摘要:

Statisticians are increasingly finding applications which require separate linear models for a response of interest and this response's variance. A crucial question then becomes what are reasonable experimental strategies which will allow the estimation of both of these functions. This paper pursues two distinct approaches: a one-step approach which, in the absence of any information about the process variance, initially assumes that the process variance is constant over the region of interest; and a one-step, semi-Bayesian approach which attempts to develop an appropriate experimental plan in light of prior information about the nature of the variance function. These two approaches are compared in a simulation study to illuminate their relative advantages and disadvantages. An example illustrates the proposed methodology.

ISSN:0022-4065    

DOI:10.1080/00224065.1996.11979654

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

Designs for fitting first-order response surfaces over spherical regions are often constructed from the vertices of regular geometric figures. The well-known method of generating a simplex design for any number of factors gives the factors unequal, asymmetric ranges. The unequal, asymmetric ranges of the coded design factors create a problem in applying the designs: the geometric and statistical properties of the design must be distorted to give the experimental factors the desired ranges. Symmetric orientations are given for the simplex designs for 4–6, 8–10, 12, and 13 factors. In the new orientations, the simplex designs have up to six levels of the factors.

ISSN:0022-4065    

DOI:10.1080/00224065.1996.11979655

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

Parameter design does not take into account the common occurrence that some of the uncontrollable factors are observable during production. The extra information any observable uncontrollable factors provides should enhance our choice of values for the controllable factors that both keeps the mean response on target and reduces the variance. This paper describes an approach to explicitly introduce uncontrollable factors into a designed experiment.

ISSN:0022-4065    

DOI:10.1080/00224065.1996.11979656

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

One of the most popular classes of models that people fit empirically to data is the class of polynomials. One reason for this is, over limited-sized regions of interest, lower-degree polynomials (specifically, degrees 1, 2, and at most 3) have stood the test of time by proving their versatility when it comes to fitting a wide variety of different surface shapes. However, when faced with modeling a surface over an experimental region whose boundaries extend beyond some localized neighborhood or limited-sized region of interest, a polynomial of degree 2, or even of degree 3, may not be adequate. For this situation we propose fitting an interaction model which is a reduced form of a higher-degree polynomial. Several examples of actual experiments are presented to illustrate the improvement in fit by an interaction model over that of a standard polynomial, even for response surfaces with uncomplicated shapes.

ISSN:0022-4065    

DOI:10.1080/00224065.1996.11979657

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

The purpose of this article is to demonstrate how to conduct a response surface investigation concerning a linear model that contains, in addition to fixed polynomial effects, a random effect representing an extraneous source of variation. The model also contains interactions involving the random effect. Estimates of the polynomial effects are obtained in a two-stage procedure. The variance components of the random effects are first estimated by applying the method of restricted maximum likelihood. The resulting values are then used to compute generalized least-squares estimates of the polynomial effects. This procedure leads to an expression for predicting the response within a certain region of interest,R.Optima of the predicted response are determined over portions ofRin which the prediction variance falls within specified bounds. Finally, a procedure is described for establishing operating conditions that result in a predicted response close to some target value. A numerical example is given for illustrative purposes.

ISSN:0022-4065    

DOI:10.1080/00224065.1996.11979658

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

An alternative to Taguchi's robust parameter design has been recently presented. However, neither Taguchi's approach nor the alternative approach is capable of dealing satisfactorily with the frequently encountered siutations in which all the noise variables cannot be studied simultaneously. Based on the ideas from response surface modeling, linear models theory, and random effects models, we provide a method for estimation in the robust parameter design in such situations.

ISSN:0022-4065    

DOI:10.1080/00224065.1996.11979659

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

Control charts used for process monitoring traditionally take samples from the process using a fixed sampling interval (FSI) between samples. In recent years variable sampling interval (VSI) control charts have been developed. A shorter sampling interval is used if the control statistic is close to but not outside the control limits. A longer sampling interval is used if the control statistic is not close to the control limits. VSI charts are able to detect most process changes substantially faster than FSI charts. One disadvantage to VSI charts as usually formulated is that the prediction of the times at which samples will be taken cannot be done for more than the next sample. This paper considers a modification of the VSI idea in which samples are always taken at specified, equally-spaced, fixed-time points with additional samples allowed between these fixed times when indicated by the process data. The location of these fixed times typically would be determined by administrative considerations or by the requirements of the process. This variable sampling interval with fixed times (VSIFT) feature is applied to theX̄chart with and without the runs rule, to an S chart used with theX̄chart, and to the exponentially weighted moving average chart. Simple methods are given for designing VSIFT charts for practical applications. For a given average sampling rate, VSIFT charts can be designed to give faster detection of process changes than the traditional FSI charts. Alternately, VSIFT charts can provide a required level of protection against process changes with a lower sampling cost than FSI charts.

ISSN:0022-4065    

DOI:10.1080/00224065.1996.11979660

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

The Hodges-Lehmann control chart was proposed as a nonparametric alternative to the classical control chart. The proposed technique for establishing control limits produces control charts with in-control average run lengths (ARL0s) quite different from the anticipated ARL0s. In this paper two alternative methods for obtaining a Hodges-Lehmann control chart with a specific ARL0are provided. The first alternative modifies the method of constructing the control limits and the second alternative modifies the statistic plotted. A numerical example of the three control charts is provided. The alternative control charts and the control chart are compared in their robustness to changes in distributional form.

ISSN:0022-4065    

DOI:10.1080/00224065.1996.11979661

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

Process quality improvement usually can be achieved through reducing output variability and process failure rate. Traditional economic decisions about the target of process quality improvement focus on the tradeoff between investment costs and the direct benefit realized from the improved process. Given characteristics of an improved process, a scheme for statistical process control may be redesigned to have appropriate values of inspection interval, sample size, and control limits. This approach treats the determinations of the process improvement target and the control chart parameters both independently and sequentially.Through computational experiments, this research compares the cost effectiveness of simultaneous decisions on the process improvement target and on the control chart parameters to a sequential approach. The system examined is monitored with anX̄control chart. Process quality of two kinds - output variability and process failure rate - are discussed. The cost of process improvement was assumed to be a logarithmic function. The results reveal that pursuit of a lofty process improvement target can decrease total system costs.

ISSN:0022-4065    

DOI:10.1080/00224065.1996.11979662

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

Multivariate quality control problems involve the evaluation of a process based on the simultaneous behavior ofpvariables. Most multivariate quality control procedures evaluate the in-control or out-of-control condition based upon an overall statistic, like Hotelling'sT2. AlthoughT2is optimal for finding a general shift in the mean vector, it is not optimal for shifts that occur for some subset of variables, a variable at a time. When this occurs, the optimal procedure is to utilize a Finite Intersection Test (FIT). In this article we show how to use a single step and stepdown FIT to evaluate whether a multivariate process is in control or out of control.

ISSN:0022-4065    

DOI:10.1080/00224065.1996.11979663

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor