TY - JOUR
T1 - Simultaneously monitoring frequency and magnitude of events based on bivariate gamma distribution
AU - Cheng, Yuan
AU - Mukherjee, Amitava
AU - Xie, Min
PY - 2017/6/13
Y1 - 2017/6/13
N2 - The occurrence of an event, for example, some mishaps in manufacturing processes or natural disasters such as floods or earthquakes, is often characterized by its frequency and magnitude. Procedures for simultaneously monitoring the event frequency and the event magnitude usually assume that the frequency and magnitude are two independent variables. However, the dependence between frequency and magnitude is very common in practice. In this paper, a bivariate gamma distribution is considered for modelling the event frequency and the magnitude with certain dependence structure. Based on this bivariate gamma distribution, a multivariate exponentially weighted moving average (MEWMA) procedure is designed for jointly monitoring the shifts in mean values of the frequency and the magnitude of an event. Some comparisons are carried out via Monte-Carlo simulations. The results show that our proposed MEWMA procedure has significant performance advantages in many situations for different shift domains. A realistic example is given to illustrate the construction mechanism.
AB - The occurrence of an event, for example, some mishaps in manufacturing processes or natural disasters such as floods or earthquakes, is often characterized by its frequency and magnitude. Procedures for simultaneously monitoring the event frequency and the event magnitude usually assume that the frequency and magnitude are two independent variables. However, the dependence between frequency and magnitude is very common in practice. In this paper, a bivariate gamma distribution is considered for modelling the event frequency and the magnitude with certain dependence structure. Based on this bivariate gamma distribution, a multivariate exponentially weighted moving average (MEWMA) procedure is designed for jointly monitoring the shifts in mean values of the frequency and the magnitude of an event. Some comparisons are carried out via Monte-Carlo simulations. The results show that our proposed MEWMA procedure has significant performance advantages in many situations for different shift domains. A realistic example is given to illustrate the construction mechanism.
KW - Bivariate gamma
KW - event frequency
KW - event magnitude
KW - joint monitoring
KW - MEWMA procedure
KW - multivariate control procedure
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85011856674&origin=recordpage
U2 - 10.1080/00949655.2017.1284846
DO - 10.1080/00949655.2017.1284846
M3 - 21_Publication in refereed journal
VL - 87
SP - 1723
EP - 1741
JO - Journal of Statistical Computation and Simulation
JF - Journal of Statistical Computation and Simulation
SN - 0094-9655
IS - 9
ER -