Now that we know where you've been and what you wish to accomplish next, I can still give you some suggestions.
1. Get IPC-7912. Use it to evaluate your CM's. Especially if you have multiple contractors supplying like products. You will quickly see who has the lower PPM's. Find out why. Use the "why" as a benchmark to get the others up to quality spec.
2. You are asking for attributes of why. Good question. Once the attributes are identified, then you have to establish what variations are possible.
Your example listed an attribute of: A. Different component batches may vary and can change the tolerances of Vref, Timing, Power-consuption, Start-up time.
This is your job to determine and should not be part of the CM's responsibility to decide. If they have specific experiences and can offer suggestions, listen and take the advice back to your engineers. The point is, a CM must follow your BOM, either consignment provided or turn key purchased for you. Your engineers should have considered lot to lot variations during Design Review. Those component types deemed acceptable should be on the AVL of the BOM.
B. Solder paste thickness. Can be measured via e.g. laser. SPC is possible during a batch run.
This is an attribute that you could be investigating. Better yet, consider volume. Use IPC 7525 "Stencil Design Guidelines" to determine if your CM has the right apertures in the stencil. The apertures are dependent on land pattern design. Land patterns are a variable that can affect paste volume. A good CM will alter the apertures to accomodate lands that are not sized correctly. Only so much can be done, you may have to change the fab to match the parts and paste volumes needed to get a good solder joint. Other variables for printing include make and model of printer, squeegee type and pressure, sweep speed, angle, seperation rate. These all can vary from CM to CM, depending on how they set up their process.
C. Solder quality.
Another attribute. Variables include: shelf life, temperature, viscosity, sphere size (screen mesh), flux chemistry (water soluble, no clean, aggressive, long tacky life, etc.)
Next is placement. More attributes such as placement accuracy (dependent on make and model of machine), speed, etc. Variables include maintenance (clean nozzles, feeder calibrations, x-y offset (differs from each individual machine), etc.)
Reflow. Attributes: make and model, technology (IR, vapor phase, convection) Variables - reflow profile, maintenance, calibration, nitrogen.
This is a basic outline, many more details exist. You need to go to each process step, find the attributes, determine the variables, decide what may possibly promote defects you are experiencing, SPC (Pareto of defects - concentrate on the highest rates - in my experience, if you solve for the 3 highest defect rates, usually the other random events are solved or reduced significantly).
I'm sure my collegues here at the 'net can provide more details of attributes and vaiables.
I will stop here because this is turning into a windy novella.
Good luck
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