Analytical formulas for risk assessment for a class of problems where risk depends on three interrelated variables

We derive general analytical formulas for assessing risks in a problem domain where therisk depends on three interrelated variables. More specifically, we derive general analyticalformulas for propagating beliefs in a network where three binary variables, A, B and C, arerelated to a fourth binary variable Z through an ‘AND’ relationship. In addition, we assume thatvariables A, B and C are interrelated in that a change in one variable may affect the value of eachof the other two. The analytical formulas derived in this article determine the overall belief andplausibility that Z is true or not true, given that we have beliefs on variables A, B and/or C. To demonstrate the importance of the general results, we use the results to developmodels applicable to three real-world situations. The first model can aid external auditors inassessing the quality of an audit client’s internal audit function to determine the extent to whichthe internal auditor’s work can be relied on in the conduct of a financial audit while the secondcan aid in assessing the risk of impaired auditor independence when conducting a financialstatement audit. The third model can be used to assess the risk of management fraud in financialreporting. Assessment of such risks is of critical importance to external auditors, regulators, andthe investing public. Analytical formulas to help address these types of important business andeconomic problems have not been available prior to these derivations.