Transient detailed balance and product form for reaction networks

This paper explores the boundary of the set of reaction networks that have an exact transient (truncated) multidimensional Poisson or product-form distribution for the number of particles of different types. Motivated by the birth–death process, we introduce the notions of transient detailed balance and delay functions, and use these notions to obtain the novel transient product-form distribution in a coagulation-fragmentation process for polymers with a tree-like structure from that of the pure coagulation process.     

An asymptotic confidence interval for the process capability index Cpm

Abstract

The use of indices as an estimation tool of process capability is long-established among the statistical quality professionals. Numerous capability indices have been proposed in last few years. C_pm constitutes one of the most widely used capability indices and its estimation has attracted much interest. In this paper, we propose a new method for constructing an approximate confidence interval for the index C_pm. The proposed method is based on the asymptotic distribution of the index C_pm obtained by the Delta Method. Under some regularity conditions, the distribution of an estimator of the process capability index C_pm is asymptotically normal.     

The robust economic statistical design of the Hotelling's T2 chart

ABSTRACT

Economic statistical designs aim at minimizing the cost of process monitoring when a specific scenario or a set of estimated process and cost parameters is given. But, in practice the process may be affected by more than one scenario which may lead to severe cost penalties if the wrong design is used. Here, we investigate the robust economic statistical design (RESD) of the T² chart in an attempt to reduce these cost penalties when there are multiple scenarios. Our method is to employ the genetic algorithm (GA) optimization method to minimize the total expected monitoring cost across all distinct scenarios. We illustrate the effectiveness of the method using two numerical examples. Simulation studies indicate that robust economic statistical designs should be encouraged in practice.     

Optimal design of complex experiments with qualitative factors of influence

A complex experiment with qualirarive factors influencing the outcome of the experiment can be seen as a general ANOVA setup. A design of such an experiment will be the assignment at which of the possible levels of the factors the actual experiment should be performed. In this paper optimal designs of such experiments will be characterized with respect to three different optimality criteria including the so called uniform optimality of a design. The possible applications of the main optimization result providing these characterizations can be used to more general experiments. The particular results on these generalizations will be indicated at the end of this paper.     

The occurrence of fingerprint characteristics as a two-dimensional poisson process

The individuality of n fingerprint is based on the configuration of occurences of the ten Galton characteristics ( ridge endings, forks, etc. ). A model ( Osterburg, Parthasarthy, Raghavan, Sclove, 1977 ) for the occurence of these characteristics, in terms of a grid of cells, is further developed. The occurence of the characteristics is modelled as a two-dimensional multivariate Poisson process. This approach allows one to treat multiple occurrences in a more satisfying way than in Osterburg, Parthasarathy, Raghavan and Sclove ( 1977 ) or Sclove ( 1978 )     

A time series approach to life table construction

This paper deals with the construction of the life table. A discussion of basic facts about the life table is followed by the proposal of a nonstationary, autoregressive model for the life table. The moment structure of the nonstationary, autoregressive model is developed. Some estimation procedures are proposed followed by several examples.     

On the recovery of intra- and interblock information in n-ary designs

This note presents an extension of Q-method of analysis for binary designs given by Rao (1956) to n-ary balanced and partially balanced block designs. Here a linked n-ary block (LNB) design is defined as the dual of balanced n-ary (BN) design. Having a note on Yates’ (1939, 1940) method of P-analysis, we further extend the expressions for binary linked block (LB) designs given by Rao (1956) to linked n-ary block (LNB) designs which admit easy estimation of parameters for these type of all n-ary designs.     

Effect of systematic sampling on arima models

Given a general homogeneous non-stationary autoregressive integrated moving average process ARIMA(p,d,q), the corresponding model for the subseries obtained by a systematic sampling is derived. The article then shows that the sampled subseries approaches approximately to an integrated moving average process IMA(d,l), l≤(d-l), regardless of the autoregressive and moving average structures in the original series. In particular, the sampled subseries from an ARIMA (p,l,q) process approaches approximately to a simple random walk model.     

Use of balanced bipartite weighing designs as chemical balance designs

This paper deals with the use of balanced bipartite weighing designs as chemical balance designs when there Is a restriction on the number of objects that can be placed on either pan..The variance of each estimated weight and the covarlance of each pair of estimated weights are worked out.The use of additional weighing when the design matrix is singular is discussed.     

The mad estimator: when is it non-linear? applications to two-way design models

The mean absolute deviation (MAD) estimator has recently received a great deal of attention as applied to full-rank linear regression models. This paper provides a necessary and sufficient condition for the MAD estimator to be a non-linear estimator, in which case conditions for the variance of the MAD estimator to be larger or smaller than those for OLS are, in general, unknown. The non-linearity of the MAD estimator is examined for several two-way designs; in particular (1) randomized block design (2) two-way nested design (3) two-way classification with interaction and (4) partially balanced incomplete block design