The control chart is a fundamental tool for statistical quality, and the determination of its action limits is important for the statistical control of processes. In this paper, we consider the loss of production quality and production cost. We determine action limits which minimize the average risk on the basis of a certain loss function and prior distribution.

We give a new algorithm for nonliinear programming problems with nonlinear constraints. This algorithm belongs to gradient projection methods and is globally convergent the technique used to select projection hyperplanes plays an important role.

Consider the linear model X_ic_iβ+e_ii=1,2,…,n,where β is the parameter of the model and e_i are residuals. Suppose e_i,i=1,…,n are i. i. d. and e_i have common distribution F,where F is assumed to be absolutely continuous with known density on the interval(-a,b),a>0,b>0, and arbitrary otherwise. In this paper simultanuous estimation of β and σ is considered and under certain conditions the M-estimator of (β,σ)is proved to be asymptotically normal. Finally, the robust M-estimator of parameters (β,σ) is obtained.

Linear abstract control systems with a distributed control in Hilbert space are considered. The necessary conditions for exact controllability are obtained by using a family of associated minimization problems. These conditions are sufficient when a system has approximate controllability. Unlike time-optimal control problems, the minimwn norm. optimal control has a similar exlolicit formula if and only if the target state belongs to some subset of the reachable seat. 1n this case the family of minimizing elements of associated minimization problems converges strongly to the minimum norm optimal control. But it is illustrated that this strong convergence is not sufficient for a target state to belong to the dense subset of the reachable set even if the system has approximate controllability.

This paper generalizes Duncun's filtering equation to a class of non-Markovian processes, for which the state depends on all of the past observations. Such a generalization is important, for the stochastic control problem. The unique n ess of the solution is also shown for the heneralized filtering equation.

In this paper we propose a method for estimation of the parameters of ARMA processes by using sample autocorrelations , where m=0 (lon n)and,is tile number of the observations of ARMA process. The consistency and asymptotic normal distribution theorem of the method are established, and some simulations are given.

Let f(n,k) denote the number of k-combinations
a₁<a₂<…<a_k
of {1,2,…,n},in which no two selected numbers have unit separation, i. e.
|a_i-a_j|≠2,i,j=1,2,…,k.

In this paper, we obtain the distribution theorem for inflexion points and singular points of a cubic rational Bézier curve in an affine plane, so that the geometric shape of the curve can be controlled. To prove the theorem, the projective invariant method for the cubic parametric curve in a projective plane is used.

The composite operating characteristics function of a sampling scheme including tightened, normal and reduced plans together with an entire switching procedure involving the discontinuation of inspection, such as MIL-STD-I05D, hasn't been solved. This parper develops an expression for the expectation of the lots inspected under various plans, using the binary first transition probability generating function. As an example, we get the champ}osite OC function of MIL-STD-105D using the, expression. In addition, a general approach to determining the composite OC function of a sampling scheme with discontinuation using Markov chain is discussed.

When it is known a priori that the root of the regression,equation h(x)=0 lies ire some hounded closed set, a truncated stochastic approgimatilon algorithm for the measurement errors forming an ARMA process is suggested and the conditions guaranteeing its convergence with probability one to the root of the regression equation are given. We note that for the present algorithm the coefficient matrices of the AR.MA process may be unknown and the conditions imposed here are simpler.

Let S(t) represent the system state at the time t,P_i(t)=P_r{S(t)=i} is called the probability that the system appears in the state i at the time t. A(t) is called availability of the syseem at the time t.

In this paper we make use of the qualitative method of differential equation (1) to study a problem that occurs in the study of a triplemolecules model. We obtain the existence and uniqueness of the periodic solution of Eq. (1) and estimate the position of the periodic solution.

For the system
dx/dt=X, dy/dt=Y, dz/dt=Z,
if the functions on the right-hand side of (1) in G satisfy some conditions, then the absence of closed trajectories (or positively oriented or negatively oriented of (1) in G follows. Concrete examples are given.

Since the appearance of Rosen's gradieat projection method in 1960, a rigorous convergence proof of the method has remained an open question. A convergznce proof for the three-dimensional case is given in this paper The whole proof, except for one lemma, is applicable for the general case.A convergence condition is given in the main theorem for the general case.

In this article we prove that the Steiner minimal tree on vertices of regular n-th polygon is just the minimal spanning tree, if n>5.

Extending image sets of a point-to-set map can make the point-to-set map become one with some continuity. This paper will give sufficient and necessary conditions for those maps become closed maps with conditions of Zangwill's Theorem and similar results about Denel's pseudo-upper-continuity of p-decreasing families of point-to-set maps and also their applications.

In this paper., under the model that the main effects are additive, we obtain the universal optimality for some non-orthogonal augmented designs.

In this paper, we deal with a tvvo-dissimilar-unit parallel redundant system where life time distribution of only unit 1 is assumed to be Erlang, and the other three distributions to be general. By using the supplementary variable method, we derive the Laplace transfprms of the following quantities: 1. the clistribution of the first failure time of the system;2. the pointwise availability of the system;3. the idleness probability for the repair crew;4. the expected number of failures of the system during (0, t].

In this paper we study the existence of secondary algebraic limit cycle or algeb-raic periodic cycle for the n-order cLifferential system (Ē)_n. When n=2, Баутин^[10] has shown that there is not any limit cycle for second order system(Ē)₂,we may prove there can be no secondary algebraic periodic cycle. When n=3, we have proved the necessary and sufficient formula(17) with which (Ē)₃ must have secondary algebraic closed trajectory. Based on this, we have shown:There is no secondary algebraic limit cycle for third order differential system (Ē)₃, and if (Ē)₃ has a solution of secondary algebraic closed curve, then there will not be any limit cycle on the full plane, although there may still exist an algebraic periodic cycle. When n=4, system (Ē)₄ may present a secondary algebraic limit cycle, and we may give a form of differential system (Ē)₄, with secondary algebraic limit cycle: and judge their stability and other properties.

We consider the problem on optimality of the factor experiment design with any order interaction effects.In this paper, the term of broad optimality (B-optimality) is introduced and a sufficient condition on B-optimality is obtained. By computing the generalized inverse matrix of the information matrix for estimating main effects as well as interaction effects, the B-optimality of the orthogonal design with any order interaction effects is established. Because B-optimality implies A-, D-, E-optimality, our theorem includes the results in [1],[2] as a special case.

This paper establishes a new concept of "system of generating functions" by vector addition, by which a family of feasible direction methods is obtained. If we take some special functions as generating functions, some important methods, such as the improved Wolfe's method, Zangwill's convex simples method, Yue Min-yi and Han Ji-ye's method, etc., are obtained.

Let {X_n}_n≥1 be a sequence of independent random variables and X_n a.s. converge.

The weak dual theory for maximizaing the posynomial problem with posynomial constraints is presented by the dual theory of posynamial geometric programming. Further results than that of [3] are obtained. An algorithm for seeking Kuhn-Tucker point of this king of nonlinear programming with convergence proof is included.

since Lofstgarden and Quesenberry put forward the nearest neighbor estimation (x) of the density function f (x),a number of results have been obtained in consistency and eonvergence rates for (x).

We investigate the conversion relationship between minimally 2-edge-connected graphs and criticaally 2-edge-connected graphs, and characterize them. Furthermore, a simple way of describing the structure of critically, 2-edge-connected graphs is obtained.

Stone proposed in [1] a method of estimating the regression function,m(x)=E(Y|X=x) by combining the classical LS estimate and the nonparametric weight-function estimate and established the weak consistency of this estimate. In this article we prove the mean square consistency of this estimate under appropriate conditions. The result is of interest since the sanae conclusion is shown to be valid in the case of pure weight-function estimates.

Conjugate partitions were discussed first by R. L. Graham^[1], He posed the following problem^[1].

In this paper the existence arid uniqueness of the limit cycle of a nonlinear equation presented in [4] are studied and proved by way cycle line. The partial solution^[4] is extended to the of constructing a non-tangent-whole of the plane.

This paper disensses the stability of linear and nonlinear large-scale systems with time-varying coefficients and time lags by making use of scalar Lyapunov functions.On the one hand, the assumption in [1] and [2],which demands that for every i=1, 2,…m,A_ii (t) be a symmetric matrix, and all the eigenvalues be negative for isolated subsystems
dx_i/dt=A_ii(t)x_i
is expanded into the condition that all ei}envalues of the symmetric matrix 1/2=(A_ii(t)+A_ii^T(t)) are negative for every i=1, 2,…,m.Qn the other hand the limitations of interconnected terms, time lag and nonlinear terms are expanded. For the sake of practical adjustment.and control the relation between the three limitations is given.

In this paper,a.set of generalized Rademacher functions has been defined.Its linear-independence and completeness properties have been discussed.Based on the concepts of keeping the distances between cross-zero points equal and making the set of Rademacher functions complete,some functions are added in the decimal order according to the signs of sine and cosine functions.These generalized Rademacher functions can be orthogonized in a very simple way,and could be applied in signal analysis,synthesis and processing.

Let (X,Y),(X₁,Y₁),…,(X_n,Y_n) be R^d×R-valued i.i,d.random vectors with E|Y|<∞,Let

be the kernel estimate of m(x)= E(Y|X = x),where K is a given nonnegative kernel funotion,and h_n >0 a window width.We establish the strong consistency of m_n(x) under some mild conditions,with h_n being non-random or k-nearest neighbor window width.

In this paper,we discuss the prohlems connected with the two-stage estimate of parameters under the restricted multivariate linear model.Some finite sample properties of this estimate are found.The efficiencies of certain estimates of the regression coefficients are also given.The results are a generalization of the results of Revankar^[3].

We use J_n to denote the class of all trees with n edges,and J(J_n) the class of all graphs which contain all trees in J_n as subgraphs.

This paper studies the convergence rate of the least squares estimators â_iN to the regrescion coefficient a_j in the linear model .First we discuss the conditions for the upper limit of to be zero or finite (a.s.),when {X_(n)} is a sequence of martin;gale differences and {σ_j},{b_n} are non-random sequences.Then we discuss the convergence rate of â_iN.Particularly for {X_(n)} i.i.d.with N(0,1),we obtain the best convergence rate.

This paper is concerned with the elimination method in connection with the M×N flow-shop sequencing problem in [1] or [2].As a supplement,a rule is given,which is not,concerned with the calculation of the branch and bound type,and the calculation mentioned in [2] for the estimation formula of the branch and bound type,that is,B(S…S'),has been improved,so that we can estimate the value for B(S…S') more precisely.

A data analysis method of accelerated life testing-step-stress models under the exponential distribution case is given,anal a practical example is presented.

This paper deals with the nonparametric regression model.In Stone's paper [1],an optimal rate of convergence for nonparametric estimation in regression model is obtamed.Roughly speaking,when the regression function is p-times differentiable,the optimal rate of convergence is r=p/(2p+1).In this paper,under certain conditions,the sequence of estimators of the regression function with optimal rate of convergence is constructed and its asymptotic normality is proved.

In this paper,we propose an equalization principle of the sets of best linear unbiased estimates for estimating missing observations in the most general case.The estimate of missing observations obtained by fisher's technique is shown to be the simplest,and a unique reasonable one in some circumstances.It is also proved that there exists an estimable subspace S dependent on missing observations,so that the variance of the best linear unbiased estimate of c'β,c∈S,will be invariant ignaring the missing observations.An analogue for the prediction case,is discussed as well.

In this paper,we consider the equivalency^[1] between systems (1.1) and (1.2) in the stability problem,and a simple method for calculating the lag limit in system (1.2) is introduced.Besides,necessary and sufficient criteria for unconditional stability^[3] with respect to arbitrary lag limit for system (1.2) is given.These results improve and include several well-known results.