An Algorithm for the Economic Design of <Emphasis Type="Italic">np</Emphasis> Charts for a Multiplicity of Assignable Causes

Chiu, in 1976, studied the economic design of np charts for processes subject to a multiplicity of assignable causes. Chiu developed a two-step minimization procedure to obtain the three control variables, namely, the sampling interval, the sample size and the acceptance number. Although Chiu's two-step minimization procedure is simple, applicable and down to earth, it is rather inefficient and has some drawbacks. This paper presents an algorithm to overcome these drawbacks. The results and the execution times of all numerical examples show that the accuracy and the efficiency of the algorithm is reasonably good.     

Nonexistence and symmetry theorems for elliptic systems in R N

In this paper we study Liuoville type results for the system of elliptic equations $$ - \Delta u = F(u) u \geqslant 0, u \ne 0 in R^N ,$$ when the function $F:\bar R_ + ^m \to \bar R_ + ^m $ is regular, quasi-monotone, fully coupled and has suberitical growth. WhenF has a radial dependence on the space variable we also prove symmetry results. The nonexistence theorems of the nature studied here have consequences on existence results on bounded domains, through the blow-up technique and degree theory. Our results are proved using the moving planes method.