Showing papers in "Technometrics in 1962"
TL;DR: 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.
Abstract: 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-o...
1,303 citations
TL;DR: In this paper, a procedure to estimate appropriate transformations in this context is described and illustrated, and a simple functional form in transformed variables rather than with a more complicated form in the original variables is presented.
Abstract: 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.
768 citations
TL;DR: In this paper, the main effect plans for asymmetric factorial experiments are described, which permit uncorrelated estimates of all main effects when the interactions are negligible, and the possibilities of blocking these main-effect plans, the randomization procedure and the method of analysis are presented.
Abstract: Plans for asymmetrical factorial experiments which permit uncorrelated estimates of all main effects when the interactions are negligible are described. The construction of these plans is based upon the principle of proportional frequencies of the factor levels. The possibilities of blocking these main-effect plans, the randomization procedure and the method of analysis are presented.
673 citations
TL;DR: In this paper, a method for calculating corrected sum of squares and products is presented. But this method is not suitable for counting the number of items in a set. And it is computationally difficult.
Abstract: (1962). Note on a Method for Calculating Corrected Sums of Squares and Products. Technometrics: Vol. 4, No. 3, pp. 419-420.
614 citations
TL;DR: In this paper, Satterthwaite et al. proposed a factorial factorial design in which the number of factors exceeds the number number of observations, called supersaturated factorial designs.
Abstract: 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.
331 citations
TL;DR: In this paper, a procedure for constructing plans which permit uncorrelated estimation of all main effects and some specified number of two-factor interaction effects for symmetrical factorial arrangements is developed.
Abstract: Procedures for constructing plans which permit uncorrelated estimation of all main effects and some specified number of two-factor interaction effects are developed for symmetrical factorial arrangements. These plans can then be adjusted to yield plans with similar properties for asymmetrical factorial experiments.
188 citations
TL;DR: In this paper, a number of useful tests for contingency tables and finite stationary Markov chains are presented based on the use of the notions of information theory and 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.
Abstract: 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.
162 citations
TL;DR: In this article, the authors discuss two methods for generating random vectors from a multivariate normal population with a specified variance-covariance matrix, and compare them with the two methods described in this paper.
Abstract: : The simulation of a process may require the use of sampling techniques involving the generation of random vectors from a multivariate normal population with a specified variance-covariance matrix. This is an expository paper which discusses two methods for generating such vectors. (Author)
159 citations
TL;DR: In this paper, sampling plans for truncated life tests from the normal and lognormal distributions are obtained, and the operating characteristic functions of these plans are obtained and for a wide range of values of practical interest these functions are graphed in order to facilitate selection of an appropriate plan in a given situation.
Abstract: Sampling plans for truncated life tests from the normal and lognormal distributions are obtained. The tables of this paper give the minimum sample size necessary to assure a certain mean or median life when the experiment time is tied in advance. The modification necessary to assure any other quantile (percentile) of the distributions is obtained. Thus, sampling plans for establishing other percentiles of the distributions are shown to be obtainable from the tables of this paper. The operating characteristic functions of these plans are obtained and for a wide range of values of practical interest these functions are graphed in order to facilitate selection of an appropriate plan in a given situation. Producer's risk is discussed and a table is given for the ratio of the true median life to the specified median life (or the difference between the true mean lie and the specified mean life) to insure that the producer's risk does not exceed α = .l0, .05. An approximation is given for the minimum sample size...
136 citations
TL;DR: In this paper, a technique is developed to obtain optimal accelerated life designs for estimating the parameters describing the mean lifetime of a device under a standard environment, and five examples involving variations of models and experimental design are studied.
Abstract: A technique is developed to obtain optimal accelerated life designs for estimating the parameters describing the mean lifetime of a device under a standard environment. Five examples involving variations of models and experimental design are studied. An exponential distribution of lifetimes is assumed in each of the five problems. The general approach, applyin g a method of Elfving, is applicable to a large variety of models.
120 citations
TL;DR: In this paper, a method for designing experiments with mixtures has been devised by Scheffe, where points of composition in a regular simplex are explored in accordance with a lattice arrangement, and responses are represented by simplified general polynomials.
Abstract: 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.
TL;DR: In this article, a simple technique useful in iterative model-building is described, in which a statistical analysis is applied to the estimated parameters rather than to the observations directly, which can point out the source and nature of possible inadequacies and suggest what modifications are necessary for improvement.
Abstract: A simple technique useful in iterative model-building is described. In this a statistical analysis is applied to the estimated parameters rather than to the observations directly. This mode of procedure pinpoints the source and nature of possible inadequacies and these, interacting with the experimenter's special knowledge of the problem, can suggest what modifications are necessary for improvement. The cycle may be repeated till an adequate model, which should of course be checked by additional critical experiments, is found.
TL;DR: In this paper, the authors proposed methods for estimating the number of individuals in the sample for the situation where the x i are continuous variates, the sampling random, and the probability density function f(x) known.
Abstract: In life testing observations, x 1, x 2, … x i , … x r are often recorded in time until only a fixed number r are obtained. The total number n of individuals in the sample may be unknown. Methods for estimating n are proposed for the situation where the x i are continuous variates, the sampling random, and the probability density function f(x) known.
TL;DR: A procedure for preparing probability plots for random samples from an assumed gamma distribution for any specified value of the shape parameter, η, is presented in this article, and a complete mechanization for the IBM 7090, from input to plot, is described.
Abstract: A procedure is presented for preparing probability plots for random samples from an assumed gamma distribution for any specified value of the shape parameter, η. Computational procedures for finding values of quantiles are developed, and tables of quantiles for a range of values of η[0.1(0.1)0.6(0.2)5.0(0.5)10.0(1.0)20.0] and various precentage values are presented. Also a complete mechanization for the IBM 7090, from input to plot, is described. Various examples of gamma plots are presented to illustrate the characteristics of the procedure. A number of areas of application of gamma plotting in statistical analysis are discussed, with examples.
TL;DR: In this paper, the authors surveyed the existing methods of estimating the spectrum of a stationary time series from the point of view of the user of spectral techniques, and the role of the spectral bandwidth in the design of estimates was emphasised.
Abstract: 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.
TL;DR: In this article, the two-stage group-screening procedure is extended to multiple stages for the case when responses are observed with negligible error, and a formula is developed for the expected number of runs, and for a fixed number of factors is minimized with respect to the sizes of the group factor at various stages.
Abstract: The two stage group-screening procedure is extended to multiple stages for the case when responses are observed with negligible error. Because of their potential usefulness, three and four stage procedures are treated in some detail. The general n + 1 stage procedure is defined, a formula is developed for the expected number of runs, and for a fixed number of factors is minimized with respect to the sizes of the group-factors at various stages. Finally the procedures at different stages are compared with respect to the minimum expected number of runs.
TL;DR: In this paper, a sequel of two previous papers on the subject of the Folded Normal Distribution appeared in Technometrics, S, pp. 543-550 and 551-562, (1961).
Abstract: This paper is a sequel to two previous papers on the subject of the Folded Normal Distribution appearing in Technometrics, S, pp. 543–550 and 551–562, (1961). In these earlier papers methods for estimating the parameters of the Folded Normal Distribution were proposed. Thii paper gives approximations for the standard errors for the maximum liklihood estimates of these parameters.
TL;DR: In this paper, a class of designs for the case of three factors at levels m, n and p were described for which the total number of experiments required is a fraction of mnp.
Abstract: A class of designs are described for the case of three factors at levels m, n and p respectively for which the total number of experiments required is a fraction of mnp.
TL;DR: The paper proposes that the efficiency and effectiveness of statistical simulations can be increased through the adaptation of experimentadl esign principles which exploit any qualitative knowledge surrounding the problem understudy.
Abstract: Various methods for improving the efficiency of statisticals imulation of complex systems are described and illustratedf or simple queuing situations. The paper proposes that the efficiency and effectiveness of statistical simulations can be increased throught he adaptation of experimentadl esign principles which exploit any qualitative knowledge surrounding the problem understudy. Some techniques explored are: proportional sampling fixed sequence sampling importance sampling and the use of concomitant information.
TL;DR: In this article, an exact parameter-free tolerance interval based on the first r ordered observations from a sample of size n from an exponential distribution is developed, and various criteria for goodness of tolerance intervals are examined, and certain optimum properties of these intervals are demonstrated.
Abstract: Exact parameter-free tolerance intervals based on the first r ordered observations from a sample of size n from an exponential distribution are developed. Various criteria for goodness of tolerance intervals are examined, and certain optimum properties of these intervals are demonstrated. The asymptotic behavior of these intervals is studied. Comparisons are made between these intervals and nonparametric tolerance intervals. Finally, the effect of assuming an exponential distribution, when in fact the distribution is a mixture of two exponentials, is discussed briefly.
TL;DR: In this paper, an attempt is made to formulate a specified type of "bulk sampling" as an abstract field for general study, and the problems of randomness, bias and blending are discussed.
Abstract: An attempt is made to formulate a specified type of “bulk sampling” as an abstract field for general study. Recommendations are made for definitions of terms. Populations involved are described and means are defined. The problems of randomness, bias and blending are discussed. The formulation of theoretical variance models and their use in attaining optimum sampling plans are illustrated with particular reference to fertilizer and coal. The need for large amounts of empirical research and the desirability of current controls are indicated.
TL;DR: In this article, the effect of using redundant components on the operation of systems which perform a given task repetitively is discussed, assuming that each component of the system has a constant probability of failure at every cycle.
Abstract: This paper discusses the effect of using redundant components on the operation of systems which perform a given task repetitively. It is assumed that each component of the system has a constant probability of failure at every cycle. A question which immediately arises is: “What is the probability distribution for the number of the cycle of first system failure?” The solution to this problem generalizes considerations leading to the geometric distribution. The effects of replacements on the failure cycle distribution are analyzed.
TL;DR: Cusum schemes using gauging are developed for controlling the mean and standard deviation of a normal distribution in this article, which can be easily performed automatically and is more sensitive than the Shewhart schemes using measured observations.
Abstract: Cusum schemes using gauging are developed for controlling the mean and standard deviation of a normal distribution Tables are provided The schemes for the mean are generally more sensitive than the corresponding Shewhart ones and only little less sensitive than cusum schemes using measured observations The gauging schemes can be easily performed automatically
TL;DR: In this article, the problem of estimating Poisson probabilities or relative frequencies and some extensions of that problem is considered, and the minimum variance unbiased estimators based on a simple random sample of 72 observations on a Poisson process may be easily developed.
Abstract: This paper considers the problem of estimating Poisson probabilities or relative frequencies and some extensions of that problem. It is shown how minimum variance unbiased estimators based on a simple random sample of 72 observations on a Poisson process may be easily developed. Variances of the estimators and estimators for their variances are derived. Comparisons with maximum likelihood estimators and with distribution-free relative frequency estimators are made and illustrated with two examples.
TL;DR: In this paper, the authors presented nine particular rotatable designs, given previously without explanation, together with background material, the formulae needed in order to analyze the results from such designs and a worked example.
Abstract: Recent work [10] has provided a method of constructing third order rotatable designs in three factors. This paper presents nine particular designs, given previously without explanation [11], together with background material, the formulae needed in order to analyze the results from such designs and a worked example.
TL;DR: In this article, the authors discuss a class of four factor designs in which the four factors are at m, n, p and q levels respectively, and the total number of runs is less than N = mnpq.
Abstract: This paper discusses a class of four factor designs in which the four factors are at m, n, p and q levels respectively, and in which the total number of runs is less than N = mnpq. All interactions are assumed nil.
TL;DR: This attempt to cover mathematics, discussion, probability, etc., in one classification makes it seem likely that a natural linear ordering is impossible as discussed by the authors, hence the cross-references.
Abstract: This attempt to cover mathematics, discussion, probability, etc., in one classification makes it seem likely that a natural linear ordering is impossible. Hence the cross-references. In Part 2, I have made much use of the list of ‘dishonest tricks’ in Appendix I of Ref. 3. Dr. Robert H. Thouless and English Universities Press have most generously granted permission for this classification to be published. I am also indebted to the Admiralty for permission to publish.
TL;DR: (1962).
Abstract: (1962). Studies in Applied Probability and Management Science. Technometrics: Vol. 4, No. 4, pp. 616-617.
TL;DR: In this paper, optimal sequential designs for experiments to test whether a device subjected to a standard stress has an expected lifetime exceeding a specified value are investigated for the case where the reciprocal of the expected life time is a quadratic function of stress.
Abstract: : Optimal sequential designs are investigated for experiments to test whether a device subjected to a standard stress has an expected lifetime exceeding a specified value. It is assumed that the lifetime is exponentially distributed, with expectation a function of the stress and an unknown parameter; we assume this function is known (at least for some range of stresses). At each stage of experimentation, the experimenter chooses a stress level and obtains an observation of lif time at a cost proportional to the expected lifetime, i.e., proporional to the expected length of time requir d to obtain the obser ation. This cost may make it desirable to choose a greater than standard stress and perform an accelerated test. The case where the reciprocal of the expected life time is a quadratic function of stress is given particular attention. At each stage of experimentation, the optimal design involves randomizing between at most two stress levels. (Author)