ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490704

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Factorial designs of resolution III are such that all main effects are estimable, ignoring two-factor interactions and all higher order interactions. Designs of resolution IV are such that all main effects are estimable with no two-factor interactions as aliases, ignoring all higher order interactions. The general technique for producing 2ndesigns of resolution IV is a specific application of the Box-Wilson “fold-over” theorem. Recent work by Steve Webb on resolution IV designs for two-level factors is discussed and extended. The miniium run requirement for a 2nresolution IV design is 2n. It is proved that if a minimal resolution IV 2ndesign has each factor occurring equally often at its high and low levels, then the design must be a fold-over design. A proof that the minimum run requirement for a resolution IV 2n3mdesign,m> 0, is 3(n+ 2m− 1) also is included. Minimal 2nresolution IV designs are presented for various values ofn. All these designs can be run innblocks of size 2 each.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490705

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The problems of estimation and testing hypotheses regarding the parameters in the Weibull distribution are considered in this paper. The following results are given:1.Exact confidence intervals for the parameters based upon maximum likelihood estimators are presented.2.A table of unbiasing factors (depending upon sample size) for the maximum likelihood estimator of the shape parameter is given.3.Tests of hypotheses regarding the parameters and the power of the test regarding the shape parameter are developed and presented.4.Sample sizes at which large sample theory may be useful are presented.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490706

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Response surface estimators are obtained which first minimize integrated squared bias. The bias is due to specified higher order terms which may be in the model but are omitted from the fitted equation. The estimator, subject to achieving this minimum bias, minimizes the integrated variance; integration for both bias and variance being over a specified region of interest. Since the minimum integrated squared bias is attained for any design, other criteria may be satisfied by choice of design. One form of design flexibility which can be achieved is the minimization of the integrated variance of the fitted equation by choice of design. Illustrations of the application of this criterion are given for certain simple model and design settings.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490707

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490708

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

This paper presents a series of operators for ANOVA (analysis of variance) calculations by regression methods. The operators, named CøDE, RøV, MøDEL, SCP, DECøMP, PATTER, SWP, and BAKSøL, are intended to be a subset of building blocks for a computing system to perform analyses of variance. The determination of parameter aliases during computation has been shown to be an important advantage of the regression approach. The regression approach has been made more feasible for balanced experimental designs by making use of structure in the balanced case in order to use mschine store efficiency. A compact model specification method has been developed which is based on three algebraic relations, + (ØR), * (CRØSS), and ← (NEST), between factors. Careful attention has been given to numerical questions. The operators are easily exported between computers with compatible FORTRAN IV facilities.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490709

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The performance of three rules for dealing with outliers in small samples of sizenfrom the normal distributionN(μ, σ2) are investigated when the primary objective of sampling is to obtain an accurate estimate of μ. It is assumed that at most one observation in the sample may be biased, arising from eitherN(μ +aσ, σ2) orN(r, (1 + b)σ2). Performance of each rule is measured in terms of “Protection”, the fractional decrease in the Mean Square Error (MSE) obtained by using the rule when a biased observation actually is present in the sample. Although numerical results have been obtained forn≤ 10 when σ2is known, computational difficulties have prevented evaluation of protections when σ2is unknown except whenn= 3.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490710

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A compartmental model is presented for tracer experiments with a fixed and known amount of tracer material which is injected initially into a single compartment and accumulates in another compartment. The model could also arise as a description of chemical reactions. The model is represented as a system of linear combinations of exponentials with common exponential parameters. Then a simultaneous estimation procedure, which is a generalization of the Spearman estimation procedure presented by Johnson and Brown [7] for a single equation, is developed for this model under the assumption that the values of the independent variable in the model are equally spaced on a logarithmic scale. Asymptotic properties of the estimation procedure are investigated and an example is given.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490711

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

At first glance the subject-matter of this paper may appear to be rather trivial. No questions of offense or defense strategies are involved; one is interested solely in calculating the probability that a point target is destroyed by one or more weapons in a salvo. If the target, has an extended area, the probability of destruction is replaced by the expected fraction of the target destroyed. One might reasonably conclude that a few simple mathematical arguments involving independent random events are all that is required.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490712

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490713

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor