In one of the previous posts, we discussed the optical requirements and may return to that subject in our future posts, so that we ultimately produce a glossary for the augmented reality systems design. In this post we begin to discuss the optical system tolerance analysis.
Tolerance Analysis Importance
One of the most important system analysis tasks the optical designer performs before transfer to production and especially for serial production is tolerance analysis.
It is usually perceived that tolerance analysis is a major time-consuming task, and this causes some companies to skip it. At the beginning of the development process, it is possible (depending on the system complexity and the optical designer experience) to postpone the tolerance analysis to a later stage and rely on the optical designer experience in similar projects. This is very tempting, while racing against time in an effort to produce a working prototype, but then often tolerance analysis is actually skipped altogether rather than postponed. The prototype becomes a serial product.
What happens when skipping tolerance analysis
The problems arise when the serial production starts and the systems fail the acceptance tests, leading to rejects, low production yield, delays and penalties, or even worse – the customer receives a product that does not meet the requirements.
In such cases, the engineering department receives the task to understand the source of the problem and clear the production bottleneck and the struggle begins:
Is there a problem with the optical elements mounting (mechanical parts do not meet the requirements)?
Is there a problem/mistake with the mechanical parts tolerance analysis?
Is there a problem with optical elements not meeting the requirements?
Is there a problem/mistake with the optical elements' tolerance analysis?
Is there a problem in system assembly or calibration?
The task of finding the problem source is nearly impossible, since the systematic tolerance analysis had not been performed and there is no way to trace back or correlate the system performances failure to a specific parameter, or often more that one failing parameter. Therefore, any solution other than tolerance analysis (and at this point there usually is no time and resources to perform the full analysis) will be like finding your way in complete darkness.
The production yield problems keep coming back and that causes a major waste of time and money to the company, immeasurably greater than the time and money the systematic tolerance analysis done in time would have taken.
The bottom line is – tolerance analysis in the design stage saves a lot of time and money in production stage.
Tolerance Analysis Process
Having said that, here is how the tolerance analysis process should be done.
Tolerance analysis consists of two main stages:
1. Sensitivity Analysis
In sensitivity analysis each parameter in the system is changed from the nominal value and system's performances are evaluated in order to test the performances decrease as a result of a change of each parameter separately. This actually is a kind of relative comparison between all the system parameters. Of course, the more sensitive the parameter, the tighter tolerance will be required.
This process gives a good indication of the "weak points" of the system or more critical (sensitive) parameters, where the tolerances need to be tightened, and the "strengths" of the system or more indifferent (less sensitive) parameters, where the tolerances can be released. It is important to note that during this analysis each parameter is evaluated separately and no interaction or correlation between parameters is taken into account.
This analysis does not predict the real (as built) systems' performances in production.
2. Monte Carlo Analysis
In Monte Carlo analysis we simulate and analyze many systems, when each parameter is changed within its defined tolerance limits and each system is a different superposition of all the parameters with their tolerances, more like the real system.
In this analysis, we can certainly simulate real (as built) systems' performances in production, but it is not clear what parameter or parameters have higher impact on the system performances.
Sensitivity vs Monte-Carlo: What is the difference?
Each analysis gives different values, so it is imperative to perform both.
Sensitivity analysis helps to understand roughly what parameters are more sensitive and what are indifferent, while Monte Carlo analysis creates a lot of statistical systems and allows predicting the performances and the production yield with a given set of requirements.
However, in many cases system requirements are flexible or simply not defined, especially at the early design stages. So, we built a calculation tool, we call it the "yield calculator", that is built on the Monte Carlo systems and allows to calculate the yield for a set of requirements that can be changed to learn the requirements influence on the production yield. Our yield calculator is a powerful tool for the system engineers, technical and project managers and helps to produce a set of requirements in cooperation with the customer. It is also useful in cooperation with the optical / opto-mechanical elements manufacturers.
Other points to consider....
In this post we did not discuss the optical system assembly, calibration and testing processes, that have to be integral parts of the tolerance analysis. We will elaborate on this in the future posts ....