Lichten Award Paper: Variational Tolerance Analysis (VTA) - Design and Manufacturing Optimization Using Statistical Simulation
Authors:   Sikorsky a Lockheed Martin Co., Lavoie Andrew 
Published: October 2022

Appropriate consideration of tolerances is critical to the design and manufacture of products that meet customer requirements and defined cost targets. Tolerance analysis is most commonly conducted at the individual part or sub-assembly level utilizing basic stack-up methods (worst-case analysis) to ensure the producibility of the assembled product. A worst-case analysis assumes that each dimension in the stack-up will be manufactured on the extreme end or limit of its assigned tolerance (max or min) in such a way that all tolerances become additive. This usually results in tighter than required drawing tolerances being assigned to guarantee the product can be assembled. Modern day manufacturing processes focus on targeting the nominal dimensional value, so it is safe to assume that a higher number of parts will be produced closer to the nominal value than parts produced at the extreme end of the tolerance range. When evaluating the tolerance stack-up of a larger assembly with many parts additional tolerance analysis methods apply (Root Sum Squared, RSS), and a worst-case analysis becomes more costly and less meaningful. The RSS method of tolerance analysis takes into consideration manufacturing targets and applies normal distribution methods to assess more likely tolerance results, allowing relaxed drawing tolerances to be assigned while still maintaining a high level of confidence in a successful assembly. For analysis of complex systems or installations, tolerance studies using more sophisticated approaches to deal with variation such as Monte Carlo statistical analysis is required. Variational Tolerance Analysis (VTA) tools available today allow a typical Monte Carlo tolerance simulation to be visualized by the designer through 3-dimensional real time manufacturing simulations and sensitivity analysis. This in turn simplifies the development process and allows better identification of tolerance drivers within a large system installation; analysis of the geometric effect of tolerances within the installation; and the ability to quickly iterate the analysis to optimize designs for producibility and lower cost.
In this paper, the use of VTA is assessed and quantified to form a business case for further investment by Lockheed Martin. In the course of this work, VTA has been evaluated both before and after final designs were released to manufacturing. Before final designs are released VTA can be used for design optimization (i.e. build before you build simulations), part sequencing studies, or to gain insight into the assembly/installation process enabling advanced planning to take place up front. VTA can also address challenges discovered after final designs have been released to manufacturing and parts are on hand (i.e. during the build) such as: assembly issues, out of spec part disposition, and to inform manufacturing of any special tooling or part rework considerations aiding in corrective action or risk mitigation plans.
Cost savings to the business due to the implementation of VTA has been demonstrated in 4 distinct ways:
1.Reduced design revisions – Design optimization up front reduces future revisions caused by producibility and tolerance related discoveries.
2.Manufacturing – Through tolerance optimization, nonimpactful tolerances can be relaxed while still ensuring a successful assembly.
3.Reduced build schedule – Increased assembly awareness and advanced planning allows a streamlined production process with risk mitigation strategies in place.
4.Reduced scrap, rework, repair (SRR) – Engineering labor to disposition out of spec parts is reduced by entering as-measured tolerances into the simulation model to assess the overall impact to installation success.
The conclusion is VTA simulations provide measurable benefits to the business through robust design optimization, and multi-layered cost and risk reductions.