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Key formulas and calculations used in software engineering.
Software engineering relies on quantitative formulas for estimation, measurement, and quality assessment. These formulas transform subjective judgments into objective calculations, enabling data-driven decisions about project planning, quality targets, and process improvement. Understanding these formulas is essential for project managers estimating effort, quality engineers measuring effectiveness, and developers understanding the metrics by which their work is assessed.
Effort Estimation Formulas
Basic COCOMO (Constructive Cost Model)
Developed by Barry Boehm, COCOMO estimates development effort based on estimated lines of code:
Example
Effort (person-months) = a × (KLOC)^b
Duration (months) = c × (Effort)^d
People = Effort / Duration
Where KLOC = thousands of lines of code, and constants depend on project type:
| Project Type | a | b | c | d |
|---|---|---|---|---|
| Organic (small, experienced team) | 2.4 | 1.05 | 2.5 | 0.38 |
| Semi-detached (medium complexity) | 3.0 | 1.12 | 2.5 | 0.35 |
| Embedded (complex, constrained) | 3.6 | 1.20 | 2.5 | 0.32 |
Example: A semi-detached project estimated at 50 KLOC:
Example
Effort = 3.0 × (50)^1.12 = 3.0 × 72.4 = 217 person-months
Duration = 2.5 × (217)^0.35 = 2.5 × 6.9 = 17.3 months
People = 217 / 17.3 ≈ 13 people
Function Point Analysis
Function Points measure system size by counting functional elements:
Example
UFP = Σ(External Inputs × weight) + Σ(External Outputs × weight) +
Σ(External Inquiries × weight) + Σ(Internal Logical Files × weight) +
Σ(External Interface Files × weight)
FP = UFP × [0.65 + 0.01 × Σ(Fi)]
Where Fi are 14 General System Characteristics rated 0-5, and weights depend on complexity:
| Element | Simple | Average | Complex |
|---|---|---|---|
| External Inputs | 3 | 4 | 6 |
| External Outputs | 4 | 5 | 7 |
| External Inquiries | 3 | 4 | 6 |
| Internal Logical Files | 7 | 10 | 15 |
| External Interface Files | 5 | 7 | 10 |
Quality Metrics Formulas
Defect Density
Example
Defect Density = Total Defects Found / Size (KLOC or Function Points)
Example: 87 defects in 25 KLOC system
DD = 87 / 25 = 3.48 defects per KLOC
Defect Removal Efficiency (DRE)
Example
DRE = (Defects removed during development / Total defects) × 100%
Total defects = Defects in development + Defects found post-release
Example: 250 defects found before release, 15 found after
DRE = 250 / (250 + 15) × 100% = 94.3%
Mean Time Between Failures (MTBF)
Example
MTBF = Total operating time / Number of failures
Example: System runs 2,160 hours with 3 failures
MTBF = 2,160 / 3 = 720 hours between failures
Mean Time To Repair (MTTR)
Example
MTTR = Total repair time / Number of repairs
Example: 3 failures took 2, 4, and 6 hours to fix
MTTR = (2 + 4 + 6) / 3 = 4 hours average repair time
System Availability
Example
Availability = MTBF / (MTBF + MTTR) × 100%
Example: MTBF = 720 hours, MTTR = 4 hours
Availability = 720 / (720 + 4) = 99.4%
Nines of Availability
| Availability | Downtime/Year | Common Name |
|---|---|---|
| 99% | 3.65 days | Two nines |
| 99.9% | 8.76 hours | Three nines |
| 99.99% | 52.6 minutes | Four nines |
| 99.999% | 5.26 minutes | Five nines |
Complexity Metrics
Cyclomatic Complexity (McCabe)
Example
V(G) = E - N + 2P
Where:
E = number of edges in the control flow graph
N = number of nodes
P = number of connected components (usually 1)
Simplified: V(G) = Number of decision points + 1
(Count if, while, for, case, catch, &&, ||, ternary operators)
Halstead Metrics
| Program Length | N = N1 + N2 (total operators + total operands) |
| Program Vocabulary | n = n1 + n2 (unique operators + unique operands) |
| Volume | V = N × log2(n) |
| Difficulty | D = (n1/2) × (N2/n2) |
| Effort | E = D × V |
Project Scheduling Formulas
Critical Path Method
Example
Earliest Start (ES) = Max(EF of all predecessors)
Earliest Finish (EF) = ES + Duration
Latest Finish (LF) = Min(LS of all successors)
Latest Start (LS) = LF - Duration
Float (Slack) = LS - ES = LF - EF
Critical Path: Activities where Float = 0
PERT Estimation
Example
Expected Time = (Optimistic + 4×Most Likely + Pessimistic) / 6
Standard Deviation = (Pessimistic - Optimistic) / 6
Example: O=10 days, M=15 days, P=26 days
Expected = (10 + 4×15 + 26) / 6 = 16 days
SD = (26 - 10) / 6 = 2.67 days
Test Coverage Formulas
Example
Statement Coverage = (Statements executed / Total statements) × 100%
Branch Coverage = (Branches executed / Total branches) × 100%
Condition Coverage = (Conditions tested true+false / Total conditions × 2) × 100%
Productivity Metrics
Example
Productivity = Size (FP or KLOC) / Effort (person-months)
Cost per Function Point = Total Project Cost / Function Points
Defect Detection Rate = Defects found per hour of review/testing
These formulas provide the quantitative foundation for software engineering management—enabling objective estimation, measurement, and improvement of software development processes and products.
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