Bayesian Monitoring of Times Between Events: The Shewhart t_r-Chart

Abstract

The traditional (frequentist) t_r-chart is a Shewhart-type chart useful for monitoring times between events (interarrival times) following an exponential distribution. This problem often arises in high-yield processes where the defect rate is low and hence the conventional attribute charts such as the c-chart and the u-chart are often ineffective. We consider this problem under the Bayesian framework and propose a Bayesian t_r-chart when the exponential rate parameter is unknown. The Bayesian t_r-chart is a Shewhart-type chart that incorporates parameter uncertainty via a prior and a posterior distribution, unlike the traditional t_r-chart. The control limits are constructed from the predictive distribution of a plotting statistic. The performance of the proposed chart is evaluated and comparisons are made with the traditional t_r-chart. The Bayesian chart is seen to be advantageous in certain situations. An illustrative example is given and a summary and conclusions are offered.

• Bayesian and Frequentist Control Charts
• Exponential Distribution
• Performance Metrics
• Predictive Distribution
• Prior and Posterior Distributions

Additional information

Notes on contributors

Nirpeksh Kumar

Dr. Kumar is an Assistant Professor in the Department of Statistics. His email address is [email protected]. He is the corresponding author.

Subha Chakraborti

Dr. Chakraborti is a Professor in the Department of Information Systems, Statistics, and Management Science. His email address is [email protected].