Date of Award
12-2024
Degree Name
Master of Science in Engineering
Department
Industrial and Entrepreneurial Engineering and Engineering Management
First Advisor
Lee Wells, Ph.D.
Second Advisor
James Burns, Ph.D.
Third Advisor
Daniel Santos, Ph.D.
Keywords
ARL, EWMA control charts, false alarms, shewhart control charts, shift detection, statistical process control
Access Setting
Masters Thesis-Open Access
Abstract
The Average Run Length (ARL) is a performance measure of Control Charts widely used within Statistical Process Control. In this study we propose a new approach for the computation of the ARL that is based on a novel interpretation of out-of-control signals produced by a Control Chart. Specifically, out-of-control signals used to calculate traditional ARLs may correspond to Type I errors and may not reflect a Control Chart’s true performance. To compensate for this issue, for Shewhart and EWMA charts, constraints are applied to the calculation of ARLs so that only out-of-control signals that occur when the corresponding statistic is in the same direction of the shift are considered. The performances of Shewhart and EWMA charts using this new ARL performance metric are compared to traditional ARL calculations. The results presented in the document and the complementary analyses indicate that the proposed new approach for ARL calculation does not compromise the ability to detect false alarms and improves our ability to compare two competing charts, given that it approaches Type I errors in a way that they may better translate to the Control Chart’s true performance by disregarding any signal opposed to the shift occurred. The analysis performed also corroborates that the appropriate choice of 𝜆, the use of time-varying control limits, and the implementation of counter reset within Shewhart and EWMA Control Charts are key elements that can lead to substantial improvements Control Chart performance. Integrating these findings with economic analyses and practical applications in real environments will be important steps to validate and expand the applicability of these methodologies.
Recommended Citation
Sousa, Gonçalo, "A Novel Interpretation of Average Run Length for Assessing the Performance of Control Charts" (2024). Masters Theses. 5445.
https://scholarworks.wmich.edu/masters_theses/5445
