
When googling Hoshin Kanri, you will sooner or later come across an X-Matrix. It is a visually very impressive tool, but I am in serious doubt about its usefulness. It focuses on the creation of the Hoshin items, but to me this approach is overkill, and – even worse – may distract the user from actually following the PDCA, especially the Check and Act parts. While the article is highly critical, I hope reading it and understanding the shortcomings help you better understand how Toyota thinks.
Introduction
Setting the right goals and filtering them through the organization is important in Hoshin Kanri. In my first post I talked in detail about this as the „to-do list.“
These simple to-do lists can be modified to be quite elaborate, eventually leading to the X-Matrix. They are also sometimes called x-matrices (instead of matrix) or target-mean matrices. The origins of this matrix is a bit fuzzy, but it seems that Japanese professor Yoji Akao (1928–2016) and Bob King (owner of a quality lean-related publishing house) were involved.
In any case, looking at the matrix, I have the strong feeling that this was not developed by a practitioner in the field but more likely by an academic or consultant who has the need to impress others with fancy methods. But before I go into details of the criticism, let me briefly show how the matrix works.
The Fields in the Matrix
The X-Matrix has a number of fields. To fill it out, you start at the bottom (usually called „South“) with the long-term objectives. Next comes the annual objective (left, or „West“), then the top-level priorities (top, or „North“), and finally the targets to improve (right, or „East“). At the end on the very far right (running out of compass directions here …) comes the people responsible for the different tasks. Let’s have a (critical) look at the steps. In the corner intersections, you mark down if the points are related, or even how related they are.
- South: Long-Term Goals: The first step is the long-term goals. What is the overall direction you want to move your company (department)?
West: Annual Objectives: Out of the long-term objectives the annual objectives are developed. What do you want to achieve this year? In the matrix between the long-term goals and the annual objectives, you mark which long-term goal is aligned with which annual goal.- North: Top-Level Priorities: Next you develop the different activities you want to do to achieve the annual results. In the matrix in the corner, you again connect the previous annual objectives with the different priorities to achieve these objectives.
- East: Targets to Improve: Based on the top-level priorities, you create (numeric) targets to achieve this year. Again, in the field between the top-level priorities and the targets, you mark which priority influences which target. Some examples also have a matrix that connect the targets to improve back to the long-term goals. (Which may lead to inconsistencies if an entry in a step 1 long-term goal going through steps 2 and 3 does not influence any entry step 4 targets to improve, but the matrix leading back to step 1 sees a connection. Best not to use a matrix here.)
- Responsible: On the very far right you add which person is responsible for what top-level priorities.
Like the „normal“ Hoshin Kanri, this document is done at different levels in the hierarchy, starting with the top executive. These are named rather straightforward as top-level matrix, second-level matrix, and third-level matrix.
Criticism
From my point of view, there are a lot of things flawed with the X matrix.
- Long-term goals not long-term enough: The long-term goals I see online usually describe long term as three to four years … which for me coming from Toyota is too short. I would much prefer to have here the truly long-term visions or the foundations of the corporate philosophy here.
- Often redundant focus on numeric goals: Most examples I have seen online are overly numeric. The sequence could be as follows (actual example): 1)Long-Term Objectives: Gain market share to 40% -> 2) Annual Goal: Increase market share to 25% -> 3) Top-Level Priorities: Develop growth strategies -> 4) Targets to Improve: Increase market share to 25%. For this I do not need a fancy matrix! In this example, 2) and 4) are absolutely identical. In many examples I see online, the connection between the different fields feel forced and often redundant. In the original Hoshin Kanri, the focus is much more on having a process rather than having numeric targets.
- Diluting responsibilities: The Hoshin Kanri I know are always documents for one person. THIS person is responsible for the document, and has to work on implementing it. While he may work with his subordinates, the Hoshin document is his responsibility. This is different in the X-Matrix. Already as part of the design, the responsibilities are handed out right away to others. The person who made the X-Matrix is already no longer responsible. This to me is a very wrong mind-set!
- Where’s the PDCA?: Probably the biggest gripe I have is that the X-Matrix distracts from the PDCA! In the original Hoshin Kanri at Toyota, the PDCA is clearly part of the process. The X-Matrix, on the other hand, is devoid of any hints of the PDCA. While many articles about the matrix mention PDCA, it just feels like it is not there. Some articles see the X-Matrix as the first step to get the items to fill out a proper Hoshin Kanri, but they rarely go into detail for the actual Hoshin Kanri afterwards. Even if the X-Matrix is in preparation for an actual Hoshin, many of the fields feel redundant with the Hoshin. But again, if the PDCA is nonexistent, then the approach will have serious problems implementing it.
When to Use the X-Matrix?
Personally, I would try to avoid the X-Matrix, as I think it is introducing unnecessary overhead while losing some of the power of the original Hoshin Kanri. However, there are a few instances where it may be of use:
First, if you are already using it and it works for you. If that’s the case, then keep on using it. If you manage to use the X-Matrix successfully (that means with a PDCA) and you want to continue, then I am not going to stand in your way. To me, lean is whatever works, not a set of dogma-like methods.

Second, you may be in the unfortunate position that your boss or your client wants flashy and fancy methods. In this case, the X-Matrix may be a nice thing to bedazzle your client or boss. It won’t really make the works easier, but it looks sooo much cooler than the normal Hoshin Kanri to-do list and PDCA crossover. Just make sure that the implementation actually happens and the PDCA includes the C&A … but then, with this kind of boss or client, a fancy presentation with colorful slides may be substituted for actual progress. I don’t like it, but then … some people do want to be lied to.
But, if you are not yet using it and your boss is at least somewhat reasonable, then my advice is to avoid the X-Matrix and rather put the effort into the classical Hoshin Kanri. In my next post I will tell you a bit about the history of Hoshin Kanri and how the Kanri Noryoku program saved Toyota. Until then, stay away from overcomplicated tools, do the normal Hoshin Kanri, and go out and organize your industry!
P.S.: Many thanks to Isao Yoshino for his input!
Series Overview
- Hoshin Kanri – Part 1: The To-Do List
- Hoshin Kanri – Part 2: PDCA
- Hoshin Kanri – Part 3: Hierarchical Hoshins
- Hoshin Kanri – Part 4: The X-Matrix?
- Hoshin Kanri and the Kanri Noryoku Program: Rejuvenating Toyota
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