The Nature And Data Analysis Of Conditional Sequential Design

Experimentation is one of the most common activities of human beings.It involves all aspects of scientific research,production and life.The experimenter can compare the effects of different states of the system affected by changing the settings(levels)of the input variables(factors,components)in a system to achieve goal of t he optimal selection of factor levels.The experimental design is an integration of relevant knowledge and technology,which allows the experimenter to implment the experiment more reasonably,analyze the data effectively and establish the relationship between the analytical results and the research purposes.The order of addition of components may have an effect on the results of the experiment.The experiment in which the order of addition of components affects the experiment results is called an order of addition experiment.The scope of the application of the order of addition experiment is very wide,ranging from the preparation of food in the family,to the research on the new missile in the national defense technology.The purpose of the experiment is to find the optimal factor addition sequence,thereby improving production efficiency or optimizing the test,results.The literature introduces methods for studying the order of addition experiment,such as the models of the order of addition experiment given in Van Nostrand(1995)and Mee(2017)and the ordered orthogonal array in Voelkel(2019).These methods are proposed to make us have a deeper understanding about order of addition experiment.However,the order of addition of components is limited in many cases.These limits may be empirically obtained or necessary to prevent the risk of testing.For example,in the test of concentrated sulfuric acid and water,water must be added first and then concentrated sulfuric acid,or the water will boil and splash.This article is based on the order of addition experiment to study the restricted order of addition experiment,that is,the conditional order of addition experiment.Voelkel(2019)proposed and introduced the conditional order of addition experiment.The definition of the conditional main effect of the pair-wise ordering(PWO)factor is defined.This definition is similar to the definition of the conditional main effect.It can be obtained by calculating the difference between the average of all observations at high levels and the average of all observations at low levels.we use the definition of the conditional main effect of the PWO factor to study the orthogonality of conditional the main effect of the PHO factor and the D-efficiency.When studying the orthogonality,the relationship between the root effect and interaction effects of the conditional main effect of the PWO factor divides the PWO factor conditional main effect into four categories,and the orthogonality can be obtained by calculating the inner product of two elements in the class separately.The relationship between the multi-conditional main effect and the conditional main effect of the PWO factor is found and conditional order of addition model is constructed using this properties.Finally;the conditional addition model is analyzed by two examples.