Failure Rate Calculation


Let’s see how Patty, Rob, and Pete are doing helping Mike Madigan establish his Zero Defects program.

“So let me see if I got this straight: if I want to establish that the defect rate is 1 per million or less, I need to have 3 million in the field with no fails?” Mike asked.

“That’s correct,” Rob responded. “Patty and I developed an Excel spreadsheet that will calculate the number of samples needed, with no fails, to verify a given defect rate. I sent a copy to your email account. Open it.”

“Select the sheet titled,  ‘Calculate Number of Samples.’ Now enter ‘95’ in the blue cell after ‘Percent Confidence Desired’ and 1E-6 in the blue cell after ‘Failure Rate to Verify.’ The number of samples needed to verify this defect rate is in the gray cell. Note that it is a little short of 3 million.”

From a different perspective,” Patty added, “if you have a certain number of samples in the field and want to verify the defect rate they can support, if none fail, the sheet ‘Calculate Failure Rate’ will make that calculation.”

“Let me see if I can use it,” Mike replied.

Mike entered 95% and a desired defect rate of 1E-6.

“Wow! It works!” Mike exclaimed, “It says I need a little less than 3 million samples.”

“So how many samples do you need to demonstrate 0 defects?” Pete teased.

Mike thought for a while and then responded, “Three times infinity! Yikes!”

“I think three times infinity is infinity,” Pete teased again.

Patty glared at Pete.

The group ended by discussing the nobility of a zero defects plan, but the futility of demonstrating it by field sampling.

After they hung up, Patty looked a little agitated.

“Sometimes you two act like 12-year-olds,” she scolded.

Both Rob and Pete had a “Who? Me?” look.

“Why do you say that?” Rob asked sheepishly.

“Both of you laughed when Mike proposed a sample size of 20 to demonstrate zero defects, and then Pete teased about 3 times infinity equals infinity,” Patty responded. “Mike deserves to be treated with respect. We shouldn’t laugh at people when they don’t know or understand something that we do. Especially now that we are all at Ivy U, we are here to help people learn.”

“But he was so annoying when we worked at ACME,” Pete shot back.

“That doesn’t matter. And besides, for whatever reason, we all agree he is much nicer now.”

Both Pete and Rob murmured in agreement.

“Ma’am, we will be better in the future,” Rob and Pete teased in unison.

“Hey, Patty. Remember your concern that almost 50% of Ivy U students did not know who wrote A Christmas Carol?” Rob asked.

“Sure,” Patty responded.

“I asked Pete and he said J. K. Rowling,’” Rob said.

“Well at least I got the right country,” Pete replied.

Patty couldn’t help herself; she burst out laughing with the other two.


Dr. Ron

  1. If you would like a copy of the Excel Spreadsheet that performs the defect rate calculations discussed in this post, send me an email at [email protected].