Phase II synthetic exponential charts and effect of parameter estimation

Exponential charts for monitoring time-between-events data are widely
studied recently as it has shown a wide range in different applications.
To improve the sensitivity of the simple exponential chart, this paper
develops a synthetic control chart to monitor the two-sided shifts in the
exponential mean. This synthetic chart consists of an exponential sub-chart
and a conforming run length (CRL) sub-chart and it is designed from two
new perspectives. Previous synthetic charts are constructed based on the
optimization program for a specified shift size, which proves to be difficult
to predict in practice. In this paper, the synthetic chart is constructed
based on a new design method which takes the mean (ARL) and the
standard deviation (SDRL) of the run length into consideration. The other
improvement is that the exponential sub-chart is designed to ensure that
the CRL sub-chart only needs a lower control limit and that the proposed
synthetic chart is ARL-unbiased. The effect of parameter estimation on
the proposed synthetic chart is also studied in this paper. Performance
comparisons show that our proposed chart has a better performance in
general.