BUKU ABSTRAK - Universiti Putra Malaysia

Solution of an Infinite System of Differential Equations
Keywords: Differential equation, infinite system, Hilbert space, solution
Robust Individuals Control Chart using a Change Point Formulation
Assoc. Prof. Dr. Habshah Midi
Ng Kooi Huat
Institute of Mathematical Research, University Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
+603-8946 6876; habshahmidi@gmail.com
193
Science, Technology & Engineering
Assoc. Prof. Dr. Gafurjan Ibragimov
Fateh Abdo Ali Allahabi
Faculty of Science, University Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
+603-8946 6818; gafur@science.upm.edu.my
Some of the control problems for parabolic and hyperbolic partial differential equations can be reduced to
the control problems described by infinite systems of ordinary differential equations by using the decomposition
method. It is natural that the solution space of this infinite system is closely connected with the differential
operator in the parabolic or hyperbolic equation. In this paper, we study an infinite system of differential equations
of second order in one frame separately from the partial differential equations mentioned above. At the same
time, the system we considered largely extends the system obtained from partial differential equation. We prove
the existence and uniqueness theorem in a Hilbert space. In addition, we establish continuity of the solution in
the norm of that space. The proved theorem enables the investigation of an optimal control and differential game
problems described by such a system.
Control charts are one of the most powerful tools used to detect aberrant behaviour in industrial process. In
addition to their uses in the context of statistical process control, control charts are also used as an exploratory
tool in the context of exploratory data analysis. In view of monitoring a process that has contaminated data with
traditional control charts such as Shewhart chart and Range chart, results in excessive number of false alarms.
Robust control chart is a better alternative to traditional charts for a process with contaminated data as the effects
of the outlying data values are eliminated. In this article, we develop a control charting procedure that meets the
needs of exploratory analysis and has its purpose of detection the assignable causes of variation by revealing
evidence of variation sources. The proposed methodology is demonstrated with a real-life example. A numerical
example was given and a simulation study was conducted to illustrate the performance of the proposed method.
Keywords: Contamination, control charting, statistical process control, in-control, out-of-control, outlier, robust estimation,
Shewhart chart