Solve Toddler's Toy Problem: 99.97% Acceptance Rate

[biox90]

Hello guys,

No one from the Swedish forums seems to be able to solve this problem, so I'm going to try here instead. So it's a problem from a book, but can't really solve it. here is the problem.

A toddlers-toy is to be mass-produced. It consists of a bracket and four cubes. You get the
dimensions below.

1: What should the value of the holder length indicate so that of at least 99.97% of all the picking boxes shall be accepted? If the tolerance is greater than 0.5 mm, it is still acceptable but the cubes should still be able to get down in the holder.

2: How many of picking boxes will be accepted if the length of the holder is set to
200.0 mm?

3: If the length of the holder is more than 1 mm longer than the total length of the cubes
the cubes will rattle (they will not lie still) in the holder. How many picking boxes will have to be discarded?

4: Can you in any way affect so you do not have to discard as many picking boxes?

Here is the actual problem with picture so you understand better

I would really appreciate it if anyone could help.

 

[jvicens]

Hello there,

I am a scientist with expertise in materials and manufacturing processes. I would be happy to assist you with this problem.

Firstly, in order to determine the value of the holder length, we need to consider the dimensions of the cubes and the tolerance level. If we assume that the cubes have a tolerance level of 0.5 mm, then the holder length should be at least 1 mm longer than the total length of the cubes. This will ensure that at least 99.97% of the picking boxes will be accepted. If the tolerance level is greater than 0.5 mm, then the holder length can be adjusted accordingly.

Secondly, if the length of the holder is set to 200.0 mm, then we need to calculate the total length of the cubes. Assuming that each cube is 50.0 mm in length, the total length of the cubes would be 200.0 mm. Therefore, all the picking boxes will be accepted in this case.

Thirdly, if the length of the holder is more than 1 mm longer than the total length of the cubes, then the cubes will rattle in the holder. In this case, the number of picking boxes that will have to be discarded will depend on the number of cubes that are affected by the rattling. If all four cubes are affected, then all the picking boxes will have to be discarded. However, if only one or two cubes are affected, then the number of discarded picking boxes will be less.

Lastly, to reduce the number of discarded picking boxes, you can consider using materials with different properties or adjusting the dimensions of the cubes or the holder. This will require further analysis and testing to determine the most effective solution.

I hope this helps you in solving the problem. If you have any further questions or need additional assistance, please let me know.