Design of experiments

We understand as Lye [2], the Design of Experiments (DoE) as a methodology for systematically applying statistics to experimentation. It consists of a series of tests in which purposeful changes are made to the input variables (factors) of a product or process so that one may observe and identify the reasons for these changes in the output response [3]. DoE provides a quick and cost-effective method to understand and optimize products and processes. Although these techniques are commonly found in statistics and quality literature, they are hardly used in industry.

The DOE methodology is an effective tool for upgrading the level of measurement and assessment. In any design, planning or control problem the designer is faced with many alternatives. He/she is challenged to develop design approaches that can meet both quality and cost criteria. The way experiments are designed greatly affects the effective use of the experimental resources and the easiness with which the measured results can be analyzed. This paper does not present new evi- dence based on designed experiments. Its objective is solely to show how useful application of multifactor experiments is in a variety of circumstances and decision making scenarios. The paper reviews three published examples where this method was used in different contexts: quality con- trol, flexible manufacturing systems (FMS) and logistics systems. The physical experiment has been carried out to improve the quality of a special type of batteries. The simulation experiment has been carried out to investigate the impact of several flexibility factors in a flexible manufac- turing system. The numerical value of a complex analytical expression representing a customer oriented logistics performance measure has been calculated for different values of its parameters, i.e. the given numerical values of the investigated factors. It enabled a methodical examination of all factor effects and especially their interactions, thus shedding light on complex aspects of the logistics decision problem. In these examples, cases from different contexts were presented, en- abling to view design of experiments as a powerful ingredient for improving decision making in a variety of circumstances.

For OWT analysis the Kriging surrogate models gained particular attention with the work developed in (Yang, Zhu, Lu, & Zhang, 2015) where a tripod structure is optimized supported by results from the Kriging surrogate models. In this work a Finite Element model is used to generate very accurate Design of Experiments (DoE) points and then the Kriging is used to extend the responses calculated to the full response of the system. A methodology of reliability based design optimization is then developed to optimize the support structure to extreme responses from Normal operating conditions and Seismic conditions.

Most design of experiments in agricultural applications are complex operations in nature because of numerous process variables, feed material attributes, and raw material attributes that can have significant impact on the performance of the process. Design of experiments (DOE)-based approach offers a solution to this conundrum and allows for an efficient estimation of the main effects and the interactions with minimal number of experiments. This study investigates on the most effective factors contributing in grass growth. All the factors are set in two levels to create a full-factorial 2 k design. A systematic methodology is proposed for construction of the model and for precise prediction of the responses which is lawn growth. The results indicate that water is the most significant factor that the cultivator can directly control and cheap seeds found to be suitable for the grass growth applications under consideration.

Abstract. Photovoltaic energy has, nowadays, an increased importance in electrical power applications. However, the output power provided via the photovoltaic conversion process depends on solar irradiation and temperature. Tracking the Maximum Power Point (MPP) of photovoltaic (PV) systems is the most important part of the PV systems. In this paper, modeling and parameter extraction methods are proposed to describe the optimal current, voltage and power of the photovoltaic cells. The aim is to nd a formula that considers these factors and to study the interactions between these various factors. The design of experiments is a powerful tool to understand systems and processes. Experiments are often run so that the eect of one factor is unknowingly confused with the eect of another factor. A brief comparison between classic modeling is presented. In order to model the optimal current, optimal tension and optimal power, a methodology of experimental design is presented. The obtained results show the merits of the proposed mathematical model, which makes the study of the interactions between various climatic factors possible.

Design of experiments (DOE) is a powerful technique used for discovering a set of process variables (or factors) which are most important to the process (or system) and then determine at what levels these factors must be kept to optimize the process (or system) performance [1]. It provides a quick and cost-effective method to understand and optimize any manufacturing processes. It is a direct replacement of the hit or miss approach of experimentation which requires a lot of guess work and luck for its success in real life situations. Moreover, the hit or miss approach does not take into account interactions among the factors (or variables) and therefore there is always a risk of arriving at false optimum conditions for the process under investigation.

HRON JAN, MACÁK TOMÁŠ: Application of design of experiments to welding process of food packaging. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 2013, LXI, No. 4, pp. 909–915 Design of experiments is one of the many problem-solving quality tools that can be used for various investigations such as fi nding the signifi cant factors in a process, the eff ect of each factor on the outcome, the variance in the process, troubleshooting the machine problems, screening the parameters, and modeling the processes. The objectives of the experiment in this study are two- fold. The fi rst objective is to identify the parameters of food packaging welding, which infl uence the response strength of a weld. The second objective is to identify the process parameters that aff ect the variability in the weld strength. The results of the experiment have stimulated the engineering team within the company to extend the applications of DOE in other core processes for performance improvement and variability reduction activities.

ysis when performing an experiment. This means that the trial results are indepen- dently and normally distributed random values of equal variances. In other words, the experimental results in each trial are obtained with certain probability so that the distribution of such values in each trial is subject to the normal distribution law, and variances typical for them are practically equal. The law on the distribution of experiment results is observed because, the random value is defined if its distribu- tion law is known. The stress is on the normal distribution for then the used mathe- matical model is the most efficient. The law on normal distribution of data is most frequently met in practice. The fact that some experimental results do not submit to this law is not upsetting as by mathematical transformations, given in section 1.5, such results may be brought down to the normal distribution law. Equality of ran- dom-value variances is of particular importance in experiments with a minimal number of runs or design of experiments due to their confidence level. This condi- tion is fulfilled if the variance of one trial is equal to the same variance of any other trial. This variance equality is checked by tests from section 1.5. In the case of inequality, it is solved by identical transformations, same as for the normality of data distribution. These checks may be easily performed since replication of trials is available and replicated trials are a principle of design of experiments.

A Steering Knuckle is one of the critical components of vehicle which connects brake, suspension, wheel hub and steering system to the chassis. It undergoes varying loads subjected to different circumstances, while not distressing vehicle steering performance and other desired vehicle characteristics. The knuckle is the major pivot in the steering mechanism of a car or other vehicle, free to revolve on a on single axis. The knuckle is vital component that delivers all the forces generated at the Tier to the chassis by means of the suspension system. The design of the knuckle is usually done considering the various forces acting on it which involves all the forces generated by the road reaction on the wheel when the vehicle is in motion. The design also includes various constraints that are related to the knuckle such as brake system, steering system, drive train and suspension system. Knuckle is an important part on the car, its main function is to load and steering, which support the body weight, transfer switch to withstand the front brake torque and braking torque so on. Therefore, the shape of the structure and mechanical properties knuckle, there are strict requirements. The project deals with creation of geometric model of steering knuckle (LUV) in solid works after that that model will be imported to NFX Nastran for finite element modelling where the meshing properties , element properties will be generated. Loads and model conditions applied to model there by generating .nas file that file will be submitted to solver (Nastran) and linear static structural analysis will be performed. To conduct model analysis to understand the dynamic behavior of the structure and thereby followed by transient structural response analysis. Then in the post processing analysis input and output parameters will be listed down after that Design of Experiments process will be done from that by getting response surface the results of it will be used for optimization. If it gives does not give desired results in the optimization point of view then again linear static structural analysis, model analysis and transient structural response analysis be done till we get desired results keeping input and output parameters same for every iteration under the same DOE and response surface.

this approach, a critical question that still persists is: how should one obtain a high quality initial sampling X for which the data f (X ) is acquired or generated? This challenge is typically referred to as Design of Experiments (DoE) and solutions have been proposed as early as (Fisher, 1935) that optimized agricultural experiments. Subsequently, DoE has received significant attention from researchers in different fields (Garud et al., 2017). It is also an important building block for a wide variety of machine learning applications, such as, supervised machine learning, neural network training, image reconstruction, reinforcement learning, etc. (for a detailed discussion see Section 10). In several scenarios, it has been shown that success crucially depends on the quality of the initial sampling X . Currently, a plethora of sampling solutions exist in the literature with a wide-range of assumptions and statistical guarantees; see (Garud et al., 2017; Owen, 2009) for a detailed review of related methods. Conceptually, most approaches aim to cover the sampling domain as uniformly as possible, in order to generate the so called space-filling experimental designs (Joseph, 2016) 1 . However, it is well know that uniformity alone does not necessarily lead to high performance. For example, optimal sphere packings lead to highly uniform designs, yet are well known to cause strong aliasing artifacts most easily perceived by the human visual system in many computer graphics applications. Instead, a common assumption is that a good design should balance uniformity and randomness 2 . Unfortunately, an exact definition for what should be considered a good space-filling design remains elusive.

Traditional design methodologies — based on physical prototyping of a system — are often seen expensive and time-consuming processes. In order to optimize a design process while reducing design costs, the Design of Experiments (DOE) approach is a widely advisable solution. The use of DOE technique, in conjunction with computer simulation, allows for more efficient analysis of the simulated models. In this paper, the DOE technique was introduced and evaluated. In particular, the effect of significant factors and their interaction with the objective functions of electromagnetic simulations were investigated. The use of this technique was illustrated using three case studies. The results presented in the paper demonstrated that the DOE approach has a great potential to reduce the required simulation time in all cases. In more detail, the number of factors was reduced from 5 to 2 and from 8 to 3 in the first and second cases, respectively. In the third case, the DOE was applied to a multi-objective design and optimization process related to a magnetic refrigeration system. The study showed that the application of DOE can reduce the number of simulations from 256 to 16, thereby reducing the computational cost significantly (by approximately 94%). From the results of this case study, one can analyze the influence of each parameter on each output of the multi- objective function. Since magnetic refrigeration systems involve many design parameters, it was demonstrated that the DOE technique would be very helpful in the design and optimization of such systems.

For high dimensional spaces, the central composite design is no longer practical, because the number of points increases too fast. One possible solution is to keep the 2n runs which perturb a single variable, but to have an fractional factorial design to replace the 2 n vertices. However, while the number of vertices increases as 2 n , the number of polynomial coefficients increases as (n + 1)(n + 2)/2. Consequently, the type of fractional design used has to be modified as n increases. Instead there is a block design (Matlab bbdesign), first introduced by Box and Behnken (1960), where the number of experiments increases at the same rate as the number of polynomial coefficients. The two-variable block design is based on perturbing only two variables from the nominal value. That is, at each point, we have a pair (I, j), such hat x i  1 , x j  1 , and x k  0 for

From the main effects plot which is a graph of the mean values for each factor, the influence of the factors for each product baking process can be determined. Factor A, B, and D have significant effects on the coil baking where the slope is very steep. The factor C has no significant effect on the baking and the slope is not steep. The experiments require least changes of coil thickness before and after baking. Therefore the factors that significantly affect the coil are A, B, and D and the optimal factors are A 1 , B 2 , C 1 , and D 1

These arguments are particularly apposite with respect to asymmetric factorials. The first argument has been considered in earlier chapters when dealing with the design requirements (see algorithm ENFAC). The second answers the problem with which we opened this chapter: so long as we can find the best smallest basic subdesign, then we can add any number of points we like to it. The third argument also suits us. The special shape of the region specified by our design variables, is that it must have as many dimensions as there are contrasts to be estimated and the variable represented in each of these dimensions can be set at one of only two values. This matter of coding the contrasts, and an algorithm to effect it, will be described fully in section three of this chapter. In that section I shall also present a new contribution to this field: an algorithm for choosing the best smallest basic

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interactions) may be confounded with the terms in the model. However, higher-order terms can often be assumed to be negligible compared to main effect and 2-factor interaction terms. When we created the design catalog, our goal was to only make available designs that have adequate power. As a result, we eliminated the 2-factor design with 4 runs and instead we use a replicated 4-run design for 2 factors.

Clearly, the standard similarity method could be improved with a more elaborate weighting scheme to closer approximate the concept of adaptability. However, such improvements would implicitly include the knowledge that is explicitly used in the AGR method. Furthermore, the tailoring of similarity metrics is a complex trial and error process that depends greatly on the current state of the system. Finally, as we shall see in the other experiments, it is not clear that such remedial adjustments actually result in any computational gain over AGR (see Experiment 3).

The experiments should be designed so that students can focus on relevant course concepts. This involves attempting to design the appearance of the experiments in a manner similar to how problems are presented in course learning material. It is considered that attempting to replicate „real‟ industrial style engineering systems on a laboratory scale would only serve to cloud a student‟s perception of the relationship between the theory and reality of Stress Analysis concepts. Similarly the experiments should not be designed to focus a student‟s attention on the use of automation equipment or remote access technology. As such this project aims to produce experiments which appear familiar to students and are easy to understand. The goal is to make the concepts appear as elementary and unintimidating as possible. Figure 2.2 and 2.3 are indicative of the style in which problems are presented in the course text book, Mechanics of Materials by Beer and Johnston (2009).