Advanced Audit Analysis Report System Documentation

1. Overview

The Advanced Audit Analysis Report System is a sophisticated PHP-based web application meticulously crafted to execute detailed financial audits. By leveraging transaction data from a database, it employs a blend of statistical methodologies and rule-based algorithms to uncover irregularities, culminating in a visually enriched report. Key enhancements include role-based access control, advanced statistical analyses such as Benford’s Law, and bespoke fraud detection metrics, notably the newly integrated "Suspicious Entries" analysis.

2. Performance

Execution Flow

1. Session Initialization: Verifies user authentication and role.
2. Database Connection: Establishes a connection to a PDO-based database (connection.php).
3. Settings Retrieval: Retrieves configuration from the settings table or applies defaults.
4. Form Submission: Accepts start_date and end_date via POST request.
5. Audit Execution: Invokes performComprehensiveAudit() upon run_audit submission.
6. Report Generation: Produces results in HTML with Bootstrap styling and Chart.js visualizations.

Runtime Considerations

• Complexity: \( O(n) \) for most analyses, where \( n \) is the number of transactions; Benford’s Law incurs additional array operations.
• Database Queries: Executes multiple SQL queries (approximately 10 in the audit function), optimized with prepared statements.
• Scalability: Suitable for moderate datasets (thousands of transactions); larger datasets may necessitate indexing.
• Dependencies: Requires PHP, PDO, Bootstrap 5.3, Chart.js, and Font Awesome.

Output Format

• HTML Report: Structured into Executive Summary, Anomalies, Fraud Indicators, Statistical Analysis, Material Accounts, and Recommendations.
• Visuals: Features a doughnut chart (findings), bar chart (Benford’s Law), and boxplot (amount distribution).
• Notes: Small-font explanations elucidate each section’s purpose.

3. Calculation Formulas

The system employs a suite of formulas for statistical and audit-specific computations, detailed below.

3.1 Benford’s Law Analysis

Purpose: Detects fraud by comparing the first-digit distribution of transaction amounts to Benford’s expected distribution.

Formulas:

• Expected probability for digit \( d \) (1–9): \( P(d) = \log_{10}(1 + \frac{1}{d}) \)
• Actual frequency: \( F(d) = \frac{\text{count of transactions starting with } d}{\text{total transactions}} \)
• Deviation: \( D(d) = |F(d) - P(d)| \)

Threshold: Deviation > 0.15 triggers a fraud indicator.

Implementation: Iterates through amounts, tallies first digits, and computes deviations.

3.2 General Ledger Balance

Purpose: Identifies material accounts with significant imbalances.

Formulas:

• Total Debits: \( TD = \sum (\text{amount where debit account matches}) \)
• Total Credits: \( TC = \sum (\text{amount where credit account matches}) \)
• Balance: \( B = TD - TC \)
• Materiality Check: \( |B| > \text{audit_threshold} \) (default 1000)

Output: Accounts where \( |B| > 1000 \) are listed.

3.3 Transaction Amount Statistics

Purpose: Analyzes distribution to detect anomalies.

Formulas:

• Mean: \( \mu = \frac{\sum x_i}{n} \)
• Median: Middle value of sorted amounts (or average of two middle values if \( n \) is even).
• Standard Deviation: \( \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n-1}} \) (sample formula).
• Skewness: \( S = \frac{\sum \left(\frac{x_i - \mu}{\sigma}\right)^3}{n} \) (if \( n > 2 \)).
• Kurtosis: \( K = \frac{\sum \left(\frac{x_i - \mu}{\sigma}\right)^4}{n} - 3 \) (if \( n > 3 \)).
• Z-Score: \( Z = \frac{|x - \mu|}{\sigma} \) (flags outliers if \( Z > 3 \)).

Output: Statistical measures and outliers.

3.4 Round Number Detection

Purpose: Identifies potential manual entries.

Formulas:

• Condition: \( x = \text{round}(x) \) or \( x \mod 1000 = 0 \) or \( x \mod 500 = 0 \)
• Percentage: \( P = \frac{\text{count of round numbers}}{\text{total transactions}} \times 100 \)

Threshold: \( P > 15\% \) prompts a recommendation.

Filter: Excludes legitimate patterns (e.g., “salary”).

3.5 Manual Journal Entries

Purpose: Counts entries to expense accounts.

Formula: \( MJ = \text{count of transactions where gl_account_code_debit in ('5000', '6000')} \)

Threshold: \( MJ > 10 \) flags a fraud indicator.

3.6 Suspicious Entries

Purpose: Identifies entries by non-trusted users.

Formula: \( SE = \text{count of transactions where created_by not in (1, 2, 3)} \)

Threshold: \( SE > 5 \) flags a fraud indicator and contributes to risk score.

3.7 Risk Assessment Score

Purpose: Quantifies overall risk.

Formula: \( RS = (FI \times 5) + (A \times 2) + (RNP > 15 ? 10 : 0) + (AHT > 5 ? 8 : 0) + (SE > 5 ? 8 : 0) \)

Where:

• \( FI \): Number of fraud indicators.
• \( A \): Number of anomalies.
• \( RNP \): Round number percentage.
• \( AHT \): After-hours transactions.
• \( SE \): Suspicious entries.

Levels: Low (\( RS \leq 15 \)), Medium (\( 15 < RS \leq 30 \)), High (\( RS > 30 \)).

4. Definitions of Abbreviations

5. Relevant Standards Employed

The system adheres to established accounting and auditing standards to ensure reliability and compliance.

5.1 International Standards on Auditing (ISA)

• ISA 240: The Auditor’s Responsibilities Relating to Fraud – Implemented via fraud indicators (e.g., Benford’s Law, round numbers, suspicious entries).
• ISA 315: Identifying and Assessing Risks – Materiality threshold and risk scoring align with risk assessment.
• ISA 330: Responses to Assessed Risks – Recommendations provide actionable responses.

5.2 Generally Accepted Accounting Principles (GAAP)

• Materiality: Configurable threshold (default $1000) identifies significant accounts.
• Completeness: Ensures all transactions within the period are analyzed.

5.3 Statistical Standards

• Benford’s Law: Forensic accounting method for fraud detection.
• Z-Score: Statistical measure for outliers (threshold: 3 standard deviations).

5.4 Internal Control Standards (COSO Framework)

• Control Activities: SOD check aligns with separation of duties.
• Monitoring: Supports ongoing financial process oversight.

6. Output Details

6.1 Executive Summary

Content: Material accounts, anomalies, fraud indicators, risk level.

Purpose: Offers a high-level overview for decision-makers.

Note: Shows a summary of key findings and risk level.

6.2 Anomalies Detected

Content: Transactions with Z-scores > 3.

Purpose: Highlights statistical outliers.

Note: Lists transactions with unusual amounts (>3 SD from mean).

6.3 Fraud Indicators

Content: Benford deviations, round numbers, duplicates, after-hours entries, manual journals, suspicious entries.

Purpose: Flags potential fraud risks.

Note: Highlights risks like round numbers or suspicious user entries.

6.4 Statistical Analysis

Content: Transaction count, mean, standard deviation, after-hours, round numbers, manual journals, suspicious entries.

Purpose: Provides quantitative insights.

Notes:

• After-hours: Counts entries between 8 PM and 6 AM.
• Round numbers: Counts round amounts not tied to common patterns.
• Manual journals: Counts debits to expense accounts (5000, 6000).
• Suspicious entries: Counts entries by users not in trusted list (IDs 1, 2, 3).

6.5 Material Accounts

Content: Accounts exceeding materiality threshold.

Purpose: Identifies significant financial impacts.

Note: Lists accounts with balances above the threshold.

6.6 Recommendations

Content: Actionable suggestions based on findings.

Purpose: Guides follow-up actions.

Note: Suggests actions based on detected risks.

7. Conclusion

The Advanced Audit Analysis Report System offers a robust, standards-compliant solution for financial auditing. By integrating statistical methods (Benford’s Law, Z-scores), rule-based checks (round numbers, suspicious entries), and compliance controls (SOD), it delivers thorough analysis and actionable insights. Its extensible design accommodates additional metrics or thresholds as required.