sizes, and audits where coverage depends on staff availability. If the count of units is fixed every time, a simpler chart will do. If it moves, the u chart is the honest option.

The Control phase use is specific. You set a chart running on the improved process. You hand it to the people who own the work. They plot new points as the data arrives. If a point breaks a rule, they act. If no rule breaks, they leave the process alone.

The example that follows uses the built-in sample data that ships with the tool. It is fictional. No real organisation, store or order is described here. It exists so you can see the mechanics without needing your own dataset to hand.

The scenario is defects per order across three stores. Each store contributes two subgroups. Store 1 reports 5 defects in 80 units inspected, then 6 defects in 95 units. Store 2 reports 4 defects in 75 units, then 7 defects in 110 units. Store 3 reports 14 defects in 85 units, then 6 defects in 100 units.

Look at that fifth row before you go further. Fourteen defects is the largest count in the set, and it sits on the smallest-but-one inspection size. Raw counts would make it look alarming. The point of the chart is to test whether it is actually a signal or just the normal scatter of a process that is behaving.

The tool asks for four things per row. Two are required. Two are optional but useful.

Units inspected is the denominator. This is the count of items, orders, forms or square metres covered by that subgroup. Defects found is the numerator. This is the total number of defects observed across those units, not the number of units that had at least one defect. Mixing those two up is the single most common setup error.

Group or stratum lets you tag each row. In the sample data the tag is the store. Series or scenario names the measure you are tracking, here recorded as defects per order. Tags do not change the arithmetic. They change what you can see when you come back to the chart later and need to ask which part of the operation a point came from.

Keep the subgroups in time order. A control chart reads left to right as a sequence. If you sort by store or by defect count, you destroy the time signal the chart exists to detect.

The tool reports six points, a centre line of 0.0771, and zero out of control points. The vertical axis runs from 0 to 0.18 with gridlines at 0.045, 0.09 and 0.135. The measure plotted is defects per unit.

The centre line of 0.0771 is the pooled rate. It is total defects divided by total units inspected across all six subgroups, not the average of the six individual rates. That distinction matters because larger subgroups carry more weight, which is exactly what you want when inspection size varies.

The signals panel says no rule was triggered. The tool then adds a caution worth repeating. The process is in statistical control over this period, which means it is predictable, not that it is good enough. Predictable and acceptable are different tests. The chart answers the first. Your customer, your specification and your business case answer the second.

Note the line under the chart. Limits were calculated from all six points. You can instead set a baseline so that later data is judged against an earlier period. In the Control phase that is usually what you want. Freeze the limits on the post-improvement period, then let new data be tested against them.

The tool also offers an AI review of the result, which walks through what the chart is showing in plain language.

Return to Store 3 and its 14 defects in 85 units. In a management report built on raw counts, that number gets circled in red. Someone asks what went wrong at Store 3. A meeting is scheduled. A corrective action is written.

The chart says no rule was triggered. The point sits inside its limits. Acting on it would be tampering, which is responding to normal variation as though it were a special cause. Tampering adds variation. It does not remove it.

This is the practical value of the tool during Control. It gives the people running the process a defensible answer to the question of whether to act. Not a feeling. Not a comparison to last week. A decision rule that was agreed before the data arrived.

The first mistake is counting defectives instead of defects. If you record how many orders had a problem rather than how many problems there were, you need a different chart. The u chart assumes a unit can carry several defects.

The second is an unstable definition of a defect. If the inspection standard tightens halfway through the monitoring period, the chart will show a shift that has nothing to do with the process. Lock the definition before you start plotting.

The third is recalculating limits every time new data arrives. Do that and the limits chase the data. A slow drift away from your improvement gets absorbed into the centre line and never appears as a signal. Set the baseline on the improved period and hold it.

The fourth is reading too much into six points. Six subgroups is enough to demonstrate the mechanics and enough to start. It is not enough to be confident about subtle patterns. Keep plotting.

The fifth is treating in control as a pass. The tool says so itself. Control means predictable. Capability is a separate question.

The u chart will not tell you why a signal happened. It flags the point. The investigation is yours. The chart has no knowledge of a staff change, a supplier switch or a system update.

It will not tell you whether 0.0771 defects per unit is acceptable. That number is a description of the process as it currently runs. Whether it meets a commitment, a cost target or a customer expectation sits outside the chart entirely.

It will not fix bad data. If units inspected is estimated rather than counted, or if defects go unrecorded when the shift is busy, the chart will plot those errors with the same confidence it plots good data. Measurement discipline has to be in place before the chart means anything.

It will not detect a problem that moves every subgroup together. If a change raises the defect rate at all three stores at once and your limits were calculated from that same period, the chart will look settled. This is the argument for setting a baseline from a known-good period rather than from all available data.

And it will not sustain anything on its own. A chart that nobody plots and nobody reviews is a file. The Control and Sustain phases work when a named person owns the chart, a cadence is agreed, and a response plan exists for the day a rule does trigger. The tool supplies the evidence. People supply the discipline.