Analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing

Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.

The impact of *experience, industry characteristics, and individual differences on audit risk and the extent of testing decisions: An empirical investigation

The first part of the study examined the effect of industry risk changes on perceived audit risk at the financial statement level and whether these changes depended on individual differences such as experience and tolerance for ambiguity. ^ Forty-eight auditors from two offices of one of the “Big 5” CPA firms participated in this study. The ANOVA results supported the effect of industry risk in the assessment of audit risk at the financial statement level. Higher industry risk was associated with higher perceived audit risk. Tolerance for ambiguity was also significant in explaining the changes in the assessment of audit risk. Auditors with a high tolerance for ambiguity perceived lower audit risk than auditors with a low tolerance for ambiguity. Although ANOVA results did not find experience to be significant, a t-test for experience showed it to be marginally significant and inversely related to audit risk. ^ The second part of this study examined whether differences in perceived audit risk at the financial statement level altered the extent, nature or timing of the planned auditing procedures. The results of the MANOVA suggested an overall audit risk effect at the financial statement level. Perceived audit risk was significant in explaining the variation in the number of hours planned for the total cycle and the number of hours p1anned for the tests of balances and details. Perceived audit risk was not significant in determining the analytical review procedures planned, but assessed inherent risk at the cycle level was significant. The higher the inherent risk the more analytical procedures were planned. Perceived audit risk was not significant in explaining the timing of the procedures, but individual differences were significant. The results showed that experienced auditors and those with a high tolerance for ambiguity were less likely to postpone the performance of the interim procedures or the time at which the majority of audit work would be done. ^

Analytical Approximations to Predict Performance Measures of Manufacturing Systems with Job Failures and Parallel Processing

Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.