[This paper presents a reliability model of a control system with control components in series. The results show that output reliability may increase or decrease as new control components are added to the series, depending on the characteristic reliability parameters of the control components. The results are compared with Bodnar's [1975] results that led him to the paradoxical conclusion that fewer control components are better than more in a serial system. It is observed that no such paradox exists when the controls are modeled properly.]
Relates belief functions to the structure of audit risk and provides formulas for audit risk under certain assumptions. Review of literature; Structure of audit evidence; Control factors and accounting systems; Plausibility interpretation of audit risk; Limitations in the application of the models; Derivation of audit risk formulas.
[This article relates belief functions to the structure of audit risk and provides formulas for audit risk under certain simplifying assumptions. These formulas give plausibilities of error in the belief-function sense. We believe that belief-function plausibility represents auditors' intuitive understanding of audit risk better than ordinary probability. The plausibility of a statement, within belief-function theory, measures the extent to which we lack evidence against the statement. High plausibility for error indicates only a lack of assurance, not positive evidence that there is error. Before collecting, analyzing, and aggregating the evidence, an auditor may lack any assurance that a financial statement is correct, and in this case will attribute very high plausibility to material misstatement. This high plausibility does not necessarily indicate any evidence that the statement is materially misstated, and hence, it is inappropriate to interpret it as a probability of material misstatement. The SAS No. 47 formula for audit risk is based on a very simple structure for audit evidence. The formulas we derive in this article are based on a slightly more complex but still simplified structure, together with other simplifying assumptions. We assume a tree-type structure for the evidence, assume that all evidence is affirmative and that each variable in the tree is binary. All these assumptions can be relaxed. As they are relaxed, however, the formulas become more complex and less informative, and it then becomes more useful to think in terms of computer algorithms rather than in terms of formulas (Shafer et al. 1988). In general, the structure of audit evidence corresponds to a network of variables. We derive formulas only for the case in which each item of evidence bears either on all the audit objectives of an account or on all the accounts in the financial statement, as in figure 1, so that the network is a tree. Usually, however, there will be some evidence that bears on some but not all objectives for an account, on some but not all accounts, or on objectives at different levels; in this case, the network will not be a tree. We assume that all evidence is affirmative because this is the situation treated by the SAS No. 47 formula and because belief-function formulas become significantly more complex when affirmative and negative evidence is combined. This complexity is due primarily to the renormalization involved in Dempster's rule for combining belief functions. The variables in the network or tree represent various audit objectives, accounts, and the financial statement as a whole. We assume these variables are binary. For example, we assume that an account either is or is not materially misstated. This assumption is clearly too restrictive for most audit practice. Often, for example, an auditor must consider immaterial errors in individual accounts that could produce a material error in the financial statement when they are aggregated. We derive formulas for plausibility of material misstatement at three levels: the financial statement level, the account level, and the audit objective level. The formula at the audit objective level resembles the SAS No. 47 formula, but the formulas at the other two levels are significantly different. Because our model does distinguish evidence gathered at the three different levels, audits based on our formulas are sometimes significantly more efficient than audits based on the SAS No. 47 model or on the simpler Bayesian models.]
This paper presents a reliability model of a control system with control components in series. The results show that output reliability may increase or decrease as new control components are added to the series, depending on the characteristic reliability parameters of the control components. The results are compared with Bodnar's [1975] results that led him to the paradoxical conclusion that fewer control components are better than more in a serial system. It is observed that no such paradox exists when the controls are modeled properly.
Les auteurs ont pour but de faire progresser la recherche dans le domaine de l’évaluation de l’audit interne en élaborant un modèle d’évaluation de la fonction d’audit interne qui tient compte des relations entre les facteurs précis qu’utilisent les auditeurs externes pour évaluer la solidité de cette fonction. Le modèle repose sur trois facteurs définis par les normes d’audit et par les travaux de recherche antérieurs : la compétence, la qualité du travail et l’objectivité. Les auteurs élaborent une expression analytique du modèle à l’aide du cadre de référence des fonctions de croyance afin de dépasser les limites des études antérieures. Leurs résultats révèlent que la modélisation de la relation « et » est essentielle à l’évaluation de la solidité de la fonction d’audit interne. Au chapitre des relations, l’analyse montre que, lorsque celle qui unit ces trois facteurs est solide ou parfaite, la fonction d’audit interne demeure d’une grande solidité, même en présence d’éléments probants positifs ou négatifs à l’égard de l’un des facteurs. Ce résultat persiste dans la mesure où les niveaux de croyance au sujet des deux autres facteurs sont élevés. Les auteurs démontrent en outre comment la qualité de la gouvernance d’entreprise influe sur l’évaluation de la fonction d’audit interne et comment il est possible de recourir à l’analyse coûts‐avantages dans ce contexte pour mieux déterminer la quantité de travail d’audit externe qu’exige le respect des normes. L’analyse des auteurs révèle que l’étendue du travail d’audit devant être réalisé par l’auditeur externe dépend de la solidité de la fonction d’audit interne et de l’importance des coûts associés aux litiges et au respect de la réglementation auxquels le vérificateur externe doit faire face.
The purpose of this paper is to advance research in internal audit (IA) evaluation by developing an IA assessment model that considers interrelationships among specific factors used by external auditors to evaluate the strength of the IA function. The model is based on three factors identified by auditing standards and by prior academic research: Competence, Work Performance, and Objectivity. We develop an analytical expression of the model using the belief function framework in order to overcome limitations of prior research. Our results reveal that modeling the “And” relationship is essential for assessing the strength of the IA function. As far as interrelationships are concerned, the analysis shows that, when the three factors have a strong or a perfect relationship, the strength of the IA function remains high even if there is positive or negative evidence about one of the factors. This result holds as long as there are high levels of belief about the other two factors. Further, we demonstrate how the quality of corporate governance affects the evaluation of the IA function and how a cost–benefit analysis can be applied to this framework to help determine the amount of external audit work needed to comply with standards. Our analysis reveals that the extent of external audit work to be carried out by the external auditor depends on the strength of the IA function and the amount of litigation and regulatory costs likely to be faced by the external auditor.
The purpose of this paper is to advance research in internal audit (IA) evaluation by developing an IA assessment model that considers interrelationships among specific factors used by external auditors to evaluate the strength of the IA function. The model is based on three factors identified by auditing standards and by prior academic research: Competence, Work Performance, and Objectivity. We develop an analytical expression of the model using the belief function framework in order to overcome limitations of prior research. Our results reveal that modeling the And relationship is essential for assessing the strength of the IA function. As far as interrelationships are concerned, the analysis shows that, when the three factors have a strong or a perfect relationship, the strength of the IA function remains high even if there is positive or negative evidence about one of the factors. This result holds as long as there are high levels of belief about the other two factors. Further, we demonstrate how the quality of corporate governance affects the evaluation of the IA function and how a costbenefit analysis can be applied to this framework to help determine the amount of external audit work needed to comply with standards. Our analysis reveals that the extent of external audit work to be carried out by the external auditor depends on the strength of the IA function and the amount of litigation and regulatory costs likely to be faced by the external auditor.