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Chemistry / Quantitative Chemical Analysis 8 / Chapter 2 / Problem 2-25

Quantitative Chemical Analysis | 8th Edition | ISBN: 9781429218153 | Authors: Daniel C. Harris

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A simple model for the fraction of micropipets that operate within specifications after

Chapter 2, Problem 2-25

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QUESTION:

A simple model for the fraction of micropipets that operate within specifications after time t is where tm is the mean time between failure (the time when the fraction within specifications is reduced to 50%). Suppose that tm 2.00 years. (a) Show that the equation predicts that the time at which 50% remain within specifications is 2 yr if tm 2.00 yr. (b) Find the time t at which pipets should be recalibrated (and repaired, if necessary) so that 95% of all pipets will operate within specifications. 2

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QUESTION:

A simple model for the fraction of micropipets that operate within specifications after time t is where tm is the mean time between failure (the time when the fraction within specifications is reduced to 50%). Suppose that tm 2.00 years. (a) Show that the equation predicts that the time at which 50% remain within specifications is 2 yr if tm 2.00 yr. (b) Find the time t at which pipets should be recalibrated (and repaired, if necessary) so that 95% of all pipets will operate within specifications. 2

ANSWER:

Step 1 of 3

(a)

We may substitute these values for the specified fraction within specifications in the preceding equation to demonstrate that the equation predicts that the time at which 50% remain within specifications is 2 years if

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