I have a collection of SOA components that can handle a series of business processes. For example one SOA component imports user data, another runs analytics on it.
I'm familiar with business process modeling for manufacturing, i.e. calculating WIP, throughput, cycle times, utilization etc. for each process. Little's Law, theory of constraints, etc.
Can I apply this approach to capacity planning for my SOA architecture, or is there a more rigorous / more widely accepted approach?
A bit of a broad question. Some guidelines for you but there is no real perfect answer here.
What you are looking for is Business Activity Monitoring used together with performance metrics reported from your servers.
BAM/Business Activity Monitoring will allow you to measure how many orders per seconds you are processing. How many sales you have made today etc. You all then monitor and collect information such as CPU usage, network bandwidth, disk io performance, memory usage and other technical performance metrics. In windows you can use performance counters for this. In the Linux world there is various tools and techniques that you can use.
Using the number of orders placed you can then look at the performance statistics of the systems used by the order placing software to give you some indication of what is happening.
For example we process 10 orders a second on average using roughly 8GB of ram on the ESB server where the orders service is hosted. We are seeing a average increase of 25% per month in the order coming through. We have noticed several alerts about swapping to disk when orders are at their peak. To ensure that we can cater with the demand we will need to double the memory on the server every 4 months. Thus in a year we will need 3*8GB of memory extra or another 32GB of memory. Now you can decide on the implementation do you create a cluster with 4 machines with 8GB of ram in or do I load balance.
Using this information you can start to get a good idea of where your limits are and what you need to budget for in the future.
Go look at some BAM tools and some monitoring tools and see what suits you.