摘要:

The Average Run Length of a Cusum chart for controlling a normal mean is calculated by solving the systems of linear equations which approximate the integral equations for the required quantities. The accuracy of approximation by this method is numerically evaluated and the results are compared with those obtained by other approximate methods. The construction and use of a new nomogram based on the contours of Average Run LengthsLa. andLrdrawn in theh√n/σ—|μ –k|√n/σ plane is discussed. Numerical examples are given to illustrate the flexibility and convenience provided by this nomogram in the design of Cusum charts.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488778

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Response surface designs are often used with a number of added center points. In such cases, when the basic design without center points is non-singular, a useful split of the lack of fit sum of squares can be effected which isolates the contribution of a contra between center and non-center points and enables additional information on possible biases to be obtained. Two general examples illustrate this, and some numerical illustrations are also provided.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488779

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

This catalogue of small incomplete factorial designs was compiled to provide designs for two- and three-level factors with 20 or fewer runs. It is assumed that the three-level factors are quantitative. The designs are suitable for estimating a selection of interactions, including the linear-by-linear components of interactions between the three-level factors. Ad hoc methods were used to construct the designs, so that there is no particular uniformity in the designs and no general property of optimality which they satisfy. Designs were selected on the basis of a measure of efficiency which is presented. No claim is made that the given designs are the best possible, and others should be encouraged to try to develop more efficient designs. A detailed example based on a real experiment is presented.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488780

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

In this paper balanced optimal fractional factorial designs of 2mseries which allow the estimation of the general mean, main effects and two factor interactions are described. Such designs are presented for eachmwith 4 ≤m≤ 6, and for a range of practical values ofN, whereNdenotes the total number of level-combinations. The covariance matrices of the estimates of the effects are also presented for each design, with a set of simple formulae for calculating these estimates.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488781

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The situation in which results are available on both components and simple systems consisting ofmidentical, but independent components in series or in parallel is considered. The cases considered are attribute testing both at single and multiple stress levels and life testing. The method of maximum likelihood is used to obtain estimates; and approximate tests of hypotheses and confidence intervals are obtained using the asymptotic variances of the maximum likelihood estimates.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488782

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Zelen and Dannemiller [8] proposed a general life distribution function using a weighted sum of Laguerre polynomials (with non-constant weights). Their results are extended here by obtaining the distribution of the ratio of two random variables having this general life distribution. This result is used to examine the robustness of the two-sample exponential likelihood ratio test for comparing means. The test is found to be markedly nonrobust.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488783

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

This paper considers the maximum likelihood estimator (m.l.e.) of the scale parameter of the exponential distribution in a life-testing situation, where the stopping rule is a prestated time. The life-test is examined periodically and the number of items that have failed since the previous inspection are counted. Approximations to the m.l.e. are considered along with their properties.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488784

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

One of the major problems in trajectory and orbital estimation is to obtain a realistic estimate of the accuracy of the trajectory and other important parameters. In the orbital case, some of the parameters which may not be solved for are geopotential constants, survey, etc. These factors will affect the total uncertainty in the orbit and, of course, ephemeris predictions. A statistical technique is described that performs a variance-covariance propagation so as to obtain accuracy estimates based on random and unmodeled errors. An example of the unmodeled error propagation is shown for the Geos B satellite.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488785

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Previously quadrature approximations were developed to determine the moments of a distribution of the response of a multivariable function when each of the variables is a random variable from a normal distribution. The error was shown to be of the order of the sixth power of the standard deviations of the random variables, but a more useful bound is desired in applied work. Only limited success has been achieved in this direction. It is shown that the best approximating distribution is a Beta distribution of the first kind with β2equal to 3 and mean, variance, and β1obtained by quadrature, where β1and β2are standard measures of skewness and kurtosis, respectively. A parametric study of the functionX=Co(ao, ±y1±y2± … ±yn)m+bowhere theyiall have the same standard deviation, σ, is conducted both analytically and by quadrature. The mean and variance obtained by quadrature are essentially exact in the range of interest. It is shown that for a large range of σ the above distribution is both a good approximation and a much better approximation than either a normal approximation with the same mean and variance or a linear approximation. The example also shows that the β2obtained by quadrature is a poor indicator of the precision of the quadrature approximation.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488786

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

An aggregate is assumed to contain particles of different types and different sizes. The problem is to determine whether or not the various types of particles are thoroughly mixed. A test for homogeneity is presented and the asymptotic distribution of the test statistic is derived.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488787

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor