Shujin Wu

A One-Sided EWMA Control Chart for Monitoring Process Means

Great efforts have been devoted to two-sided exponentially weighted moving average (EWMA) control charts, while less attention has been paid to one-sided EWMA charts. This article proposes an improved one-sided EWMA chart (IEWMA) for rapid detection of upward or downward changes in the process mean. The basic idea is to accumulate positive (or negative) observations only and reset negative (or positive) observations to zero in the iterative computation of the EWMA estimate for the purpose of quickly catching the upward (or downward) change in the process mean. The comparison result of the IEWMA chart with other control charts favors the former.

p-Moment stability of stochastic differential equations with jumps

In the paper, p-moment stability of stochastic differential equations with jumps is considered. First, some preliminary notes are given. Then, several theorems on p-moment stability of these equations are established using Liapunov function. At last, an example is present to show application of the obtained results.

p-Moment stability of functional differential equations with random impulses

By means of Liapunovs direct method coupled with Razumikhin technique some sufficient conditions for (uniform, uniform and globally asymptotic, uniformly globally asymptotic, and globally exponential) p-moment stability of the zero solution of functional differential equations with random impulses are presented, where the parameter @l(t) in (dV(t, x(t)))/dt is not required to be negative definite. Thus the obtained results are convenient to apply.

The Euler scheme for random impulsive differential equations

Random impulsive differential equations (RIDEs) are a kind of mathematical models with extensive applications. In this paper, the Euler scheme for RIDEs is first brought forward, one of whose important applications is to generate the whole approximate trajectories of RIDEs. Thus the proposed Euler scheme allows us to approximate moments, functionals and the distribution for the underlying process and perform Monte-Carlo type analysis. The obtained results show that the Euler scheme is at least 1-order of step h when the right terms of equation satisfy Lipschitz conditions and the waiting times of random impulses follow the mutually independent exponential distribution with the same parameter λ. Thus it is an efficient method for numerical simulation.