Various tolerance stack up analysis methods are used to calculate optimized tolerance values. Each method has its own advantages, limitation, and application. Out of these Worst Case and Statistical Tolerance Analysis methods are more popular. Let’s discuss these methods in detail.

Standard deviation is calculated by considering manufacturing process is 3σ capable. Mathematically standard deviation is equal to two times of process capability because the process is distributed on both sides. Therefore standard deviation for 3σ process is given by:

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I’ve brought this bag to many places, and it has just the most understated elegance. I love the classic silhouette; the bag has accompanied me to some lovely places. It’s brought so much joy – just the memory of taking her out – I’m so grateful and appreciative that I could enjoy a bag as wonderful as the Hermes Kelly.

Can you provide a presentation or resources to guide in creating tol stack analysis stack diagrams, to include any assembly of 3 or more parts with a fixed fastener screw rectangular pattern? Simple disc stackup is clear but I am not clear how to handle more difficult aforementioned multipart ‘fixed fastener’ assy stack up.

Nice writeup. Please note that there is a typo for the 3 sigma area under the curve of the normal distribution bell curve. It should read 99.72% rather than 95.72%. Regards.

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But it also looks insanely good with a pop of colour – here, brigh hues of blues, greens and purple does wonders to the bag.

Over the next 6 months, my dear SA actually offered me TWO holy grail bags. One was the Constance 18 in the sweetest shade of Rose Confetti (read more about it here).

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How should we deal with uneven tolerances (e.g. +0.1/-0.3)? Do we “normalize” it to +0.2/-0.2 (& adjust the nominal value accordingly)?

Note: If you love bags, feel free to follow me on Social Media. Especially instagram; i post lots of bag pictures there and would love for you to join me on my bag journeys.

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When I got the message from the SA that she had a Kelly for me, I was so overjoyed I nearly screamed. And even then, I was not expecting that she actually got me my top choice of colour – the classic Gold on Gold combination.

As such, I don’t really recommend it as a crossbody. The strap is best used hung on the shoulder on ONE side of the body… or to hang behind a door when using the bathroom. Lol.

Sir, Can you help in calculate pin diameter and their distance tolerance for manufacturing tolerance for gauge design ? Assuming three holes are diameter 10+/- 0.1,diameter 15+/- 0.2 and diameter 25+/-.1 these holes distance is 120+/-1,100+/-0.5 and 80+/-1.5 respectively. Please share with formula to my Email

Worst Case tolerance stackup analysis method utilizes simple arithmetic (addition and subtraction) operations to calculate optimized tolerances. In this method, all dimensions are assumed at the extreme limit. For low production volumes, worst case tolerance analysis is recommended.

How do you calculate if an element in the stack-up has unbalanced tolerance? For example X +0.5/-0.1 or X +1/-0? Do you shift the “nominal” and then balance the tolerance, or is there a more accurate way to calculate the final tolerance stackup?

In your bell curve normal distribution curve there is an error – for 6 sigma, instead of 99.72% you have marked 95.72%, and as a newbie I spent 20 minutes to re-affirm that… just wanted to let you know. Thanks for this article and calculator, it’s really helpful!

Ahd here’s everything else – the A5 notebook, eye shadow, lipstick, and key holder. It might be possible to squeeze a lipstick in the smaller side pockets – but i struggle with it a little – perhaps my lipstick casing is too fat, lol. A pen or slimmer lipstick would easily go in there however. Not that i find it a problem – this way all items are easily within reach.

Your spreadsheet is incorrect. For – 1.05 +0/-.01, the two values that are calculated are -1.06 and -1.05. The two values should be -1.05 and -1.04.

We suggest you read this article on Process Capability Analysis Cp and Cpk for better understanding on Statistical Tolerance Analysis.

Similar to worst case tolerance analysis, the first step in RSS tolerance stackup analysis is to create the dimensional chain. It is used to determine the direction of tolerance. In the above example, all dimensions are in a positive direction.

I don’t understand the RSS scaling of the total tolerance band by 1/(2×3) to get the total standard deviation. If we assume the errors are uniform distributed – the standard deviation should = tolerance band/sqrt(12) = tolerance band/3.46. This is close to the factor of 3 used – but I don’t see where the additional factor of 2 comes in….

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Since then, I have added a few more Hermes items to my collection, namely, the oh-so-cute Picotin 22 in Gold, the Long Bearn Ostrich wallet in Mykonos blue (got it as a birthday present – thank you hubby!), and the Bolide 27 in classic black.

In fact, when i DO wear jeans and flats, the bag elevates the overall look. Never underestimate the power of an awesome bag, people. Lol.

Tolerance Stackup analysis is a design tool used to analyse and optimize product design for assembly. It is used to calculate the cumulative effects of part tolerances in an assembly. Therefore tolerance stackup analysis ensures smooth part assembly on the production floor. In this article, we will discuss the worst case and RSS methods to solve tolerance stack up problems.

Why do we need to determine the process capability index in the first place? Is the answer that first we need to determine the manufacturing process capability (e.g. 3 sigma) – and second we need to determine the process capability for the assembly “event” (that can differ from 3 sigma)?

Most of the time, I carrry it slung on one side of the shoulder. This is my favourite way of using it – it’s easier to be hands-free, and I can most easily get in and out of the bag in this position.

Granted, in the above pictures, I was dressed more formally – in work clothes – a formal top, dressy pants, and high heels. However, I have worn this bag with jeans and flats – and the Hermes Kelly looks just as good.

Once all items are packed, I simply pop the 7rp insert right into the Hemes Kelly. It goes in easily, and fits like a glove.

After acquiring the Birkin 30 as a push gift for the birth of my second child, my lovely sales associate (In Singapore, from the Marina Bay Sands branch) did ask me – are there any other bags on my wishlist? I told her – yes, I would LOVE to have a Kelly (either in size 25 or 28), or a Constance 18. Colour-wise – there was some flexibility. As the Birkin 30 was already in a fun Rose Extreme colour, I requested a Kelly bag in a neutral colour – either classic gold, etoupe, or black. However, I also made it clear that I would accept blues, pinks, and greens as well, if a classic colour was difficult.

Hi, I like using your stack up calculator spread sheet. Can you share the password so I can name my project? Thanks Sean

Informative log Clears my all confusions of tolarrlence stack up analysis… Language used is very easy to understand and satal.

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If you look at the results from Worst case and RSS method. In the RSS method, the tolerance band is reduced. Therefore designers can give more flexibility to manufacturers.

In this example maximum and minimum disk stackup height is calculated by adding nominal dimension with upper and lower tolerance respectively considering required process capability value is 3σ.

The colour is simply the BEST shade of neutral. Not only does it go with everything in the most idiot-proof way, I can literally put ANY twilly on it, and it instantly gives the bag a new look without clashing in colour.

in above formula denominator (6) defines the distribution of dimensions. Denominator “6” indicates process is 3σ capable with cpk value equal to 1. If your manufacturing process is 6σ capable value ‘6’ need to be changes to 12.

Statistical tolerance analysis is based on the Bell curve and normal distribution. For example, when a thousand disks of the same size are manufactured. Disk thickness will vary from upper limit to lower limit. But all disks will not measure the same because their thickness will be distributed.

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One thing however – the Kelly strap, while useful, is a little on the short side. Hence, I personally do not use it as a crossbody bag.

I’ve always loved Hermes’ as a fashion house – for the history, the quality of the items and the amazing functionality of the stuff that I’ve bought from them so far. I’m not just a bag lover – I also own a few belts and shoes from Hermes.

If you think we missed Something?  You can add to this article by sending a message in the comment box. We will do our best to add it to this post.

As you said, Mathematically standard deviation is equal to two times of process capability because the process is distributed on both sides. based on above, for ‘3 sigma’ the total tolerance of each dimension is divide by 6 (i.e. 2×3) to calculate standard deviation. but at the time of total tolerance zone calculation ‘sigma assembly’ multiplied by only 3 for ‘3 sigma’ capacity. my concern is, just like at the time of total tolerance calculation we divide each total dimension tolerance value by 6. like wise we need to multiply by 6 to ‘sigma assembly’ to get total tolerance zone. because process is distributed on both sides of mean value. please provide your feedback.

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In the above example, the total stacked disks height / thickness will vary from 65.5 mm to 68.5 mm. We suggest you also use this calculator to calculate total disk height using worst case tolerance analysis.

Let’s consider an example of five different size disks with different tolerances stacked on one another. We will calculate the overall maximum and minimum total stacked disk height using RSS Tolerance Stack up Analysis method. RSS tolerance stackup analysis for a given problem can be done in the following steps:

I do not have much knowledge of the sampling theory approach. But my understanding is we can use it since it is based on statics only.

In the above example, the total stacked disk height/thickness will vary from 66.258 mm to 67.74 mm. We suggest you also use this calculator to calculate total disk height using worst case tolerance analysis.

Thanks Edward for your feedback. This is a linear tolerance calculator, that simply works by adding the tolerance. Here -ve sign shows the tolerance direction. So ideally output shall be irrespective of sign. So i agree with you and we will improve on this point. But at the same time, i believe it has no impact on end results as this is calculated based on cumulative values. We recommend you to also check our online tolerance calculator where we tried to over come the limitations of excel: https://www.smlease.com/entries/product-design/online-tolerance-stackup-calculator/

Total nominal disk thickness is calculated similarly to done during worst case tolerance stackup analysis by adding the nominal thickness of all disks. Therefore

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Tolerance stackup analysis is used to calculate optimized part tolerances. It can be done manually or using stackup analysis software.

Statistical tolerance Analysis does not focus on the extreme dimensional limits. Because variation in manufactured part dimensions is not linear. Each dimension has a unique distribution based on the part manufacturing process, machines, and other parameters.

In this example, maximum and minimum disk stack-up height is calculated by adding nominal dimensions with upper and lower tolerance respectively.

Dear readers – Do you love other Hermes bags? Or Bags in General? Check out the Hermes bag tag for everything Hermes featured on this blog, and to see what bags I own, click on the link below to see what’s in my bag collection (As of August 2020).

To sum up, Tolerance stackup analysis is a very important part of product design. It also helps in reducing part cost. Various tolerance stackup analysis methods are available.

Hello, I have the same question asked by Nagaraju. So how does the worst case analysis has disadvantage over RSS method? Compared to Worst case, in RSS, you allow some parts rejection. But what about the cost of those rejected parts? How exactly RSS method is advantageous over worst case?

You mentioned in your calculation the direction of the stack. if you have a 6th step, lets say an etching step, that removed a portion of the last disk, would you include the statistical tolerance calculation of that 6th subtractive step into the same way you did for the RSS of the first 5? or would you RSS the 5 additive steps and then get a tolerance analysis done, followed by an RSS of the 5 steps with the subtractive step?

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The first step in doing tolerance stackup analysis is to create the dimensional chain. It is used to determine the direction of tolerance. In the above example, all dimensions are in a positive direction.

Though most of the time, I tend to leave the bag unbuckled, with the sangles hanging – it generally gives the bag a more relaxed feel (plus it’s easier to get in and out of the bag this way).

Interior: comes with a total of 8 pockets. There are 4 larger pockets on the length (x2 each length-wise), and 4 small pockets on the sides (x2 per side)

If I calculate the total deviation (not std deviation) I get 1.4832… that is +- 0.74162 (the same as in your calculation). My formula that I used: (0,5+0,5)^2+(0,1+0,1)^2 .. (0,4+0,4)^2)^-0,5 ~ 1.48324.

Tolerance: The difference between the maximum and minimum size limits of a part. Fit: Relationship between an external feature of size and an internal feature ...

Mathematically tolerance zone is equal to the multiple of required process capability and total standard deviation for the assembly. Lower the value of process capability, narrow will be the tolerance zone and higher will be the rejection.

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For my holy grail bags, I decided to invest in the best inserts one can find on the market: these are the ones by 7 Rue Paradis, also known as 7rp.

Even with an extremely colourful twilly. the Hermes Kelly doesn’t look too busy – the neutral gold just absorbs the colour and just looks like a beautifully dressed up bag.

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On the side – the leather of the Hermes Kelly is so luxurious and soft. While I was flexible with either the Sellier (structure) or Retourne (relaxed) style that Kelly bags come in- I’m so glad to have the Retourne; it makes getting in and out of the bag so much easier.

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Yes; It wont help machining supplier ; However this may help to casting supplier in case wall thickness calculation. If there is a defect on casting surface and it could lead to reduction in wall thickness. Due to RSS method machining tolerance will be reduced and in result increase in wall thickness.

Production of closely mating parts without tolerances is economically unfeasible. Tight tolerances can result in an increased rejection rate and manufacturing cost. Whereas loose tolerances can affect product function. Therefore it is always recommended to define optimized tolerances. Part tolerance optimization increases the part tolerance band. It also helps in reducing part manufacturing costs.

In RSS, the tolerace band is reduced. How it will help the supplier to produce parts. reduced tolerance band is the constraint for supplier, right?

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According to the worst case tolerance stack up analysis disk stack height can vary from 65.5 mm to 68.5 mm. Whereas according to the RSS method disk height can vary from 66.2584 mm to 67.74162 mm.

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Let’s consider an example of five different size disks with different tolerances stacked on one another. We will calculate the overall maximum and minimum total stacked disk height using Worst Case Tolerance Stackup Analysis method.

Root sum square (RSS) tolerance stack up analysis works on a statistical approach. It is assumed that most of the parts fall to the middle of the tolerance zone.

How did I get so lucky? I honestly have no idea. When I wrote about how I acquired the Birkin 30, I felt that it came down to: having a good relationship with the SA, using the stuff that you bought in front of them, and generally enjoying the Hermes journey without being overly caught up about getting a bag.

In RSS tolerance band is not reduced, you actually allow some rejection compared to worst case tolerance. And the advantage of this allowable rejection can be given to supplier in term of tolerance.

One question is troubling me. “Standard deviation is calculated by considering manufacturing process is 3 sigma capable.” -> Std deviation = total tolerance/ (2×3). This one I understand.

For a good understanding of tolerance stack up. We suggest you first read this article on What are Limit, Fits, and Tolerance?

Because otherwise, if the there is only one and the same process capability value to be used after it’s chosen – there is no need the include it to the calculation. Or am I missing something?

You can also use our worst-case and RSS method tolerance stack-up calculator for tolerance stack-up calculations. You can Download Tolerance stack-up calculation sheet here.

I’ve been told if there is a sequence of just 2 dimensions then RSS is not required. I can’t find where this rule originates. Can you confirm?