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The optimal control chart procedure

Jaroslav Skřivánek — 2004


The moving average (MA) chart, the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart are the most popular schemes for detecting shifts in a relevant process parameter. Any control chart system of span k is specified by a partition of the space k into three disjoint parts. We call this partition as the control chart frame of span k . A shift in the process parameter is signalled at time t by having the vector of the last k sample characteristics fall out of the...

Bounds of general Fréchet classes

Jaroslav Skřivánek — 2012


This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fréchet classes. Algebraic search for the bounds is interpreted as a solution to a linear system of Diophantine equations. Classical analytical specification of the bounds is described.

Basic bounds of Fréchet classes

Jaroslav Skřivánek — 2014


Algebraic bounds of Fréchet classes of copulas can be derived from the fundamental attributes of the associated copulas. A minimal system of algebraic bounds and related basic bounds can be defined using properties of pointed convex polyhedral cones and their relationship with non-negative solutions of systems of linear homogeneous Diophantine equations, largely studied in Combinatorics. The basic bounds are an algebraic improving of the Fréchet-Hoeffding bounds. We provide conditions of compatibility...

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