Matrix (Grid Analysis)

What’s a Matrix?

As shown in Figure 8-1, a matrix is nothing more than a grid with as many cells as needed for whatever problem is being analyzed. A matrix is one of the handiest, clearest methods of sorting information. Any time I can reduce information to a matrix, I find it analytically illuminating.

Figure 8-1 (description: a generic grid)

For example, a suspect in a crime is answering a detective’s questions. The detective wonders whether the answers are truthful. But there are actually four essential scenarios, which the matrix in Figure 8-2 clearly distinguishes:

• Scenario A: Suspect is guilty and tells truth
• Scenario B: Suspect is guilty and lies
• Scenario C: Suspect is innocent and tells truth
• Scenario D: Suspect is innocent and lies

Figure 8-2 (description: 2x2 matrix of truthfulness vs guilt)

Because each scenario (each cell) requires a different interrogation strategy (different questions, different sequences of questions, and so on), the detective would be well advised to plan the four strategies beforehand. The matrix helps organize that preparation.

Like sorting pieces of a jigsaw puzzle, a matrix enables us, among other things, to:

• Separate elements of a problem
• Categorize information by type
• Compare one type of information with another
• Compare pieces of information of the same type
• See correlations (patterns) among the information

Example: Baking Problem Chronology

The matrices in Figures 8-3 through 8-5 show when each crew started each of its first five batches, when each batch was removed from an oven, and which batches used the new flour. Each crew prepared one batch every hour, using its ovens sequentially.

Crew 1 (Figure 8-3): Had one sack of old flour left when work began at 4:00 P.M. Used it for first and second batches. Third batch (6:00 P.M.) and subsequent used new flour. First and second batches (old flour) came out all right; third and fourth (new flour), removed at 11:00 P.M. and midnight, were overbaked. Consistent with new flour causing overbaking.

Crew 2 (Figure 8-4): Had two sacks of old flour. Didn't start new flour until fifth batch at 8:00 P.M. (removed at 1:00 A.M.). Pattern consistent with new flour.

Crew 3 (Figure 8-5): Had one and a half sacks of old flour. Used on first three batches. Fourth and fifth batches used new flour. Fourth batch (begun 7:00 P.M., removed midnight) overbaked. Pattern consistent.

Across these three chronologies, overbaking follows the switch to new flour. That makes the flour a candidate cause to test; the timing alone does not establish the cause.

Combining a matrix with a chronology makes it easier to compare changes in materials with the timing of defects.