Synthetic exponential control charts with unknown parameter. Issue 8 (14th September 2018)

• Record Type: Journal Article
• Authors: Sun, Lirong; Wang, Bing Xing; Guo, Baocai; Xie, Min
• Is Part Of: Communications in statistics. Volume 47:Issue 8(2018)
• Page Start: 2360
• Page End: 2377
• Publication Date: 2018-09-14
• Subjects: Conditional average run length -- Exponential distribution -- Parameter estimation -- Standard deviation of average run length -- Synthetic chart; Primary 62-XX -- Secondary 62P30; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2017.1343840
• Languages: English
• ISSNs: 0361-0918

Abstract

ABSTRACT: The existing synthetic exponential control charts are based on the assumption of known in-control parameter. However, the in-control parameter has to be estimated from a Phase I dataset. In this article, we use the exact probability distribution, especially the percentiles, mean, and standard deviation of the conditional average run length (ARL) to evaluate the effect of parameter estimation on the performance of the Phase II synthetic exponential charts. This approach accounts for the variability in the conditional ARL values of the synthetic chart obtained by different practitioners. Since parameter estimation results in more false alarms than expected, we develop an exact method to design the adjusted synthetic charts with desired conditional in-control performance. Results of known and unknown in-control parameter cases show that the control limit of the conforming run length sub-chart of the synthetic chart should be as small as possible.