摘要:

Three-component mixture experiments are very common. Reasons for their popularity are: (i) ease in selecting the component combinations to run experiments on, (ii) ease in fitting empirical models to the data collected, as well as interpreting the coefficients in the fitted models, and (iii) ease in displaying the surface shape characteristics of the particular response of interest by plotting surface contours or the response surface itself. In this paper we discuss the selection of a design for a three-component mixture experiment (reason (i) above). Two ten-point design arrangements are suggested. One is the {3, 3} simplex-lattice arrangement consisting of nine points equi-spaced on the perimeter of the triangular composition space with one point at the centroid, while the other design is the simplex-centroid design augmented with three interior points. The two design patterns are compared using the properties (variance and bias) of fitted mixture models, starting with the Schefféfirst-degree model and building up to the special cubic model. As anticipated, if the shape of the response surface is best described by the use of quadratic or cubic terms in the model involving pairs of components, then the {3, 3} simplex-lattice is preferable. On the other hand, if the shape of the response surface inside the triangle (the response to complete blends) is vastly different from the shape of the surface near the boundaries of the triangle, higher degree terms such asβ123x1x2x3orγ1223x1x22x3are needed in the model, and the augmented simplex-centroid design must be used. Data from an artificial sweetener experiment are used to illustrate the differences between the types of response surfaces just mentioned, and summary recommendations are made for selecting one design over the other for particular mixture systems.

ISSN:0022-4065    

DOI:10.1080/00224065.1986.11978980

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

Methods are described by which it can be judged from a sample of measurements whether the population from which the sample was drawn is distributed acceptably tightly about the population mean. The decision is generally based on the value of the sample coefficient of variation. The assumptions made make these methods particularly applicable to the evaluation of content uniformity for mixtures prepared in closed containers.

ISSN:0022-4065    

DOI:10.1080/00224065.1986.11978981

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

A procedure for controllingαprocess mean to a target midway between two specified values is presented. It is assumed that the process variable has a normal distribution with unknown mean and variance, and that the data consists solely of counts of the number of observations in a sample which are above, below, and between specified gauge values. Charts are given for conveniently accomplishing the test and for estimating the amount of adjustment needed. Finally, the choice of gauge limits is discussed and comparisons are made with variables procedures.

ISSN:0022-4065    

DOI:10.1080/00224065.1986.11978982

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

When test measurements of items differ from the true product values because of random measurement error it is possible to reject satisfactory items and to accept inferior ones. Confidence bounds for these misclassification probabilities are obtained, assuming that the true product values and measurement errors are independently distributed normal variates. Both joint and conditional probabilities are investigated. These probabilities are functions of the proportion of measurement error variability (relative to the total variance). Methods are presented for situations where this proportion is known or is estimated from sample data. Tables are provided to simplify the computations required.

ISSN:0022-4065    

DOI:10.1080/00224065.1986.11978983

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

The capability indicesCp, CPU, CPL, kandCpkare presented and related to process parameters. These indices are shown to form a complementary system of measures of process performance, and can be used with bilateral and unilateral tolerances, with or without target values. A number of Japanese industries currently use the five indices and the U.S. automotive industry has started using these measures in a number of areas. Various applications of the indices are discussed along with statistical sampling considerations.

ISSN:0022-4065    

DOI:10.1080/00224065.1986.11978984

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

A modification of moment estimators for parameters of the three-parameter gamma distribution, in which the third moment is replaced with a function of the first order statistic is presented in this article. Calculations are made easy with the aid of accompanying charts and tables. The modified moment estimators enjoy advantages over the traditional moment and maximum likelihood estimators with respect to both estimate bias and variance. Unlike the maximum likelihood estimators, which break down in the presence of a high degree of skewness and which often lead to computational difficulties when samples are small, the modified moment estimators exist and are easy to calculate for all possible parameter values even when samples are small. Two illustrative examples are included. Also included are results of a simulation study in which sampling behavior of the modified moment estimators is compared with that of moment and maximum likelihood estimators.

ISSN:0022-4065    

DOI:10.1080/00224065.1986.11978985

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

It is generally recognized that acceptance sampling by attributes is an important tool for industrial quality control. Various models have been proposed that can be used to determine a sampling plan. Some of these, including the one discussed in this paper, incorporate costs. The plan described here minimizes the maximum cost subject to an appropriately chosen constraint. A basic assumption used is that one knows the probability that the number of nonconforming items in a lot does not exceed“break even”quality. Plans are easily found with a computer.

ISSN:0022-4065    

DOI:10.1080/00224065.1986.11978986

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

A program is presented that finds the binomial double sampling plan satisfying:P(p1)≥1–αP(p2)≤βwhile minimizingw0ASN(p0) +w1ASN(p1) +w2ASN(p2). HereP(p) is the probability of accepting a lot with fraction nonconformingp, and ASN(p) is the average number sampled per lot for a series of lots with fraction nonconformingp.Values ofp0,p1,p2,α,β, w0, andw1are specified by the user (w2= 1–w0–w1). This program provides an exact solution for the binomial distribution that does not require any restrictions on the five parameters describing a double sampling plan. Using this program, it is possible to obtain double sampling plans that are more efficient than those currently in use. An example is given showing that double sampling plans may be selected that are as efficient as the multiple sampling plans in Mil-Std-105D.

ISSN:0022-4065    

DOI:10.1080/00224065.1986.11978987

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

ISSN:0022-4065    

DOI:10.1080/00224065.1986.11978988

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

ISSN:0022-4065    

DOI:10.1080/00224065.1986.11978989

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor