Guide with a filled sample
X-matrix: what it is, how to read it and how to build one
Short answer
An X-matrix is the one-page plan used in hoshin kanri. Four lists sit around a central X: breakthrough objectives at the bottom, annual objectives on the left, improvement priorities on top and targets on the right. Dots in the four corners show which item supports which, and a column of owners sits on the right edge.
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The definition
What is an X-matrix?
An X-matrix puts a whole year's plan on one page. The bottom lists the breakthrough objectives, the left the annual objectives, the top the improvement priorities and the right the targets that measure them. Grids in the four corners mark which item supports which, and a column of owners shows who is responsible.
Hoshin kanri is the method and the X-matrix is the page it is usually drawn on. The hoshin kanri guide covers the method, the yearly cycle and catchball. This guide is about the page: what goes where, how to read the dots and how to build one.
Christoph Roser describes the same layout in compass terms: long-term goals to the south, annual objectives to the west, top-level priorities to the north, targets to improve to the east, and the responsible people at the far right. Each corner between two lists is a grid that marks whether items are related.
Clockwise from the bottom
How do you read an X-matrix, quadrant by quadrant?
Start at the bottom and go clockwise. Pick one breakthrough objective, go left to the annual objective that serves it, up to the priority that delivers that, and right to the target that shows it is working. Each step is a dot in a corner grid. A row or column with no dot is the thing to question.
Below is a filled sample for an illustrative plant, laid out the way the matrix is read. The highlighted items are the thread traced after the list of sides. On a phone the four lists stack in reading order; on a wide screen they sit around the X.
Breakthrough objectives
- L1 OEE of 85% on every line by 2028
- L2 Zero recordable incidents
- L3 Customer PPM under 50 by 2028
Annual objectives
- Y1 OEE from 71% to 76% on Lines 1 to 3
- Y2 Press changeover from 40 to 28 minutes
- Y3 Recordables from 4 to 1
- Y4 Customer PPM from 180 to 120
Improvement priorities
- P1 SMED on Presses 1 to 4Owner: Engineering. Helps: Production, Maintenance.
- P2 Autonomous maintenance on Lines 1 to 3Owner: Production. Helps: Maintenance.
- P3 Near-miss reporting on every shiftOwner: Safety. Helps: Production.
- P4 Error-proofing at final assemblyOwner: Quality. Helps: Engineering.
- P5 Start-up standard work and first-piece checkOwner: Production. Helps: Quality.
Targets to improve
- T1 OEE, Lines 1 to 3: 76% in December
- T2 Average press changeover: 28 minutes
- T3 Unplanned stops, Lines 1 to 3: under 30 hours a month
- T4 Near misses reported: 40 or more a month
- T5 Customer PPM: 120 or lower
- T6 Recordables: 1 or fewer this year
bottom, Breakthrough objectives
The few results the plant wants in three to five years, three or four at most. Each is a measurable end state, such as OEE of 85% on every line by 2028, not a theme such as operational excellence.
In the sample: L1 OEE of 85% on every line by 2028
Ask: If we got this, would the business look different?
left, Annual objectives
What this year must deliver toward each breakthrough objective, written as a number with a start and an end. Four to six is workable.
In the sample: Y2 Press changeover from 40 to 28 minutes
Ask: Which breakthrough objective does it serve, and can we tell in December whether it was met?
top, Improvement priorities
The few programs or projects that will deliver the annual objectives. Five to eight. A priority that serves no annual objective comes off the list.
In the sample: P1 SMED on Presses 1 to 4
Ask: Which annual objective does it deliver, and who owns it?
right, Targets to improve
The measures, each with a baseline and a target, that show whether the priorities are working. Each becomes a row on the bowling chart.
In the sample: T2 Average press changeover: 28 minutes
Ask: Which priority does it measure, and who enters the number every month?
A column at the right edge, beside the priorities, shows who owns each one and which functions help. One owner per priority is the aim. Roser notes that a hoshin document is normally the responsibility of one person, and warns that the X-matrix can spread that responsibility around.
One thread, traced
- 1
Bottom: L1
OEE of 85% on every line by 2028. It says where the plant is going. It does not say what to do on Monday.
- 2
Left: Y2
This year's step toward it is press changeover from 40 to 28 minutes, a cut of 12 minutes, or 30%. The dot in corner A joins Y2 to L1.
- 3
Top: P1
SMED on Presses 1 to 4 delivers Y2, and the dot in corner B says so. P1 also delivers the OEE objective Y1, so it has two dots in that column.
- 4
Right: T2
Average press changeover, 28 minutes, is the target that shows P1 is working. The dot in corner C joins T2 to P1, and the dot in corner D joins T2 back to L1.
- 5
Edge: the owner
Engineering owns P1, with Production and Maintenance helping. One owner means one person to ask when T2 goes red.
- 6
Next: the bowling chart
T2 becomes a row on the bowling chart with a plan for each month, 40 in January and 28 by November. The matrix is drawn once a year. The bowling chart is how it is checked.
The four grids
What do the corner grids and dots mean?
Each corner grid joins the two lists on either side of it. A dot says the row's item supports the column's item. Many versions use two kinds of dot, for a strong link and a weaker one. An empty row is a priority or objective that connects to nothing. That is a finding, not a gap to fill.
| Aspect | Where | Joins | The question it answers |
|---|---|---|---|
| Corner A | Bottom left | Breakthrough objectives and annual objectives | Which annual objective serves which breakthrough objective? |
| Corner B | Top left | Annual objectives and improvement priorities | Which priority delivers which annual objective? |
| Corner C | Top right | Improvement priorities and targets | Which target measures which priority? |
| Corner D | Bottom right | Targets and breakthrough objectives | Which target shows progress on which breakthrough objective? |
Not every version has all four. Roser advises against the grid that links the targets back to the breakthrough objectives, because it may lead to inconsistencies. If you keep it, check that it agrees with the other three.
Corner B, top left: Which priority delivers which annual objective?
| Improvement priority | Y1OEE from 71% to 76% on Lines 1 to 3 | Y2Press changeover from 40 to 28 minutes | Y3Recordables from 4 to 1 | Y4Customer PPM from 180 to 120 |
|---|---|---|---|---|
| P1 SMED on Presses 1 to 4 | Delivers Y1 | Delivers Y2 | No link | No link |
| P2 Autonomous maintenance on Lines 1 to 3 | Delivers Y1 | No link | No link | No link |
| P3 Near-miss reporting on every shift | No link | No link | Delivers Y3 | No link |
| P4 Error-proofing at final assembly | No link | No link | No link | Delivers Y4 |
| P5 Start-up standard work and first-piece check | Delivers Y1 | No link | No link | Delivers Y4 |
| P6 A monthly lunch-and-learn series | No link | No link | No link | No link |
P6 has no dot in the corner grid. Either an annual objective is missing, or the priority is not worth doing this year. Both are worth finding out before the plan is agreed.
Four checks before you sign it
- AEvery breakthrough objective has at least one annual objective under it.
- BEvery priority has a dot, and every annual objective has at least one priority working on it.
- CEvery target measures a priority, and every priority has a target.
- EdgeEvery priority has exactly one owner.
Building one
How do you build an X-matrix?
Build it in the order you read it: breakthrough objectives, annual objectives, priorities, targets. Fill the corner grids last, then add one owner per priority. Take the draft through catchball with each level before it is final. Then turn every target into a row on the monthly bowling chart. Allow several weeks, not one meeting.
- 1
Gather what the plan has to answer
Last year's results, what customers and the business are asking for, and the three or four things leadership already believes matter. The matrix records decisions. It cannot make them.
- 2
Write the breakthrough objectives (bottom)
Three or four, each a measurable end state three to five years out. Roser thinks the three to four year examples common online are too short for real breakthroughs; pick a horizon the business can plan against.
- 3
Write the annual objectives (left)
For each breakthrough objective, the part this year must deliver, with a start and an end value. Four to six in all. If an objective cannot be measured in December, rewrite it.
- 4
Choose the improvement priorities (top)
Five to eight programs or projects. Each must answer an annual objective. This is where the list of everything the plant would like to do gets cut.
- 5
Set the targets (right)
At least one measure for each priority, with a unit, a baseline and a target. Each of these is a future row on the bowling chart, so each needs someone who can enter the number every month.
- 6
Fill the corner grids last
Put a dot wherever one item truly supports another. Then read for empty rows and columns. An empty row is a priority with no objective. An empty column is an objective with no priority working on it.
- 7
Add one owner per priority
A named person for each priority, and the functions that help. A priority with no name against it usually does not get done.
- 8
Take it through catchball, then hand it to the review
Each level answers what it can commit to, and the matrix changes. Roser describes a top-level, a second-level and a third-level matrix, each plant or department drawing its own from the one above. When it is agreed, every target becomes a row on the monthly bowling chart.
The method behind these steps, including the seven-step year and the catchball round, is on the hoshin kanri guide. Cascading the result to each facility is covered in cascading goals, and the quarterly step under each annual objective in OKR vs KPI.
Starting from a page
What should an X-matrix template have?
A good X-matrix template has the four lists, the four corner grids and an owners column, with room for about three or four breakthrough objectives, four to six annual objectives and five to eight priorities. It should also give the targets a place on a monthly bowling chart. A template with fifteen rows per list invites a list of every project.
Room for few items, not many
About three or four breakthrough objectives, four to six annual objectives and five to eight priorities. A larger template invites a list of every project.
All four corners and the owners column
If a template leaves out a corner grid, you lose one of the checks in this guide.
Baselines and units on the targets
Without them the targets cannot be put on a bowling chart.
A way to carry the targets to a monthly review
The free hoshin kanri X-matrix template on this site is paired with a bowling chart for that reason; the hoshin bowling chart is also available on its own.
A fair view
When is the X-matrix the wrong tool?
When it becomes a form to fill in. Greg Lane of the Lean Enterprise Institute has called X-matrices often a tick-the-box exercise, and Christoph Roser argues it pulls attention away from the check and act steps. The matrix is a good one-page summary. It is a poor substitute for the conversations and reviews behind it.
What the critics say
- Greg Lane, Lean Enterprise Institute, 2013: X-matrices are often a tick-the-box exercise and, in his experience, often confusing. He suggests a simpler matrix that starts a discussion at each point where an objective meets a department's possible actions.
- Christoph Roser, AllAboutLean: the X-matrix distracts from the check and act of PDCA, adds overhead, and spreads out a responsibility that one person should own.
What it is good for
- One page that shows the whole plan, so a gap is visible without reading a document.
- A shared picture for the catchball conversation with each level.
- A short list of targets that can be passed to the monthly bowling chart without being re-typed.
- Roser's own advice: if it works for you with PDCA behind it, keep using it.
Where it comes from
Where does the X-matrix come from?
According to Christoph Roser, hoshin kanri began as a Japanese adaptation of management by objectives in the 1950s and 1960s, and it is unclear who used it first. He reports that Toyota adopted it in 1979, after management by objectives fell short, with about 2,000 leaders developing their own plans on A3 paper.
Roser says the tabular format was turned into the X-matrix in the 1990s by early lean consultants and companies, among them Danaher Corporation and Hewlett-Packard, and that no single inventor is named. He adds that the X-matrix is largely unknown in Japan and that he has never seen one at Toyota. So treat it as a Western planning page for a Japanese method, and judge it by whether it helps your plan.
What goes wrong
Common mistakes with X-matrices
A list of every project in the plant
Fifteen priorities means nothing was cut. The matrix is meant to force a choice, and the corner grids only help when there are few enough rows to read.
Dots to make it look complete
A dot that nobody believes is worse than a blank, because it hides the question the blank would have raised.
Targets with no baseline or no owner
A target with no starting value cannot be tracked and one with no owner is not. Every right-hand item needs both before the matrix is signed.
Fields that repeat each other
Roser notes that many examples are heavily numeric, with the fields restating one another. If the annual objective and the target are the same sentence, one of them is not doing its job.
Drawn by leadership alone
A matrix nobody below the leadership team has answered is a draft. Catchball is where it gets tested against what each level can do.
No check and no act
The matrix is the plan. Without a monthly review and a response to red results it is, as Roser puts it, missing the check and act of PDCA. The bowling chart and the A3 are where those happen.
Sources
- Christoph Roser, Hoshin Kanri Part 4: The X-Matrix?, AllAboutLean (opens in a new tab)The layout (long-term goals south, annual objectives west, top-level priorities north, targets to improve east, responsible people far right), the correlation matrices in the corners, the top, second and third level matrices, and a critical view of the format.
- Christoph Roser, The Evolution of Strategic Management: Hoshin Kanri, AllAboutLean (opens in a new tab)Hoshin kanri as an adaptation of management by objectives, Toyota's 1979 adoption, and the X-matrix format of the 1990s.
- Greg Lane, Long Live Process Improvement?, Lean Enterprise Institute, 2013 (opens in a new tab)X-matrices as often a tick-the-box exercise, and a simpler matrix as the alternative.
- Lean Enterprise Institute: strategy deployment (opens in a new tab)Strategy deployment as a management process that aligns functions with strategic objectives through an annual plan, and catchball as the two-way discussion between levels.
- Lean Enterprise Institute: hoshin kanri (opens in a new tab)Hoshin kanri as a framework built on plan-do-check-act thinking.
In LeanSuite
The X-matrix in LeanSuite
In LeanSuite the X-matrix is a page for each year, drawn from the goals you already hold.
One page per year, at workspace level
Under Hoshin Kanri there is an X-matrix page for each year, with a horizon such as 2026 to 2028. It sits at workspace level, above any one facility.
Read clockwise from the bottom
The bottom holds the breakthrough objectives, for three to five years. The left holds the annual objectives, each shown with the KPI that measures it. The top holds the improvement priorities, which are kaizens and projects, each marked with how many facilities it is pushed to. The right holds the targets to improve, which are KPIs.
Correlation dots, measured by and resources
Correlation dots are marked Strong or Weak. Measured by joins a goal to its KPI. A Resources column shows a Lead and Support people for each item.
Select an item to see what it connects to
Selecting any item shows what it connects to and fades the rest, so one thread can be followed without the rest of the page.
Cascade with catchball replies
A goal is cascaded to the facilities you choose. Each replies in the catchball with Adopt as written, Write own version or Not applicable.
Where to look next
See it on your own goals
Try the interactive demo in your browser with sample data, or pilot LeanSuite on your own lines for 90 days, with the setup done by our team.
Read more on the X-matrix and hoshin kanri
- Hoshin kanri: meaning, the 7 steps and a filled X-matrix exampleThe method the X-matrix belongs to, with the full filled example.
- Bowling chart: what it is, how to read one and how to build itThe monthly check on the targets on the right of the matrix.
- OKR vs KPI, and where hoshin kanri fitsWhere OKRs and KPIs sit next to the matrix.
- Cascading goals and goal alignmentHow the annual objectives reach each facility and team.
- OKR meaning and OKR examples for manufacturingWriting the quarterly step under an annual objective.
- X-matrix in lean manufacturing: strategy alignment toolHow the four lists and corner grids line work up with strategy.
- How to build an X-matrix: step-by-step guideA longer walk through the build.
- Hoshin kanri X-matrix template with bowling chartA free printable matrix and chart.
FAQ
Questions about the X-matrix
An X-matrix is a one-page planning tool used in hoshin kanri. Four lists sit around a central X: breakthrough objectives at the bottom, annual objectives on the left, improvement priorities on top and targets on the right. Grids in the four corners show which items support each other, and a column of owners shows who is responsible.
Start at the bottom and go clockwise. Take one breakthrough objective, find the annual objective that serves it on the left, the priority that delivers that on the top and the target that measures it on the right. A dot in a corner grid is a link. A row or column with no dot is a priority or objective that connects to nothing.
A dot says the row's item supports the column's item. Many versions use two kinds, a filled dot for a strong link and an open one for a weaker link. The dots are most useful for what is missing: an empty row is a priority with no objective, and an empty column is an objective with no priority working on it.
Hoshin kanri is the method: choosing a few objectives, agreeing them level by level through catchball and reviewing them every month. The X-matrix is the one page the plan is usually drawn on. The method can be run without an X-matrix, and an X-matrix without the reviews is only a diagram.
This site's advice is three or four breakthrough objectives, four to six annual objectives and five to eight improvement priorities. A matrix much larger than that is usually a list of every project in the plant, and the corner grids become too crowded to check.
Yes. The free hoshin kanri X-matrix template on this site has the four lists, the corner grids and the owners column, and is paired with a bowling chart so the targets can be tracked month by month. The hoshin kanri guide also has a filled example you can copy the structure from.
The X-matrix is the plan, drawn once a year. The bowling chart is the check, updated every month. The targets on the right of the X-matrix become the rows of the bowling chart, each with a monthly plan and an actual, green or red.
An X-matrix sets the annual direction and links it to priorities and measures. OKRs are quarterly: an objective and a few key results for the next 13 weeks. They are not drawn on the matrix. In a plant that runs both, the OKRs are the quarterly step toward an annual objective on the left of the matrix.
In LeanSuite the X-matrix is a page for each year at workspace level, under Hoshin Kanri, with a horizon such as 2026 to 2028. It is read clockwise from the bottom, with correlation dots marked Strong or Weak, a Measured by link from each goal to its KPI and a Resources column with a Lead and Support people. Selecting an item shows what it connects to and fades the rest.
Want the X-matrix to stay connected to the work?
Bring your current X-matrix or your draft, and we will show you on a call how the matrix, the KPIs and the catchball replies fit together in LeanSuite.