Software Reliability Analysis

A practical implementation and comparison of classical software reliability models using Python.

This project implements three software reliability models:

• Jelinski-Moranda
• Schuman
• Nelson-Corcoran

The models are used to estimate software reliability, failure intensity, and Mean Time To Failure (MTTF). The calculations are also integrated into the Flask-based VulnMart application through a REST API endpoint.

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Project Objectives

The main goals of this project are:

• Study classical mathematical software reliability models
• Perform reliability calculations using Python
• Compare different reliability estimation approaches
• Generate reliability curves
• Integrate reliability calculations into a Flask application
• Provide reliability results through a JSON API

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Implemented Reliability Models

1. Jelinski-Moranda Model

The Jelinski-Moranda model assumes that the failure intensity is proportional to the number of remaining faults.

Failure intensity:

λ(i) = φ (N0 - i)

Reliability:

R(t) = exp(-λt)

For the practical dataset:

R(100) = 0.8187

MTTF = 500 hours

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2. Schuman Model

The Schuman model uses residual fault density per machine instruction.

Residual fault density:

εr = (E0 - Ec) / I

Failure intensity:

λ = Ks × εr

Reliability:

R(t) = exp(-λt)

For the practical dataset:

R(100) = 0.99998

MTTF = 5,000,000 hours

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3. Nelson-Corcoran Model

The Nelson-Corcoran model is a static software reliability model based on test execution results.

Nelson reliability estimate:

R = 1 - Σ (ni / Ni) × Pi

Calculated results:

Nelson: R = 0.9540

Corcoran: R = 0.9860

Simplified: R = 0.9700

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Results

Model	Reliability	MTTF
Jelinski-Moranda	0.8187	500 hours
Schuman	0.99998	5,000,000 hours
Nelson-Corcoran	0.954 - 0.986	N/A

The Jelinski-Moranda model provides the most conservative estimate.

The Schuman model provides the most optimistic estimate.

The Nelson-Corcoran model provides an intermediate estimate based on test runs and input distribution.

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Reliability Plot

The project generates:

reliability_curves.png

The graph compares the Jelinski-Moranda and Schuman models over operating time.

Target reliability level:

R = 0.95

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Flask Integration

The reliability models are integrated into the VulnMart Flask application.

Start the application:

cd vulnmart

python app.py

The application runs on:

http://127.0.0.1:5055

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Reliability API

The application provides:

GET /reliability

Example request:

curl "http://127.0.0.1:5055/reliability?t=100&i=30&Ec=30"

Example response:

{
  "corrected_errors": 30,
  "jelinski_moranda": {
    "MTTF": 500.0,
    "R": 0.8187,
    "lambda": 0.002
  },
  "nelson_corcoran": {
    "R_corcoran": 0.986,
    "R_nelson": 0.954,
    "R_simple": 0.97
  },
  "schuman": {
    "MTTF": 5000000.0,
    "R": 0.99998,
    "lambda": 2e-07
  },
  "time_hours": 100.0
}

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Project Structure

software-reliability-analysis/
 src/
    reliability_models.py
 vulnmart/
    app.py
    reliability_models.py
    requirements.txt
    templates/
 reliability_curves.png
 README.md
 .gitignore

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Technologies

• Python
• Flask
• NumPy
• Matplotlib
• Git
• GitHub

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Conclusion

Different software reliability models produce different estimates because they use different assumptions and input data.

The Jelinski-Moranda model gives the most conservative result, while the Schuman model gives the most optimistic result.

The Nelson-Corcoran model provides a practical estimate based on test execution data.

This project demonstrates software reliability modeling, mathematical analysis, visualization, and integration into a Flask application.

Future Improvements

• Add additional reliability models
• Expand API functionality
• Improve visualization and reporting