A Bayesian Quality Control Technique for the Joint Monitoring of the Parameters of the Shifted Exponential Distribution

• Activity Number: 429 - Contributed Poster Presentations: Quality and Productivity Section
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Austin Brown and Bryce Whitehead and Hend Aljobaily*
• Companies: University of Northern Colorado and University of Northern Colorado and University of Northern Colorado
• Keywords: Bayesian Estimation; Quality Control; Poisson Process; Time to Event

Abstract

In many practical quality control applications, monitoring the time between observance of some event is of interest. When these countable events follow a Poisson distribution, the time between their observance can be modeled using the exponential distribution, where its scale parameter is the mean of the underlying Poisson process. However, there are instances where the origin, and consequently the location parameter, of the exponential distribution may not be zero, and thus utilization of the shifted exponential distribution is warranted. In this study, a phase II two control chart scheme, which follows a Shewart-style framework, is presented for the shifted exponential distribution using Bayesian estimation for both parameters as well as the marginal posterior control limits. Multiple prior distributions are investigated for both the scale and location parameters, and the in-control and out-of-control average run lengths are calculated and presented. Recommendations for implementation are also given.