Complexity Analysis

The complexity analysis is based on Axiomatic Design (Suh, 1990), an engineering design theory with two fundamental axioms:

Analysis 1: Independence Analysis

Specification Types

Based on the relationship between domains, specifications fall into three categories:

Coupled Specification ❌

(Number of CNs < Number of CPs) OR (Number of FRs < Number of CNs)

• Problem: Not all problems/needs are addressed
• Action: Add missing CNs or FRs

Redundant Specification ⚠️

(Number of CNs > Number of CPs) OR (Number of FRs > Number of CNs)

• Assessment: May be acceptable if elements are not competing
• Action: Review for potential consolidation or verify independence

Ideal Specification ✅

(Number of CNs = Number of CPs) AND (Number of FRs = Number of CNs)

• Status: Each element maps 1:1 across domains
• Note: Ideal but not always achievable in practice

Independence Check Process

For each mapping (CP→CN and CN→FR), check:

1. One-to-One Mapping: Each source has exactly one target
2. No Competing Elements: Elements don't interfere with each other
3. No Functional Dependencies: Changing one doesn't require changing another

Design Matrix Analysis

Create a design matrix to visualize relationships:

         CN.1  CN.2  CN.3
CP.1     [X]   [ ]   [ ]    ← Ideal: one X per row
CP.2     [ ]   [X]   [ ]
CP.3     [ ]   [ ]   [X]

Matrix Types:

Analysis 2: Completeness Levels

Use C (Complete) and P (Partial) markers to indicate how well each element addresses its source:

CP → CN Completeness Matrix

         CN.1  CN.2  CN.3
CP.1     [C]   [ ]   [ ]    C = CN completely solves CP
CP.2     [P]   [P]   [ ]    P = CN partially solves CP
CP.3     [ ]   [ ]   [C]

Interpretation:

• C (Complete): The CN fully addresses the CP
• P (Partial): The CN helps but doesn't fully solve the CP; may need additional CNs

CN → FR Completeness Matrix

         FR.1  FR.2  FR.3  FR.4
CN.1     [C]   [ ]   [ ]   [ ]
CN.2     [P]   [P]   [ ]   [ ]
CN.3     [ ]   [ ]   [C]   [P]

Completeness Rules

1. Every CP row must have at least one C or multiple Ps that together equal C
2. Every CN row must have at least one C or multiple Ps that together equal C
3. Blank rows indicate gaps (uncovered problems or needs)
4. Blank columns indicate orphans (requirements without traced needs)

Analysis 3: Information Content

Concept

Information Content (IC) measures the probability that a design will successfully satisfy its requirements. Lower IC = better design.

Formula:

IC = log₂(1/p)

Where p = probability of success

Practical Application

For each CN, estimate:

1. Need Range: The acceptable range of outcomes
2. System Range: What the proposed solution can actually deliver

Example:

CN.1: Manager needs to know account balances within 24 hours

Need Range: 0-24 hours (acceptable)
System Range: 0-2 hours (what system delivers)

Overlap: 100% → High probability of success → Low IC ✅

Simplified IC Assessment

Output Template

When running complexity analysis, produce:

## Complexity Analysis Report

### 1. Element Count Summary

| Domain | Count |
|--------|-------|
| Customer Problems (CP) | [N] |
| Customer Needs (CN) | [N] |
| Functional Requirements (FR) | [N] |

**Specification Type:** [Coupled | Redundant | Ideal]

### 2. Independence Analysis

**CP → CN Matrix:**
[Include matrix with X markers]

**CN → FR Matrix:**
[Include matrix with X markers]

**Independence Status:** [Uncoupled ✅ | Semi-coupled ⚠️ | Coupled ❌]

### 3. Completeness Analysis

**CP → CN Completeness:**
[Include matrix with C/P markers]

**CN → FR Completeness:**
[Include matrix with C/P markers]

**Coverage Issues:**
- [List any uncovered CPs]
- [List any uncovered CNs]
- [List any orphan FRs]

### 4. Information Content Assessment

| CN | Need Range | System Range | Overlap | IC Level |
|----|------------|--------------|---------|----------|
| CN.1 | [range] | [range] | [%] | [Low/Med/High] |

### 5. Recommendations

1. [Specific recommendation based on analysis]
2. [Specific recommendation based on analysis]

When to Use This Analysis

Example: CRM System

Element Counts:

• CPs: 5
• CNs: 6
• FRs: 8

Assessment: Redundant specification (CNs > CPs, FRs > CNs)

CP → CN Matrix:

         CN.1  CN.2  CN.3  CN.4  CN.5  CN.6
CP.1     [C]   [P]   [ ]   [ ]   [ ]   [ ]
CP.2     [ ]   [ ]   [C]   [ ]   [ ]   [ ]
CP.3     [ ]   [ ]   [ ]   [C]   [ ]   [ ]
CP.4     [ ]   [ ]   [ ]   [ ]   [C]   [P]
CP.5     [ ]   [ ]   [ ]   [ ]   [ ]   [C]

Result: Semi-coupled (triangular tendency). CP.1 and CP.4 have multiple CNs but they don't compete. Acceptable.

References

• Suh, N.P. (1990). The Principles of Design. Oxford University Press.
• Suh, N.P. (2001). Axiomatic Design: Advances and Applications. Oxford University Press.
• Problem-Based SRS Dissertation (Gorski & Stadzisz, 2016) - Chapter 3, Section 3.4

Version: 1.2
Type: Optional Advanced Validation Tool
Command: /complexity-analysis