Numbers of center points appropriate to blocked response surface experiments

Tables are given for the numbers of center points to be used with blocked sequential designs of composite response surface experiments as used in empirical optimum seeking. The star point radii for exact orthogonal blocking is presented. The center point options varied from a lower limit of one to an upper limit equal to the numbers proposed by Box and Hunter for approximate rotatability and uniform variance, and exact orthogonal blocking. Some operating characteristics of the proposed options are described

Response Surface Designs Robust against Nuisance Factors

This paper discusses an algorithmic approach to constructing trend-free and orthogonally-blocked response surface designs. The constructed designs have the main effects, 2-factor interactions and second-order effects being orthogonal or near-orthogonal to the nuisance factors such as the time-trend or the blocking factors. The paper also provides a catalogue of (near-) trend-free Box–Behnkens designs and orthogonally blocked Box–Behnkens designs arranged in rows and columns

Response Surface Splitplot Designs: A Literature Review

The fundamental principles of experiment design are factorization, replication, randomization, and local control of error. In many industrial experiments, however, departure from these principles is commonplace. Often in our experiments, complete randomization is not feasible because factor level settings are hard, impractical, or inconvenient to change, or the resources available to execute under homogeneous conditions are limited. These restrictions in randomization result in split-plot experiments. Also, we are often interested in fitting second-order models, which lead to second-order split-plot experiments. Although response surface methodology has experienced a phenomenal growth since its inception, second-order split-plot design has received only modest attention relative to other topics during the same period. Many graduate textbooks either ignore or only provide a relatively basic treatise of this subject. The peer-reviewed literature on second-order split-plot designs, especially with blocking, is scarce, limited in examples, and often provides limited or too general guidelines. This deficit of information leaves practitioners ill-prepared to face the many challenges associated with these types of designs. This article seeks to provide an overview of recent literature on response surface split-plot designs to help practitioners in dealing with these types of designs

A feasibility study on using inkjet technology, micropumps, and MEMs as fuel injectors for bipropellant rocket engines

Control over drop size distributions, injection rates, and geometrical distribution of fuel and oxidizer sprays in bi-propellant rocket engines has the potential to produce more efficient, more stable, less polluting rocket engines. This control also offers the potential of an engine that can be throttled, working efficiently over a wide range of output thrusts. Inkjet printing technologies, MEMS fuel atomizers, and piezoelectric injectors similar in concept to those used in diesel engines are considered for their potential to yield a new, more active injection scheme for a rocket engine. Inkjets are found to be unable to pump at sufficient pressures, and have possibly dangerous failure modes. Active injection is found to be feasible if high pressure drop along the injector plate are used. A conceptual design is presented and its basic behavior assessed

Efficiency of blocking two-stage model-robust and model-sensitive designs.

In two-stage experimentation, it is recommended that a block effect is included in the model to capture a possible shift in the mean response between the stages. In this paper, it is investigated how the inclusion of a block effect in the model affects the design and analysis of the experiment.Bias; Blocking; Design; Efficiency; Lack-of-fit; MGD-MGD two-stage designs; Model; Model-sensitive; Posterior probabilities; Weighted mean efficiency factor (WMEF);

Multiple wavemode scanning for near and far-side defect characterisation

The combination of ultrasonic inspections using different wavemodes can give more information than is available with single mode inspection. In this work, the response of shear and Rayleigh waves to surface-breaking defects propagating on the near-side and far-side of a sample is investigated. The directivity of shear waves generated by a racetrack coil electromagnetic acoustic transducer (EMAT) is identified and used to set an ideal separation for a pair of transmit-receive EMATs. Defects are indicated by a reduction in the transmitted Rayleigh wave amplitude, and by blocking of the shear wave. Used together, these can identify features in the bulk wave behaviour which are due to near-face surface-breaking defects, and give a full picture of both surfaces. By using a combination of the two wavemodes, the angle of propagation and length of any near-side defects can additionally be identified. A scanning method for samples is proposed

Optimal designs for conjoint experiments.

Design; Model-sensitive; Optimal; Optimal design; Data;

Impedance Matched Absorptive Thermal Blocking Filters

We have designed, fabricated and characterized absorptive thermal blocking filters for cryogenic microwave applications. The transmission line filter's input characteristic impedance is designed to match $50\,\Omega$ and its response has been validated from 0-to-50\,GHz. The observed return loss in the 0-to-20\,GHz design band is greater than $20\,$dB and shows graceful degradation with frequency. Design considerations and equations are provided that enable this approach to be scaled and modified for use in other applications

Optimal exact designs of experiments via Mixed Integer Nonlinear Programming

Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studyingtheir properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariablyapplicable to the particular problem only.We propose a systematic approach to construct optimal exact designs by incorporatingthe Cholesky decomposition of the Fisher Information Matrix in a Mixed Integer Nonlinear Programming formulation. Asexamples, we apply the methodology to find D- and A-optimal exact designs for linear and nonlinear models using global orlocal optimizers. Our examples include design problems with constraints on the locations or the number of replicates at theoptimal design points

The D-optimal design of blocked and split-plot experiments with mixture components.

So far, the optimal design of blocked and split-plot experiments involving mixture components has received scant attention. In this paper, an easy method to construct efficient blocked mixture experiments in the presence of fixed and/or random blocks is presented. The method can be used when qualitative variables are involved in a mixture experiment as well. It is also shown that orthogonally blocked mixture experiments are highly inefficient compared to D-optimal designs. Finally, the design of a split-plot mixture experiment with process variables is discussed.Design; Fixed and random blocks; Minimum support design; Mixture experiment; Optimal; Optimal design; Orthogonal blocking; Process variables; Processes; Qualitative variables; Split-plot experiment; Variables;