01 · Purpose and limits of a relationship matrix
Purpose and limits of a relationship matrix
A solution–cause matrix places candidate solutions on one axis and investigated causes on the other. Its purpose is to show which proposed changes are expected to address which mechanisms. It helps prevent a team from choosing a fashionable solution that leaves the important causes untouched. It also reveals when several solutions duplicate the same coverage while another cause remains unaddressed.
Select it after cause investigation has produced a useful working model and before the team commits to a solution package. Prerequisites include clear cause statements, distinct solution descriptions, and an agreed meaning for relationship symbols or scores. The entries are hypotheses about intervention mechanisms. A high score does not prove a cause, predict an effect size, or establish that the intervention will work. A numerical matrix can look authoritative even when its cells are mostly judgment, so evidence status must remain visible.
02 · Define causes at a useful level
Define causes at a useful level
Fictional Northbank Dispatch reviews a sample of 100 late cartons and assigns primary observed delay categories: 45 unclear carrier assignments, 35 label reprints, and 20 late order releases. Further investigation suggests three actionable mechanisms: carrier assignment is unavailable before staging, damaged labels lack a prompt recovery path, and release timing is not aligned with collection cutoff. These remain working explanations with supporting observations, not a claim that every late carton has one independent cause.
The team avoids a column called “human error,” because it does not identify what a solution must change. It also avoids mixing symptoms and mechanisms in the same axis. “Late loading” is an outcome; “carrier identity unavailable before staging” is a mechanism. Where causes overlap, the team notes the overlap rather than assuming the sample categories establish independence. A carton can experience several delays even if its review record assigns one primary category.
03 · Choose and apply a local scoring convention
Choose and apply a local scoring convention
Northbank uses a local scale of 0 for no plausible direct coverage, 1 for limited or indirect coverage, and 3 for strong proposed direct coverage. These numbers label relationship strength; the difference between 1 and 3 is not a measured causal multiplier. Each nonzero cell must state the mechanism and the evidence needed. The team keeps costs, effort, and safety gates outside this matrix so the coverage picture does not answer a different question invisibly.
Early assignment with scan confirmation receives 3 for assignment availability, 0 for label recovery, and 1 for cutoff alignment because clearer lane status could support release decisions indirectly. Standard reprint handling receives 0, 3, and 0. Revised release scheduling receives 1, 0, and 3. A shared screen receives 1, 0, and 1. The team does not award strong coverage simply because a solution appears related to a cause in name.
04 · Worked coverage decision
Worked coverage decision
The assignment concept strongly targets the largest observed category, but it leaves label recovery uncovered. Combining early assignment with standard reprint handling covers two distinct mechanisms without assuming one software change solves everything. Revised release scheduling addresses the remaining mechanism, but it requires order-management and carrier coordination. Northbank therefore separates it into a later investigation rather than bundling it into the first warehouse pilot.
If the team weights the three columns by the sample counts 45, 35, and 20, early assignment gives a local score of 3 × 45 + 0 × 35 + 1 × 20 = 155. Reprint handling gives 105; revised release scheduling gives 105; the screen gives 65. These are heuristic priority points, not cartons saved or probabilities. The unequal relationship labels and uncertain sample weights mean the totals cannot be interpreted as exact benefit ratios. The unweighted coverage gaps remain more informative than the apparent precision.
05 · Turn cells into testable mechanisms
Turn cells into testable mechanisms
For the strong assignment cell, Northbank predicts that the share of cartons arriving at staging without a valid carrier identity will decrease. It measures that intermediate outcome as well as late loading, because the proposed mechanism may improve without changing the collection outcome. For the reprint cell, it measures elapsed recovery time and the rate of unreadable labels reaching the dock. The pilot can then distinguish a failed mechanism from a successful mechanism that is insufficient to change the wider result.
The team also checks for unintended relationships. A confirmation scan might detect wrong assignments but lengthen queues; faster reprinting might encourage printing labels before identity is stable. These effects do not fit neatly into positive coverage scores, so they are recorded as risks and guardrails. The matrix is a design aid that should create questions for testing, not eliminate inconvenient consequences from the decision.
06 · Weak versus strong use and advanced adaptation
Weak versus strong use and advanced adaptation
Weak practice populates every cell with a high score, weights columns using unverified opinions, or calls the leading total “the proven solution.” Strong practice names mechanisms, distinguishes direct from indirect coverage, shows uncertainty, and retains uncovered causes. It rejects double counting when several columns describe the same mechanism at different levels. It also keeps a low-frequency but severe consequence visible rather than hiding it under frequency weights.
Advanced teams add an evidence annotation to each relationship, such as observed, technically demonstrated, or untested. They can build separate matrices for prevention and detection, because a scan that detects an error does not necessarily prevent its creation. For overlapping causes, use scenario analysis rather than pretending independent additive benefits. After a pilot, update the cells with what was learned, retaining the original hypotheses. The comparison between expected and observed coverage is often the matrix’s most valuable contribution to future improvement work.
07 · Operating conditions and evidence
Operating conditions and evidence
A cause column needs an evidence boundary. Northbank’s assignment mechanism is supported by observed timing and operator search behavior, but the sample alone does not quantify how much late loading it explains across every season. The matrix records the sampled period and notes carrier mix. A later busy season may increase the importance of release timing or reveal another mechanism.
The solution package should avoid claiming additive coverage as additive benefit. Early assignment and a screen may both affect the same searching episode, so their expected benefits overlap. Reprint handling could also shorten the same carton’s delay without changing whether it misses the cutoff. Northbank uses scenario narratives and pilot measures to examine these interactions rather than adding every claimed saving. The coverage matrix remains valuable because it explains why each component exists and which mechanism it should affect, even when the total operational effect must be measured directly.
08 · Decision record and next step
Decision record and next step
The relationship matrix also supports removal of unnecessary solution elements. If an expensive display has only indirect coverage already provided by labels and scan confirmation, Northbank asks what additional mechanism justifies it. A feature can remain useful for another purpose, but that purpose should be named and assessed separately. The matrix prevents a broad improvement project from accumulating attractive components without a clear relationship to the problem.
When evidence changes, the team updates both axes. A pilot may reveal that the original assignment issue was partly a data-entry timing problem rather than a visibility problem. A solution that exposes the same late information would then have weaker coverage than expected. Retaining the original matrix beside the revised one shows what was learned. The tool is strongest when it helps the team revise its explanation and design, rather than defend an early score after contradictory observations appear.
| Candidate | Strong intended coverage | Important uncovered condition |
|---|---|---|
| Early assignment and confirmation | Carrier identity before staging and loading | Label recovery still needs a distinct mechanism |
| Standard reprint handling | Prompt controlled recovery from damaged labels | Order release timing remains outside its scope |
| Revised release scheduling | Alignment with collection cutoff | Requires coordination beyond the warehouse lane |
Connections
Related methods and phase use
Placed under Improve because of the outcome it supports. Use the method in other phases when its purpose and assumptions fit the work; the phase list is a guide to selection, not a compulsory sequence.
Sources
Professional foundations and further reading
The explanation and fictional teaching examples are written for LeanTrainingLab. Linked primary sources provide professional foundations; example values and local conventions are stated in the guide. The accepted toolset draws on Six Sigma+Lean Toolset, second edition (Lunau, editor; Springer, 2013). No book text or examples are reproduced here.