Tolerances are Stacking Up – Part 3


That evening Jordan declined to dine with the rest of the team. Actually, the look on his managers face said, “We need to close this design review tomorrow to stay on schedule – You should work late on this.”

He picked up the phone, ordered pepperoni pizza and soda, and locked himself in his hotel room to study and consider statistical methods for tolerance analysis.

“In order for a statistical analysis to be meaningful, I need to know what the requirement is for yield or probability of success.” With his phone still in hand, Jordan sent a note to Blake and got a quick reply.

He read from his phone, “Zero point nine-nine-nine-nine-four yield.”

Staring at the wall for a moment he spoke to himself, “The specification states that there must be a 0.99994 probability that the assembly will fit within the required tolerance and satisfy the necessary preload. That’s nine hundred and ninety-nine thousand, nine-hundred and forty successes in a million assemblies. I wonder how many rejects that allows.”

While the number (0.999994) was still on his screen, he subtracted it from one (1.0), and multiplied by a million. That’s sixty rejects per million.” Jordan tapped his palm on his fore-head and said, “That was stupid. I could have done that in my head.”


Jordan fired up his laptop and scrolled through the online pages describing how to do a Monte Carlo simulation for part tolerance stacks or assemblies. He drew a normal distribution or ‘bell’ curve on his engineering pad and labeled mean, standard deviation, upper and lower limits…

“Here it is. I need to know or determine,… Oops.” Jordan paused to wipe pizza sauce off his keyboard, “I need to know the probability density function or distribution for each part. If the part is machined, such as the bearing shoulder on the shaft, I need to know whether the dimension will vary normally as in a ‘normal’ distribution, or if it will vary uniformly as the machine tool wears down and cuts the dimension a little more offset each new part.”

“This looks complicated. I wish I had my old text book on…”

“The trick is getting these distributions right. It looks like I’ll need means and standard deviations for each dimension in the stack…”

“I should be able to program this on my laptop using a spreadsheet and some software scripting.” He got going.


It was now 8pm, his stomach loaded with pizza and the temperature in the room seeming to rise and he was beginning to worry as he struggled with this level of depth. “Is there an easier way than Monte Carlo? I don’t know if I can do this.”

(To be continued)

About Kenneth Richard Hardman

AncestorClips are very short stories about very real people. Each clip nurtures awareness of a time, a place, and the character of a man or woman who cultivated a path for our life. The reader feels the good, the obstacles, the happiness, the sadness, and the overcoming. They cheer us, make us resilient when challenged, give us purpose, and connect us to our multi-generational family. Each story is followed by reflections from the author and readers sharing how the story strengthened or inspired them. Ken Hardman is a son, a brother, a grandson, a great-grandson… He is also a husband, father and grand-father. Ken is a professional engineer, engineering mentor, technical writer, and associate technical fellow at a major aerospace company. He is a writer of engineering and family history stories. Please join Ken in reading, reflecting upon, or writing #AncestorClips
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