摘要:

A technique for empirical optimisation is presented in which a sequence of experimental designs each in the form of a regular or irregular simplex is used, each simplex having all vertices but one in common with the preceding simplex, and being completed by one new point. Reasons for the choice of design are outlined, and a formal procedure given. The performance of the technique in the presence and absence of error is studied and it is shown (a) that in the presence of error the rate of advance is inversely proportional to the error standard deviation, so that replication of observations is not beneficial, and (b) that the “efficiency” of the technique appears to increase in direct proportion to the number of factors investigated. It is also noted that, since the direction of movement from each simplex is dependent solely on the ranking of the observations, the technique may be used even in circumstances when a response cannot be quantitatively assessed. Attention is drawn to the ease with which second-order designs having the minimum number of experimental points may be derived from a regular simplex, and a fitting procedure which avoids a direct matrix inversion is suggested. In a brief appendix one or two new rotatable designs derivable from a simplex are noted.

ISSN:0040-1706    

DOI:10.1080/00401706.1962.10490033

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

A new method for designing experiments with mixtures has been devised by Scheffe. The fractions of components making up any mixture must add to unity, and hence factor space may be represented by a regular simplex. Points of composition in this simplex are explored in accordance with a lattice arrangement, and responses are represented by simplified general polynomials. These polynomials have been extended to include the quartic. A numerical example shows how the method has been applied to estimation of octane numbers for a ternary gasoline system. Using the method makes possible estimates of the properties of an entire system from a limited number of observations. The method should prove useful for any multicomponent system where intensive properties are to be related to composition and where the behavior of the properties is not so erratic as to preclude satisfactory approximation by low order polynomials.

ISSN:0040-1706    

DOI:10.1080/00401706.1962.10490034

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

Supersaturated designs are factorial designs in which the number of factors exceeds the number of observations. Satterthwaite has suggested constructing such designs by a randomization procedure (random balance designs). In the present paper systematic designs are constructed which are, in a certain sense, m nearly orthogonal M possible. Examples of such designs are given constructed on an electronic computer and some properties of the designs are discussed.

ISSN:0040-1706    

DOI:10.1080/00401706.1962.10490035

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

Explicit asymptotic formulas for sample size as function of lot size and for accepe ante number as function of sample size are derived for the Dodge-Romig LTPD single sampling inspection plans. Numerical investigations show that a simple finite population correction of the asymptotic formulas leads to a good approximation to the Dodge-Romig solution. Tables and graphs are provided for the asymptotic solution. Asymptotic formulas are also given for the producers risk and for the minimum amount of inspection for lots of process average quality. The main results are that sample size asymptotically is proportional to the logarithm of lot size and that the highest allowable fraction defective in the sample converges to the tolerance fraction defective, the difference being of order 1/√n.

ISSN:0040-1706    

DOI:10.1080/00401706.1962.10490036

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

The military, and many civilian organizations, require that a sufficient supply of materials be in storage at any one time to meet certain emergency needs that may arise. However, the deterioration of these materials in storage may render them unusable. It is therefore essential that a systematic program for the surveillance of such stored items be maintained in order to insure that the supply of usable items is always adequate.

ISSN:0040-1706    

DOI:10.1080/00401706.1962.10490037

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

In representing a realationship between a response and a number of independent variables, it is preferable when possible to work with a simple functional form in transformed variables rather than with a more complicated form in the original variables. This paper describes and illustrates a procedure to estimate appropriate transformations in this context.

ISSN:0040-1706    

DOI:10.1080/00401706.1962.10490038

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

The existing methods of estimating the spectrum of a stationary time series are surveyed from the point of view of the user of spectral techniques, and the role of the spectral bandwidth in the design of estimates is emphasised. A discussion on the construction of “optimum” estimates is included, and a note is added on the effect of transients on estimates obtained by means of filters.

ISSN:0040-1706    

DOI:10.1080/00401706.1962.10490039

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

Gamma ray spectroscopy has become, during the past several years, a widely used technique for the assaying of a mixture of gamma-emitting radionuclides with minimum sample alteration. As a result, considerable savings in time and labor have been achieved due to the reduction of the number of samples requiring extensive radiochemical analysis. The purpose of this paper is to present an optimal method of estimating the amount of each radionuclide present in a mixture when certain conditions are satisfied.

ISSN:0040-1706    

DOI:10.1080/00401706.1962.10490040

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

A number of useful tests for contingency tables and finite stationary Markov chains are presented in this paper based on the use of the notions of information theory. A consistent and simple approach is used in developing the various test procedures and the results are given in the form of analysis-of-information tables. Beginning with tests of hypotheses for a one-way table, tests of hypotheses of specified probabilities, independence, conditional independence, homogeneity of classifications, and symmetry are developed for contingency tables of two, three, four, and higher order classihcations. For the Markov chains, the tests include the hypotheses of a specified matrix of transition probabilities, Markovity, and homogeneity of several realizations of Markov chains. Worked examples are given throughout the paper.

ISSN:0040-1706    

DOI:10.1080/00401706.1962.10490041

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1962.10490042

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor