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I-MR chart template (individuals and moving range)
An I-MR chart (individuals and moving range chart, also called an XmR chart) is the control chart for one reading at a time: one viscosity per batch, one torque audit per shift, the changeover minutes each day. The individuals (I) chart plots each reading against a centre line and control limits. The moving range (MR) chart plots the difference between each reading and the one before, which is how the chart measures short-term variation when there are no subgroups. The limits are the mean ± 2.66 × the average moving range, and the moving range limit is 3.267 × the average moving range (NIST/SEMATECH e-Handbook of Statistical Methods, sections 6.3.2.1 and 6.3.2.2). Page 1 of the PDF has the header, 25 readings with their moving ranges, and both charts with lines for the limits and for 1σ and 2σ. Page 2 has the formulas and constants, five run rules, which chart fits which data, when to recalculate and what to do when a rule fires. Page 3 is the worked example drawn as both charts, with a reaction log. The Excel version takes up to 100 readings, sets the limits from a baseline you choose and keeps them frozen for later readings, flags five Western Electric rules on the I chart and points above the limit on the MR chart, starts a second phase with its own limits after a deliberate change, and draws both charts.
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Header fields for process, characteristic, units, gauge and specification, boxes for the baseline mean, average moving range and sigma, a table for 25 readings with date, value, moving range and rule broken, and an individuals chart with lines for the limits and for 1 and 2 sigma above a moving range chart.When to use it
When to use an I-MR chart
- When you get one measurement per period and no subgroups: a viscosity or pH per batch, a torque audit per shift, daily changeover minutes, scrap in kilograms per day.
- When readings come slowly or each one costs a lot, such as a destructive test or a lab result per lot, so waiting for subgroups of 4 or 5 would hide a change for days.
- For a number tracked once a day or week, to tell a real change from normal ups and downs before anyone reacts.
- Not when you can measure small subgroups of parts made one after another (use an X-bar and R chart), and not for the share of units defective (a p chart) or counts of defects (a c or u chart).
- Not for readings taken so close together that each one follows the last, such as an oven temperature every minute: the limits come out too narrow and the chart signals all the time.
How to fill it in
- 1
Check the measurement
The gauge or lab method has to see the variation you want to chart. A gauge R&R study answers that before you start.
- 2
Record readings in time order
One row per batch, shift or day, with the date or batch number and a note of anything that changed. The moving range is the difference from the reading before, ignoring the sign.
- 3
Set the limits from a baseline
Take 20 or more readings from normal running. Centre line = their mean; MR̄ = the mean of their moving ranges. I chart limits = mean ± 2.66 × MR̄; MR chart upper limit = 3.267 × MR̄.
- 4
Freeze the limits
Judge every later reading against the same limits. Treat limits from fewer than about 100 readings as trial limits and update them once, if nothing in the process has changed.
- 5
React to the rules
A point beyond a limit, 2 of 3 beyond 2σ, 4 of 5 beyond 1σ, 8 in a row on one side or 6 in a row rising or falling. Find what was different for that reading, fix it and log it.
- 6
Start a new phase after a deliberate change
A new machine, material or method gets its own baseline and limits. Do not recalculate because the latest points look different: catching that is the chart's job.
Run rules
The five rules the Excel version flags
The Western Electric rules as listed in the NIST/SEMATECH e-Handbook, section 6.3.2, with σ = MR̄ ÷ 1.128. Rules 2 to 5 can be switched off: each one catches smaller shifts and raises false alarms, from about one in 371 points with rule 1 alone to about one in 92 with all of them (NIST).
| Rule | Signal | Causes to check first |
|---|---|---|
| 1 | One point beyond a control limit | A one-off: a wrong setting, a different material lot, a measurement or typing error |
| 2 | 2 of 3 points in a row more than 2σ from the centre line, same side | The average starting to shift |
| 3 | 4 of 5 points in a row more than 1σ from the centre line, same side | A small shift that has held for several readings |
| 4 | 8 points in a row on one side of the centre line | The average has moved: a new lot, setting, supplier or person |
| 5 | 6 points in a row, each higher than the last (or each lower) | Drift: wear, build-up, a material that changes slowly |
| MR | A moving range above 3.267 × MR̄ (the only rule on the MR chart) | A sudden jump between two readings |
1
- Signal
- One point beyond a control limit
- Causes to check first
- A one-off: a wrong setting, a different material lot, a measurement or typing error
2
- Signal
- 2 of 3 points in a row more than 2σ from the centre line, same side
- Causes to check first
- The average starting to shift
3
- Signal
- 4 of 5 points in a row more than 1σ from the centre line, same side
- Causes to check first
- A small shift that has held for several readings
4
- Signal
- 8 points in a row on one side of the centre line
- Causes to check first
- The average has moved: a new lot, setting, supplier or person
5
- Signal
- 6 points in a row, each higher than the last (or each lower)
- Causes to check first
- Drift: wear, build-up, a material that changes slowly
MR
- Signal
- A moving range above 3.267 × MR̄ (the only rule on the MR chart)
- Causes to check first
- A sudden jump between two readings
A filled-in example
Illustrative, not a benchmarkAn example: the viscosity of a water-based coating, one reading per batch, specification 380 to 450 cP (illustrative numbers). The Excel version's Example sheet has the same 30 readings.
The example's 30 batches on the I chart and the MR chart
Individuals (I) chart, viscosity in cP
Moving range (MR) chart, cP
I chart: mean ± 2.66 × MR̄MR chart: UCL = 3.267 × MR̄
MR̄ is the average of the 19 moving ranges in the baseline: 182 ÷ 19.
- UCL =412.0 + 2.66 × 9.58= 437.5 cP
- LCL =412.0 − 2.66 × 9.58= 386.5 cP
- MR UCL =3.267 × 9.58= 31.3 cP
Individuals chart of 30 viscosity readings, one per batch, with limits from batches 1 to 20: mean 412.0 cP, UCL 437.5 cP, LCL 386.5 cP. Batch 24, at 441 cP, is the only point outside the limits, although it is inside the 450 cP specification. Moving range chart: MR-bar 9.58 cP and UCL 31.3 cP; batch 24's moving ranges, 20 and 19, are under it.
- Baseline, batches 1 to 20: mean = 8,240 ÷ 20 = 412.0 cP. The 19 moving ranges add to 182, so MR̄ = 9.58 cP.
- I chart: 2.66 × 9.58 = 25.48, so UCL = 437.5 cP and LCL = 386.5 cP. MR chart: UCL = 3.267 × 9.58 = 31.3 cP.
- Batch 24 reads 441 cP: above the UCL (rule 1), although it is inside the 450 cP specification. Its moving ranges, 20 and 19, stay under 31.3.
- The thinner flow meter had not been reset after a line flush, so batch 24 got less thinner. No other rule fires in the 30 batches.
The chart flagged a batch that the specification check passed. The meter reset was added to the flush checklist and logged. Batch 24 is outside the baseline, so the limits stay at 386.5 to 437.5 cP.
Common mistakes
Using the specification as control limits
Specification limits say what the customer accepts; control limits say what the process does. Batch 24 in the example passed the specification and still showed a change worth finding.
Limits computed from the data you are judging
Recalculating the limits each time new points come in lets a shift drag the limits along with it, so it never shows. Set them from a baseline, then freeze them.
Reacting to every point
A reading higher than the last one is not a signal. Adjusting the process for points inside the limits with no rule broken chases normal variation; act on the rules and leave the rest.
Trusting the rules on skewed or linked readings
The zone rules assume roughly normal readings. Strongly skewed data, such as time between failures, gives more false alarms, and readings so close together that each follows the last make the limits too narrow. Look at a histogram and the time order first.
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FAQ
I-MR chart template (individuals and moving range): common questions
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- Employee engagement survey templateA short anonymous pulse survey for shop floor staff: 14 statements in six drivers, two open questions, results by driver and team, and the actions.
- Hansei reflection sheet (lessons learned)A written look back at one finished project, event or launch: goals against results in numbers, causes rather than blame, lessons to keep or change, and where else they apply.
- Safety cross calendarA month drawn as the green cross, colored each day by the most serious safety event, with totals and days since the last injury.
- Daily kaizen routine boardA team's 10 to 15 minute daily routine at the board: one problem from each person, small fixes with one owner, counted every week.
- Weekly maintenance schedule templateNext week's maintenance jobs, scheduled only when ready, loaded against each craft's hours by day, with schedule compliance and break-ins at week end.
- Operational excellence assessment templateThe ten principles of operational excellence as 30 behaviors and practices you can see, scored 1 to 5 by several people, with the spread, the three lowest principles and an action plan.
- Scrum meeting agenda templateTimed agendas for the five scrum meetings, a sprint planning sheet, a retrospective sheet, and an Excel sprint backlog with a burndown.
- Toyota Production System (TPS) house templateThe TPS house for one plant or value stream: roof, two pillars and foundation, with what you do today, the evidence, a status and the next step for each element.
- EPEI and batch size calculatorHow often each part can come round on a shared machine (EPEI) and how big each batch must be, from demand, cycle times and changeovers, now and after SMED.
- Process capacity sheet templateEach machine in a part's routing with manual, auto and tool change time, its capacity per shift, and the step that limits the cell against demand.
- Team charter templateA one-page charter for a standing team: purpose, scope, roles, the KPIs it owns, which decisions it makes itself, norms and cadence.
- Chaku-chaku line plannerPlan a load-load cell: time each machine, load and walk, check that every machine is ready when the operator comes back, compare the cell cycle with takt and size the crew.
- Standard operating procedure (SOP) templateA full SOP in the hierarchical step format, from purpose and scope to the steps, records, revision history and approvals, with review checks and an SOP register.
- Process improvement method selectorEight questions about one problem, an example rule that suggests a method and a matrix of nine methods: when each fits, the usual team and time, and the template to start with.
- Safety pillar 90-day model area planThirteen weeks from the incident pyramid to safety standards on one model area, a KPI board, the day-90 gate and expansion waves.
- Autonomous maintenance 90-day model area planAM steps 0 to 3 on one model machine in 13 weeks, a KPI board, the day-90 gate and expansion waves for months 4 to 12.
- Professional maintenance (PM) 90-day model area planThirteen weeks from breakdown analysis to a running PM calendar on one model machine, a KPI board, the day-90 gate and expansion waves.
- Environment and energy pillar 90-day model area planThirteen weeks from waste and energy maps to area standards on one model area, a KPI board, the day-90 gate and expansion waves.
- Focused improvement 90-day model area planThirteen weeks from the loss Pareto to standardized fixes on one model line, a KPI board, the day-90 gate and expansion waves.
- Logistics and customer service pillar 90-day model area planThirteen weeks from the current-state map to pull on one model value stream, a KPI board, the day-90 gate and expansion waves.
- People development pillar 90-day model area planThirteen weeks from the skills matrix to trained cover on critical tasks in one model area, a KPI board, the day-90 gate and expansion waves.
- Cost deployment pillar 90-day model area planThirteen weeks from the loss map to costed, ranked projects in one model area, a KPI board, the day-90 gate and expansion waves.
- Moving from Excel to one system checklistA 34-point checklist and a file inventory for moving trackers from spreadsheets to one system: keep, move, connect or retire, clean, pilot, run both, retire.
- Prioritization matrix templateScore up to 20 improvement ideas on weighted criteria, rank them, test the ranking with equal weights and place each one on an effort and benefit grid.
- Cost per unit worksheet (manufacturing cost per good unit)One product's cost per good unit by materials, labor, machine and overhead, the gap to target, and which cost lever is worth most a year.
- Manufacturing KPI dashboard templateWeekly plant numbers in, 14 KPIs out: OEE and its parts, first pass yield, scrap, on-time delivery, recordable rate, cost and absence, each against a target.
- Training matrix template with expiry datesPeople by required trainings with expiry dates, OK, due, expired and missing flags, compliance by person and area, cover per training and a renewal list.
- Downtime reason codes template26 starter codes mapped to the six big losses, a log with drop-downs, a Pareto by code and by loss, and a code card for the line.
- Kaizen event preparation checklistEverything that has to be ready before a kaizen event and done after it: 44 items with owners and due dates from 6 weeks before day 1 to 30 days after, five go or no-go gates and a day-by-day agenda.
- Critical spare parts list and stocking levelsAssets ranked by consequence, each part classed and given a stocking policy, and min and max worked out from usage and lead time, with the downtime each stock-out would cost.
- Tier 2 meeting agenda and escalation sheetA 15-minute tier 2 agenda in ten timed blocks, fixed roles and rules, escalation triggers with time limits, and a log that ages every escalation and sends the answer back down.
- Forklift operator training and evaluation recordPer-operator training and evaluation record, a register with three-year due dates and refresher triggers, and a weighted practical evaluation scoresheet.
- REBA worksheet (Rapid Entire Body Assessment)Score up to six postures with REBA: body-part drop-downs, Tables A, B and C as lookups, final score and action level, and a before and after comparison.
- ISO 45001 internal audit checklist44 audit questions for the plant floor in 16 safety topics, each with its ISO 45001:2018 clause, the evidence to look for and the sample to take, plus 12 worker interview prompts, a findings log and a summary by clause.
- Plan for every part (PFEP) templateOne row per part: supplier, pack, container, usage, lead time and locations, with ABC classes, market and line kanban counts and a lineside space check.
- Changeover matrix templateA from-to matrix of changeover minutes with the clean each transition needs (allergen, colour, format), and a weekly planner that totals the order and suggests a shorter one.
- Overhead crane inspection checklist: frequent and periodic34 crane checks tied to OSHA 1910.179: an operator's pre-shift card, frequent and periodic inspections with signed records, a deficiency and tag-out log, and a register of next due dates.
- Maintenance job plan templateOne job planned on one sheet: steps and craft hours, parts checked against stock, tools, lockout and permits, documents, a ready check for the schedule, and technician feedback.
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A shift handover sheet, a red tag log, a changeover checklist for one machine: if your team uses it on the floor, ask.