监测Lévy稳定过程均值变点的平均运行时间估计

平均运行长度(时间)(ARL)是判断一控制图监测变点效果好坏的一个重要工具.本文主要研究Lévy稳定过程的均值变点监测问题.我们给出了三个控制图,即EWMA,GEWMA和GLR的ARL估计,并通过数值模拟比较了4个控制图监测均值变点的效果和差异.     

Covering with blocks in the non-symmetric case

Considering an infinite string of i.i.d. random letters drawn from a finite alphabet we define the cover timeW _n as the number of random letters needed until each pattern of lenghtn appears at least once as a substring. Sharp weak and a.s. limit results onW _n are known in the symmetric case, i.e., when the random letters are uniformly distributed over the alphabet. In this paper we determine the limit distribution ofW _n in the nonsymmetric case asn. Generalizations in terms of point processes are also proved.Dedicated to Endre Csáki on his 60th birthday.     

A long-time tail for random walk in random scenery

Consider a simple random walk on ^d whose sites are colored black or white independently with probabilityq, resp. 1–q. Walk and coloring are independent. Letn _k be the number of steps by the walk between itskth and (k+1) th visits to a black site (i.e., the length of itskth white run), and let _k =E(n _k )–q ^–1. Our main result is a proof that (*) lim _k k ^d/2 _k = (1 –q)q ^{d/2 – 2}(d/2) ^d/2. Since it is known thatq ^{– 1} _k =E(n ₁ n _{k + 1} B) –E(n ₁ B)E(n _{k + 1} B), withB the event that the origin is black, (*) exhibits a long-time tail in the run length autocorrelation function. Numerical calculations of _k (1k100) ind=1, 2, and 3 show that there is an oscillatory behavior of _k for smallk. This damps exponentially fast, following which the power law sets in fairly rapidly. We prove that if the coloring is not independent, but is convex in the sense of FKG, then the decay of _k cannot be faster than (*).     

Screening of key odorants and anthocyanin compounds of cv. Okuzgozu (Vitis vinifera L.) red wines with a free run and pressed pomace using GC‐MS‐Olfactometry and LC‐MS‐MS

The principal purpose of the present work is to characterize the aroma, aroma‐active, and anthocyanin profiles of Okuzgozu wines and to observe the effect of the pomace pressing technique on these parameters. A total of 58 and 59 volatile compounds were identified and quantified in free‐run juice wine (FRW) and pressed pomace wine (PW). Alcohols were found as the most dominant group among aroma compounds followed by esters and acids. However, among all these compounds, only 11 and 13 of them could be considered as key odorants in aromatic extracts of FRW and PW, respectively. According to GC‐MS‐O analysis, ethyl octanoate (fruity), phenyl ethyl acetate (fruity), and 2‐phenyl ethanol (flowery) were found as the main contributors to the overall scent of both wines. Beyond the aroma profiles, anthocyanin contents of both types of wines were also investigated, and total 14 and 15 anthocyanins were identified and quantified in FRW and PW. Malvidin‐3‐glycoside and its acetyl and coumaroyl forms were identified as the dominant anthocyanins in both wines. It is worth noting the pressing application (2.0 atm) led to an increase of some unpleasant notes in the aroma providing chemical, pharmacy, and fermented aromas in wine. On the other hand, the wines produced with pressed pomace presented higher amounts of anthocyanins.     

Profile monitoring of reflow process using approximations of mixture second‐order polynomials

Lately, profile monitoring has received considerable attention in the statistical process control research field. This paper proposes a novel monitoring framework for the reflow process data, which uses two goodness‐of‐fit criteria to select the change points in the mixture polynomial model. Among change points, the mixture second‐order polynomials are utilized to piecewisely approximate the nonlinear profile data of the reflow process. The well‐known Hotelling T² and proposed EWMA₄ control charts are then employed to monitor the parameter estimates. The experimental results demonstrate that the proposed monitoring framework presents better performances in detecting outlying profiles than the conventional methods in phase I. In phase II, the performance of the proposed framework is assessed in terms of the out‐of‐control average run length. Copyright © 2014 John Wiley & Sons, Ltd.     

监测L\'{e}vy稳定过程均值变点的平均运行时间估计

平均运行长度(时间) (ARL)是判断一控制图监测变点效果好坏的一个重要工具\bd 本文主要研究L\'{e}vy 稳定过程的均值变点监测问题\bd 我们给出了三个控制图, 即EWMA, GEWMA和GLR的ARL 估计, 并通过数值模拟比较了4个控制图监测均值变点的效果和差异.     

二元序列的自相关函数和游程的一些结果

给出了二元周期序列的自相关性质与其游程性质之间的关系,作为一个应用,我们给出了周期为1 2的零自相关窗大于等于6的所有序列.     

Derivation of the probability distribution functions for succession quota random variables

The probability distribution functions (pdf's) of the sooner and later waiting time random variables (rv's) for the succession quota problem (k successes and r failures) are derived presently in the case of a binary sequence of order k. The probability generating functions (pgf's) of the above rv's are then obtained directly from their pdf's. In the case of independent Bernoulli trials, expressions for the pdf's in terms of binomial coefficients are also established.     

Approximation for counts of 2-runs in a two state Markov chain

We consider a Markov chain X = {Xi,i = 1,2,...} with the state space {0,1},and define W =∑i=1n XiXi+1,which is the number of 2-runs in X before time n + 1.In this paper,we prove that the negative binomial distribution is an appropriate approximation for LW when VarW is greater than EW.The error estimate obtained herein improves the corresponding result in previous literatures.     

Optimal production run time for a deteriorating production system under an extended inspection policy

A deteriorating production system is subjected to random deterioration from an in-control state to an out-of-control state with a general shift distribution. In order to reduce the defective items, part inspection policy, under which production inspections are performed only at the end of the production run, and full inspection policy are both considered in the literature. Moreover, the former dominates the latter. Since the product produced towards the end of a production cycle are more likely to be defective, it can further economize the inspection costs that they are directly reworked without inspection. In this paper, we propose an extended product inspection policy for a deteriorating production system. Product inspections are performed in the middle of a production cycle, and after the inspection, all products produced until the end of the production run are fully reworked. Based on the model, we show that there exists a production run time and a corresponding unique inspection policy such that the expected total cost per item per cycle is minimized. Finally, numerical examples are provided to illustrate our extended inspection policy, and indicate that such product inspection model will reduce the quality-related cost than part inspection does.