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In the paper, Poisson-Gamma mixture process is first brought forward, which is dynamically expanded from the well-known Poisson-Gamma mixture model. Some properties on Poisson-Gamma mixture process are presented, including the distribution of increment, Markov property, infinitesimal generator, joint density function of jump/waiting times, and the limit distribution of compound Poisson-Gamma mixture process, etc., which provide a thorough grounding in application of Poisson-Gamma mixture process. At last, some premium calculation principles are presented to show the application of Poisson-Gamma mixture process, which include expected value premium, stop-loss premium, mean-variance premium, and exponential premium. [ABSTRACT FROM AUTHOR]

Great efforts have been devoted to two-sided exponentially weighted moving average (EWMA) control charts, while less attention has been paid to one-sided EWMA charts. This article proposes an improved one-sided EWMA chart (IEWMA) for rapid detection of upward or downward changes in the process mean. The basic idea is to accumulate positive (or negative) observations only and reset negative (or positive) observations to zero in the iterative computation of the EWMA estimate for the purpose of quickly catching the upward (or downward) change in the process mean. The comparison result of the IEWMA chart with other control charts favors the former. [ABSTRACT FROM AUTHOR]