Before my time at Cornell, I heard there was a professor who gave a grade based on the product of a test score and a lab grade. If you got a:

One time, I got tasked with figuring out what the probability of any natural disaster striking a biologics manufacturing plant given an estimate of the individual probabilities of said natural disaster.

So suppose:

The key to answer this question is thinking in terms of "not."

So what's the probability that nothing happens?

The same is exactly true with contaminations.

If a successful run depends on five separate operations. And the failure rates for those five operations are:

99% x 98.5% x 98% x 97.5% x 97% = 0.90%

Don't wait until crisis mode.

Further reading:

- 10 on the test and a 9 in the lab, your score: 90.
- 9 on the test and a 9 in the lab, your score: 81.
- 8 on the test and a 7 in the lab, your score: 56 (ouch!)

One time, I got tasked with figuring out what the probability of any natural disaster striking a biologics manufacturing plant given an estimate of the individual probabilities of said natural disaster.

So suppose:

Disaster | Probability |
---|---|

Earthquake | 5% |

Grass fire | 10% |

Flood | 2% |

The key to answer this question is thinking in terms of "not."

Disaster | Probability |
---|---|

Earthquake | 95% |

Grass fire | 90% |

Flood | 98% |

So what's the probability that nothing happens?

0.95 x 0.90 x 0.98 = 0.838

Even though your probabilities of the individuals are in the 90% range, the probability that not any of them happen is in the low 80's. You have an 84% chance of nothing happening, which means the probability of

*something*happening is 16%.
So the equation is thus:

1 - ( 1-pThis is one of those huge mathematical bummers... the more things that can go wrong with your process, the success rate odds are stacked against you._{1}) x (1-p_{2}) x ... x (1-p_{N})

The same is exactly true with contaminations.

If a successful run depends on five separate operations. And the failure rates for those five operations are:

- p1 = 1%
- p2 = 1.5%
- p3 = 2%
- p4 = 2.5%
- p5 = 3%

99% x 98.5% x 98% x 97.5% x 97% = 0.90%

**Five measly steps each with failure rates less than 3% and your overall failure rate is 10%.****Next time you're troubleshooting your microbial bioreactor contaminations, think about this math. If your culture success rate is 10%, your status-quo aseptic practices can be executed >97% of the time and you can still contaminate 1 in 10 runs.**

Don't wait until crisis mode.

Further reading:

## 1 comment:

That might have been Fred Rhodes.

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