The world of the optical designer – Sensitivity vs Monte-Carlo

Optical tolerance analysis is divided into two main methods - Sensitivity and Monte Carlo Analysis.

In order to know when each method is needed, it is important to understand each method and its benefits and disadvantages.

1. Sensitivity Analysis

During Sensitivity Analysis each parameter in the system is changed from the nominal value and system's performances are evaluated in order to test the impact on the performances as a result of a change of each parameter separately. Actually, this 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, on the other hand, an indication of 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

IIn 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, giving indication of the real system performances.

In this analysis, we can certainly simulate a real (as built) systems' performances in production, but it is not clear what parameter or parameters have higher impact on the system performances.

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, that is based on the Monte Carlo systems performances statistics and allows to calculate the yield for a given set of requirements. We call this tool the Yield Calculator. It also allows to change the requirements and to learn their influence on the production yield.

Our Yield Calculator is a powerful tool for system engineers, technical and project managers and helps to produce a set of requirements in cooperation with the customer. It is also very useful when working in cooperation with the optical / opto-mechanical elements manufacturers.

It is important to understand that each company / start-up project has different goals.

Since tolerance analysis is a time-consuming task, and time is one of the most important resources in the design process, it is important to choose wisely the right tolerance analysis method at the proper timing.

As an example, we define 3 different types of project objectives and our recommended tolerance analysis plan that helps to reach these objectives at shortest timeframe:

Let’s explain what stands behind these 3 different plans, based on different project goals:

  • When the project goal is POC (Proof of Concept), we want to manufacture the prototypes as soon as possible and the final performances are not that critical. Then Sensitivity Analysis is required in order to optimize the manufacturing tolerances together with optical parts manufacturers.

  • When the project goal is Production, the first stage is to perform the Sensitivity Analysis in order to produce the prototypes. Afterwards, the Monte-Carlo Analysis is performed in order to assure that the production units meet all the requirements and the yield is sufficient.

  • When the project goal is Serial Production, the design drive requirement is meeting high production yield. That’s why the first step of the Tolerance Analysis plan is to perform the Monte-Carlo Analysis, which assures that the design and the tolerances are producible with sufficient yield. Afterwards, the Sensitivity Analysis shall be performed in order to trace production process issues and problems back to the corresponding parameter tolerance and analyze the failure mechanism and solve it.

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