Time to signal distribution of multivariate bayesian control chart with dual sampling scheme

Abstract

The ability of a control chart to detect a shift in the process can be determined by the average run length (ARL), a widely used performance indicator for single sampling interval (SSI) control charts. When it comes to variable sampling interval (VSI) schemes, average time to signal (ATS) is utilized instead of ARL. Although analysis of ARL has been extensively studied for SSI schemes, calculation of the ATS for VSI control charts is still in its infancy due to several theoretical challenges. In this context, the paper derives closed-form expressions for time to signal distribution and the ATS for a spatial design of VSI multivariate Bayesian control chart referred to as the dual sampling scheme (DSS). In a DSS strategy, the process is being monitored initially with a longer sampling interval, which is changed to the shorter sampling interval at a designed switching point. Unlike previous approximate developments where the switching point is ignored, the paper derives exact expressions for computation of time to signal distribution and ATS within such a Bayesian framework. Derivations of the ATS are based on an intuitively pleasing definition of an artificial absorbing state and coded values of the posterior probability using Markov chain theory.

Keywords:

• Quality control
• average time to signal
• Bayesian control chart
• dual sampling interval
• stochastic and statistics

Disclosure statement

No potential conflict of interest was reported by the author.

Data availability statement

The data that supports the findings of this study are available from the corresponding author, F. N., upon reasonable request.

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada [RGPIN-2019-06966].

Notes on contributors

Farnoosh Naderkhani

Farnoosh Naderkhani is currently an Assistant Professor with Concordia Institute for Information System Engineering (CIISE) at Concordia University. Prior to joining CIISE, she was a Post-doctoral Fellow at H. Milton Stewart School of Industrial and Systems Engineering at Georgia Tech. Dr Naderkhani has completed her Ph.D. at Mechanical and Industrial Engineering (MIE) department at University of Toronto, Toronto, Canada. Her research interests include, Quality Control, Stochastic Modelling; Quality Assurance; Maintenance; Optimal Control of Partially Observable Processes; and Condition-based Maintenance. Dr Naderkhani is an elected member of IEEE Reliability Society Administrative Committee (AdCom), and a Leadership Team Member of the American Society for Quality (ASQ) Montreal Section 401. She was a member of the organising committee of 2021 IEEE International Conference on Prognostic and Health Management (ICPHM 2021), serving at the capacity of ‘Paper Review Chair’. She was the ‘Paper Review vice Chair’ at ICPHM 2020 conference and will serve as the ‘Program Chair’ in the upcoming ICPHM 2022 conference. She also was the ‘Local Arrangement Co-Chair’ of 2021 IEEE International Conference on Autonomous Systems (IEEE ICAS). Dr Naderkhani has received several prestigious awards including Natural Sciences and Engineering Research Council of Canada (NSERC) Postdoctoral Fellowship, two Queen Elizabeth II Graduate Scholarships and one Ontario Graduate Scholarship (OGS).