Presentation on theme: "Dual CUSUM Control Schemes for Detecting a Range of Mean Shifts Zhaojun Wang (Joint work with Yi Zhao and Fugee Tsung) Department of Statistics School."— Presentation transcript:
Dual CUSUM Control Schemes for Detecting a Range of Mean Shifts Zhaojun Wang (Joint work with Yi Zhao and Fugee Tsung) Department of Statistics School of Mathematical Sciences Nankai University firstname.lastname@example.org
Problems: How to detect the interval shifts? What Criteria to be used? How about the above charts? Any new good charts?
Background and Motivation (Cont'd) Lorden (1971) firstly provides a control scheme could be used to detect the interval shifts, but it is difficult to apply in practice and its performance is difficult to obtain due to great computational complexity.
Conclusion and Consideration As the range of the shifts or the value of ARL 0 increases, the superiority of DCUSUM schemes increases. But, for small range shifts, the CUSUM performs better than the DCUSUM as shown in Table 1. In Table 2, it’s found that there is no much difference between M3 and Q4 design, Q2 (single CUSUM) is worse than Q4 and M3 (but M3 is hard to compute). In Table 3, we also compare Q4 designs in range [0.25,3], and [0.25,5]. (almost same)
Conclusion and Consideration (Cont'd) In Figure 3, we observed that the performance of Q4 scheme is comparable to the optimal CUSUM design for most of the shifts between 0.25 and 3, except that for some very small shifts. DCUSUM schemes overall have superior performance when compared with the Shewhart-CUSUM counterparts in terms of IRARL for small and medium shift ranges.