In my opinion, the statistical optimization methods are generally beneficial with decreasing the number of the needed physical experiments, which have to be carried out, to reveal the nature of influence of the participating factors, to rank them by degree of influence on process (or result), and / or to find those combination(s) of their levels (or values) that achieve some optimal results (min or max).
As a result of the application of statistical methods, the time and cost of conducting physical experimental studies can be substantially reduced.
In my opinion you can find interesting the use of statistical methods to improve your quality assessment and to identify failures or atypical behavior of machines and systems.
On the other hand, statistical methods such as Design of Experiments can provide very useful information about new operational sets regarding the most relevant operational parameters.
I strongly recommend you to check a book ----- Design and Analysis of Experiments. Montgomery.
I think statistical optimization is a key role for determining the optimum parameters (level) with minimum numbers of experimental. So that designing your experiments based on the number of parameters and their levels you can get the optimum level for each parameters that may affects the output of the process with the minimum number of experiment. Therefore, optimizing the process parameters will definitely help to enhance the manufacturing processes.
Nowadays, there are plenty of statistical optimization techniques, such as Factorial design , Fractional Factorial design (Taguchi), Response surface modelling, and many MCDM ( Topsis etc) techniques, are currently used for the conventional and non-conventional manufacturing processes.The selection of these Techniques is quit more important in a particular manufacturing process. Improper selection may lead the wrong solution, which results cost and time consuming for searching the best solutions.