摘要:

Procedures are given for determining statistically whether the highest observation, the lowest observation, the highest and lowest observations, the two highest observations, the two lowest observations, or more of the observations in the sample are statistical outliers. Both the statistical formulae and the application of the procedures to examples are given, thus representing a rather complete treatment of tests for outliers in single samples. This paper has been prepared primarily as anexpositoryandtutorialarticle on the problem of detecting outlying observations in much experimental work. We cover only tests of significance in thii paper.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490657

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Modern computing equipment is extremely fast and can also provide graphical out-put. Prior to the computer era, problems were often formulated in terms of a single numerical criterion which could be handled conveniently on a desk calculator. Now several aspects of a problem or several criteria can be considered simultaneously and a more flexible attitude adopted. The situation then can often be easily understood by the experimenter, and compromise decisions can be made by him.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490658

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Methods of sampling an exponential population in order to obtain a prescribed accuracy in the determination of the unknown parameter are discussed. The concept of information due to Shannon is used and it leads to well known schemes.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490659

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

In many cases, data are drawn from a population which is distributed approximately normal, but with bounded, rather than infinite, domain. The traditional approach is a truncated normal, but if the population probability approaches zero at the bounds of the domain, serious errors in hypothesis testing may accompany truncation since the tails of the assumed distribution are used in error probability and critical region computation. In this paper, the truncated distribution is transformed so that the abscissa is translated to the truncation points and the curve above the new abscissa is given unit area, and then the curve is half-rectified. The result is a quasi-normal distribution with finite domain yet appearing to retain many properties of the normal. Presented is exact sampling theory, tests of hypothesis methodology, tables of associated probabilities, and illustrations from electronic reliability and oceanography.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490660

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Efficient sequential stopping rules are developed which assure fixed length lower confidence limits on lot reliability when inspection is of the rectifying type. Several models of production processes are defined and analyzed:1.A nonparametric model2.Parametric models3.Parametric models with prior distributions.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490661

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Statistical spectral analysis is much like a Model II analysis of variance in that the total variability of a data set is broken down into a number of components, the amount of variability associated with various bands of frequencies. Using the spectral density, it is possible to define a collection of what we shall call harmonic variance components. It is hoped that harmonic variance components will make the interpretation and analysis of spectra somewhat easier for those who are familiar with the ANOVA techniques, but have done little work in spectral analysis. In this paper it will be shown that an ANOVA model may be stated in terms of harmonic variance components. It will also be shown that while the variance components obtained from the ANOVA and the harmonic variance components obtained from the spectral density are not numerically equal, they may be transformed one into the other if the ANOVA assumptions are valid. The relationship between the two sets of components may be used to check on the validity of the ANOVA model.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490662

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Parzen [4] and others have noted the similarity between probability densities, spectral densities, and their sample estimates. In the familiarx2goodness-of-fit test one seeks to determine whether an observed sample distribution could reasonably have resulted from sampling some specified probability distribution. One could ask a similar question concerning the spectral density of a process. That is, could the estimated spectral density ĝ(ω) of some sampled process have reasonably resulted from a process whose true spectrum isf(ω)? Durbin [l] considers a problem of this type in testing for randomness.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490663

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

This paper is concerned with the study of time series models which are linear combinations of normal variables with zero means and variances σ2t(t= 0, ±1, ±2, …). Ifxt(t= 1, 2, …,N) is a realization of a time series, the periodogram ofX2tis employed to discover the dominant frequencies in σ2t, where σ2tis expressed in a finite Fourier series. In Part I of the paper it is proved that this periodogram is, in some sense discussed in the paper, a consistent estimator of a product of the absolute value of the Fourier coefficients and a function of the linear model coefficients; then an approximate method for estimating the Fourier coefficients separately is given.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490664

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The paper presents a stochastic model for estimation of the dimensional-errors on the surfaces machined on centerless-grinders equipped with automatic post-process gaging and reset type of feed-back control. Examples have been included to illustrate the use of the model in obtaining distributions of the controlled output (diameter of the machined surface) for different combinations of the inherent variability of the machining setup, the measurement error, the rate of tool wear, the reset magnitude, the ‘lag’, the ‘gap’ and the sample size. These distributions could be used by the designers and the users for economic comparisons whenever there is a problem of choosing one out of two or more alternative control schemes.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490665

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A computer oriented method which assists in the construction of response surface type experimental plans is described. It takes into account constraints met in practice that standard procedures do not consider explicitly. The method is a sequential one and each step covers the experimental region uniformly. Applications to well-known situations are given to demonstrate the reasonableness of the procedure. Application to a ‘messy” design situation is given to demonstrate its novelty.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490666

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor