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                Department of Mathematical Sciences                       
                   The Johns Hopkins University                           
                                                                        
                              SEMINAR                                
                                                                        
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Jiayang Sun                                       October 26, 2000
Department of Statistics                          304 Whitehead Hall
Case Western Reserve University                   Preseminar: 3:00 p.m.
                                                  Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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     A NEW JOINT CONTROL CHART: JOINT BEHAVIOR OF AVERAGE AND
                    MAXIMUM OF A GENERAL PROCESS

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                             ABSTRACT

Quality control is widely used in industries to monitor the quality of
products in a manufacturing process.  The Shewhart chart and its variants
are more effective in detecting a large mean shift, while CUSUM charts are
more effective in detecting a small mean shift.  We propose a new joint
control chart that combines the merits of Shewhart and CUSUM charts and
that can deal with general processes.  A process here can be correlated
(stationary or nonstationary) and in high dimension.  Simulations,
animations, and applications will be demonstrated/discussed.

The problem mentioned above is related to the joint distribution of
mean-max (average and maximum) of a continuous-time process, and to the
joint distribution of max-max (maxima of the process and the average
process up to time  t) of the process.  Based on a cute geometric
argument, we present general approximations to such joint distributions,
which are of interest themselves.

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