TY - JOUR
T1 - Synthetic exponential control charts with unknown parameter
AU - Sun, Lirong
AU - Wang, Bing Xing
AU - Guo, Baocai
AU - Xie, Min
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Conditional average run length
KW - Exponential distribution
KW - Parameter estimation
KW - Standard deviation of average run length
KW - Synthetic chart
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U2 - 10.1080/03610918.2017.1343840
DO - 10.1080/03610918.2017.1343840
M3 - 21_Publication in refereed journal
VL - 47
SP - 2360
EP - 2377
JO - Communications in Statistics: Simulation and Computation
JF - Communications in Statistics: Simulation and Computation
SN - 0361-0918
IS - 8
ER -