Robert Klassan​ Manufacturing, a medical equipment​manufacturer, subjected 110heart pacemakers to 5,000 hours of testing. Halfway through the​ testing, 5 pacemakers failed. If 1,100 people receive pacemaker​ implants, then the number of units that we can expect to fail during the following one year​ is what?

To be calculated:

Number of units failed during the following one year​

Given values:

Number of heart pacemakers = 110

Number of hours of testing = 5000 hours

Number of pacemakers failed = 5

Non-operating time for 5 failed pacemakers = 2500 hours (as they failed halfway through the testing time)

Number of people to receive pacemakers implants = 1100

Solution:

Failures per unit hour is calculated as;

FR(N) = Number of failures / (Total time – Non-operating time)

Total time = 5000 hours x 110 units = 550000 unit hours

Non-operating time = 2500 x 5 = 12500 unit hours

Putting these values in the above formula, we get;

FR(N) = 5 / (550000 – 12500)

FR(N) = 5 / 537500

FR(N) = 0.000009302 failures per unit hour

Failures per unit year is calculated as;

Failures per unit year = FR(N) x 24 hours/day x 365 days/year

Failures per unit year = 0.000009302 x 24 x 365

Failures per unit year = 0.08149 per unit year

Now, the number of units failed during the following one year​ for 1100 pacemaker implants is calculated as;

Failures per year = Number of pacemaker implants x Failures per unit year

Failures per year = 1100 x 0.08149

Answer: Failures per year for 1100 pacemaker implants = 89.64

 
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