John B. Neuhardt

Effects of Correlated Sub-Samples in Statistical Process Control

Abstract This paper considers the effects of correlated data within subgroups that have been defined for the purposes of statistical process control. Such correlation may arise if the grouping is accomplished because of simplicity in data collection, such as multiple but similar measurements on a single product or multiple station machines. The effect of correlated measurements within the subgroup is shown to increase the Type I error rate for the X chart. Variance charts are shown not to be affected in the same fashion when equality of covariances of the measurements is assumed. Monte Carlo simulation is used to show similarity of the effects on the range chart when the number of measurements in the subgroup exceeds two. Several examples are given.

An Empirical Model for Automobile Driver Horizontal Curve Negotiation

Continuous recordings of test drivers on rural horizontal curves indicated that test drivers exhibited a non-linear relation in velocity and lateral acceleration at the point of maximum acceleration. A model is proposed which includes a driver aspiration velocity, maximum lateral acceleration tolerance, and an expedience parameter related to the drivers willingness to trade velocity for lateral acceleration. The model provides a good fit to different types of data which include: (1) “relaxed” drive vs. “late for appointment” scenarios; and (2) familiarity of roadway. The empirical models indicate changes in the expedience parameter and aspiration velocity.

On the Selection of Multi-Factor Experimental Arrangements with Resource Constraints

Abstract The selection of experimental arrangements with resource constraints is structured as a mathematical optimization problem: maximize experimental efficiency subject to resource constraints, maintaining an integer number of observations in each cell. Three previously published measures of efficiency are examined. It is shown that the resulting integer programs can be solved using a variation on the Lawler-Bell algorithm. Eleven examples with up to 82 binary variables are solved. These examples illustrate that the measures of efficiency are inconsistent. One, due to Wald, is recommended as superior on numerical grounds.

Computational Results in Selecting Multi-Factor Experimental Arrangements

Abstract This article investigates some theoretical and computational properties dealing with the selection of an “optimum” experiment in a constrained environment. The squared Euclidean norm of the information matrix is developed as a measure of optimality for any experimental factorial arrangement. The problem of experimental layout is structured as a mathematical optimization which can be transformed into a quadratic integer program. Computational results are given.

A Dynamic program for designing factorial experiments with budget constraints

Abstract This paper develops a dynamic programming formulation of the factorial experimental design problem with budgetary constraints. The approach is valid for any number of factors if all possible interaction terms are assumed in the model. A specific structure involving no interaction terms (additive model) is also formulated. An example is presented along with some computational results.

Selection of cost-optimal 2k−p fractional factorials

Selecting an optimal 2k−pfractional factorial is structured as a mathematical programming problem. An algorithm is defined for the solution, and the case of additive costs is shown to have a known solution for resolution III designs.

Computer-Aided Design of Fractional Factorial Experiments Given A List of Feasible Observations

Abstract When attributes of experimental units serve as independent variables, locating the units possessing the required combinations of attribute values for an experimental design can be a serious practical problem. Often, however, data sets of observable experimental units exist. A computer-aided design methodology is presented which determines which two-level factorial and orthogonal fractional factorial designs are feasible, given the data set of observable experimental units. Contrary to usual practice, the number of factors to consider is an explicit experiment planning variable in the methodology. All combinations of ten and fewer factors and 210 and fewer observations (in steps of powers of 2) are represented by a feasibility matrix. For a given set of observable experimental units, the design methodology attempts to map which cells of the matrix are feasible. Dependency relationships among feasibility matrix cells are stated which allow implicit enumeration of cells. An example taken from highwa...

On the number of 2n-p fractional factorials of resolution III

An algorithm is specified and demonstrated which will compute the total number of ways a 2n factorial design may be partitioned into 2p mutually exclusive 2n-p fractional factorial designs, each having resolution III. The results of its application to all designs possessing resolution III fractions for n=5,…,20 are also given.

Selecting Cost-Optimal Main-Effect Fractions of 3′ Factorials

Abstract The process of designing orthogonal fractions of three level factorial experiments which will estimate the main effects is reviewed. Under an assumption of heterogeneous costs of observations, a cost model is proposed which allows the engineer to determine experimental costs directly from confounding scheme decisions without being required to develop the complete fraction first. This makes it possible to explore for the minimum cost fraction more efficiently. An example application to designing fractional experiments for calibrating state highway skid measurement equipment is given.

Time-History Performance of Reference Surfaces

The paper describes briefly the construction of reference surfaces for use in skid trailer correlation at the Field Test and Evaluation Center for Eastern States and discusses in detail the performance of two of these surfaces over a nine-year period. The seasonal variation in skid number widely reported for pavement surfaces in service is clearly observed in these surfaces subjected to only test traffic. One of the surfaces having an epoxy cement overspray applied at the time of construction has retained essentially the same level of skid resistance throughout the nine years; the other, without the overspray, has experienced a continuing decrease in skid resistance. It is concluded that overspraying a surface with a wear-resistant membrane, which inhibits both loss and polishing of the surface aggregate, may result in a test pad, which will maintain its original skid number for a long period of time.