This thesis gives the following contributions:1. It applies the factorial experimentation approach to design several rounds of experiments. Design of experiments (DOE) is a systematic, rigorous approach to problem-solving to ensure the generation of valid, defensible, and supportable engineering conclusions. In addition, all of these can be carried out under the constrain of minimal expenditure of engineering runs. Full factorial design creates more powerfull models than least square method and it’s extensions.2. With the improved accuracy of machine tools and surface roughness measunng devices and the increased computing power of today’s computers and software, we become able to include more parameters simultaneously with more accurate experimental data. This research discusses the computational neural networks (CNN) and mathematical model approaches for predecting surface roughness parameters (Ra, Rp, Rv, R3z, Rq and S), roundness error and straightness for specific material.The validation and comparisons with rigorous procedure are submitted to check the goodness of fit of the models developed. There are many statistics for model validation such as R2, RMSE and variance of error v(E). Numerical methods for model validation are useful, but usually to a lesser degree than graphical methods.Graphical methods have an advantage over numerical methods for model validation because it readily illustrates a broad range of complex aspects of the relationship between the observed and fitted data. Numerical methods for the model validation tend to be narrowly focused on a particular aspect ofthe relationship between the observed and the predicted. It gives a single descriptive number or test result for the intended model.3. The construction of CNN structure is a key element to success. The basic requirement for the use of a computational neural network is that a relationship exists between the proposed known inputs and unknown outputs. This relationship may be noisy. Neural network is noise tolerant. The best approach to such outliers is to identify and remove them. If outliers are difficult to detect, a block error function can be used, but this outlier-tolerant training is generally less effective.4. The neural network technique can advantageously be used in the manufacturing domain for new solutions or as an alternative of the conventional methods. It covers nearly all of the fields from the design phase, through control, monitoring, and scheduling to quality assurance.5. The neural network with two hidden layers ( 1-2-1 ) with suitable nodes are found to be the best suitable structure.6. Mathematical models are suitable in the case of small observations.7. Specified and general empirical formulae have been established for the evaluation of different parameters of surface roughness. These empirical relations are very sensitive in evaluating and predicting the different response variables under consideration. Artificial neural networks technique may be more sensitive when satisfies training.8. Although neural network is a very powerful tool to deal with complex problems, it is not appropriate for tasks with heavy noises.5.2 Future Worl{sfrom the previous analysis many future works in this field can be expectedsuch as:1. Neural network and expert systems are complementary. The weakness of expert systems are offset by the strengths of neural network and vice versa. The integration of expert systems and neural networks is therefore necessary and useful. This integration may contribute the following:- Reduced effOlt in knowledge acquisition.- New knowledge can be updated to the system automatically by presenting new examples to the neural network.- The extraction of implicit knowledge (neural network learning) is relatively easy via the help of a certain amount of explicit knowledge (rules).2. Most of the neural network applications are simulated in the conventional computers, the future step will be, the application of special very large- scale integrated (VLSI) neural chips to accelerate the computation speed of ANN.3.The construction of ANN may be improved usmg a combining of various artificial intelegent AI techniques such as expert system and fuzzy logic.4.The hybrid systems, provides the appropriate structure. In this field there are a number of possible uses. Firstly, neural networks can be used to generate the membership functions for a fuzzy system and to tune them.5. The best possible input in CNN can be selected using a genetic algorithm. The genetic controller could itself use a neural network to carry out the time-consuming task of fitness evaluation.6. Different geometric errors and micro-errors can be investigated and optimized through the mathematical model and computational neural network.