5.12 Analytical Tools Used Throughout the DMAIC Cycle

Why these seven

These are the classic seven management and planning tools, developed to handle the verbal, relational, and planning problems that the seven basic quality tools (histogram, Pareto, control chart, and so on) cannot. They appear in the Define chapter of the Body of Knowledge but are used across all five DMAIC phases, and ASQ tags them at the Apply level.

Affinity diagram

Used when the team has 30 to 100 unstructured statements -- VOC verbatims, brainstormed causes, survey comments -- and needs to find the natural themes.

Procedure: write each idea on its own card; sort silently into groups that feel related; name each group with a header that states the theme rather than the category; and split or merge until the groups are stable.

The silence matters. Sorting out loud lets the first speaker's framing anchor the group, and the resulting themes tend to reproduce the existing organizational structure rather than the structure in the data. Silent sorting reliably produces different and better groupings.

Output: themes that become stratification factors in Measure, or the top level of a tree diagram.

Tree diagram

Decomposes a general objective into progressively more specific means, level by level.

• CTQ tree: customer need to driver to measurable requirement to specification.
• Why-why tree: problem to cause to sub-cause.
• WBS: deliverable to sub-deliverable to work package.

The test at each level is the necessary and sufficient question: if all the children are achieved, is the parent achieved? If not, a branch is missing. Stop when the lowest level is directly actionable or directly measurable.

Matrix diagram

Shows the strength of relationships between two or more lists. Shapes are named by the letter their layout resembles: L (two lists, the common case), T (one list against two others), Y (three lists in a circle), X (four lists), and C (three lists in three dimensions).

Relationship strengths conventionally use 9 for strong, 3 for moderate, 1 for weak, and blank for none, which makes the strong relationships dominate row and column sums. The house of quality is the most elaborate matrix diagram; a cause-to-CTQ matrix is the simplest useful one.

Prioritization matrix

Ranks a set of options against weighted criteria. Procedure:

1. List the options and the decision criteria.
2. Weight the criteria so that the weights sum to 1.0 (or to 100).
3. Score each option against each criterion on a consistent scale.
4. Compute $\text{Score}i = \sum_j w_j \times s{ij}$ and rank.

Error-proofing wins. Two cautions: weight the criteria before you score the options, or the weights will be adjusted to justify a preferred answer; and check that every criterion is scored in the same direction (here higher is better on all four, so "cost" is scored as cost-favourability rather than as cost).

Activity network diagram

Shows tasks as a network of dependencies and computes the critical path. It answers the same question as a Gantt chart but emphasizes the dependency logic rather than the calendar, which makes it the better tool while the sequence is still being designed. The mechanics of critical path and float are covered in the project management tools section.

Process decision program chart

The PDPC extends a tree diagram by asking, at each planned step, what could go wrong and what we would do about it. It is the pre-mortem in diagram form and belongs in the Improve phase before implementation.

Implement new torque verification
|
+-- Install torque transducers
|   +-- Risk: calibration drifts       -> Countermeasure: 30-day calibration interval, verified daily
|   +-- Risk: fixture does not fit     -> Countermeasure: trial fit on line 4 before rollout
|
+-- Train operators on reaction plan
|   +-- Risk: night shift not covered  -> Countermeasure: dedicated night-shift session + level-4 trainer
|   +-- Risk: knowledge decays         -> Countermeasure: 30-day refresher and audit KBI
|
+-- Update SOP and control plan
    +-- Risk: change control delay     -> Countermeasure: submit 3 weeks ahead; named approver

PDPC differs from FMEA in scope and quantification: FMEA analyzes failure modes of a process or design with severity, occurrence, and detection ratings; PDPC analyzes risks to a plan and pre-plans responses without numeric scoring.

Interrelationship digraph

Used when many issues cause one another and the team cannot tell which to attack. Place each issue on a diagram, then for every pair ask "does A cause or influence B, does B cause or influence A, or neither?" and draw one arrow in the dominant direction only.

Then count for each node:

• Arrows out (drivers). The node with the most outgoing arrows is the root driver -- act here for maximum leverage.
• Arrows in (outcomes). The node with the most incoming arrows is the key outcome -- measure here to detect improvement.

The digraph's advantage over a fishbone diagram is that it captures relationships among causes, not just cause-to-effect. A fishbone would list all four of these as causes of a problem; the digraph shows that fixing the forecast is what moves the other three.