Unfortunately, the answer is "it depends". There is no optimum number of experimental trials. In terms of random errors... the standard deviation (and subsequently confidence intervals) decreases as the number of trials increases. Thus, the standard deviation would approach zero as the number of trials approaches infinity. Generally, you should find a confidence interval (most likely based on a Student's t-distribution) that gives you an interval that you deem satisfactory. However, increasing the number of trials only impacts the precision of your results. To increase the accuracy of your results you would have to address systematic errors (due to equipment accuracy and the propagation of uncertainty). Wheeler and Ganji have a really great text that addresses your question in detail. Reference below.

Wheeler, A. J., and Ganji, A. R., 2009, Introduction to Engineering Experimentation, 3rd Edition.

ISBN-13: 978-0131742765

Thanks Dr David for your reply and ready reference.

Dear Mahesh

As it's indicated above by Dr.David "it depends" because each results abtained by a experiment work is discrabed in its conditions. In fact, how an experiment instrument or material is abale to be in the precision requested that has a great influence in results an then on disription of phenomenon. In conclusion for experiment give a good description of really phenomenon, the conditions and the martial used must be in heigher quality.

Dr Khaoula the document sent by you is not available. If possible then check it and arrange the same.

Thanks

Thanks Dr Sahdev for your recommendation and the book you sent.

Thanks again

Hello Mahesh,

There is no easy answer to your question. It depends. I would suggest to use Response Surface Methodology (RSM) if it fits for the case you want to study. Using the RSM, you can minimize the number of experiments and get the desired results. there are so many RSM techniques which you can use. I hope you may find it useful.

Dear S Lone thanks for your reply.