Recently I came across an amusing post on one of professional forums dedicated to testing. The post was an elaborated description of how to convince management that testing needs so much time to complete. The author worked his way beautifully introducing parameters and formulas, ezplaining assumptions and proving theories with examples. Great job - no doubt! But... it's all useless :)
No manager will care to read it through and through. None!
The mere fact that the management needs to be convinced in things that SHALL BE OBVIOUS is a problem per se. With that multi-pages work author only supposed to solve the symptoms instead of targeting the disease root-cause.
What could be the root cause for the managers to doubt that testing team work efficiently? What managers need from testing to be in order to feel comfortable about its performance? I am sure you guessed right :) All they expect from your team is VISIBILITY. Just let them see what it takes to define strategy, make required environmental preparations, procure and learn tools, create tests, combine suites, execute tests, submit defects, work with fixed and rejected defects, and so on. I you manage to build a transparent process that everyone can watch in the motion you will never ever be asked to prove that you spend your resource cycles effectively.
Another important issue is getting management involved in taking all important decisions. Make them not just supervisors but active contributors. Share with managers all the important decisions, discuss and argue your position. Let them help you with their experience as well as let them see your professional level by providing them technical assistance. Once a decision is not just your but theirs as well they start feeling much better :)
In short, this is all you need to make sure that you are never asked that silly question - "Why does testing take so long?!"