# Thread: Failure rate of a electrical device

1. ## Failure rate of a electrical device

Question : The failure rate of a certain electronic device is suspended to increase linearly with its temparature. Fit a least squares linear line through the data (two measurements were taken for each given temparature)
$\displaystyle \begin{array}{c|c|c|c|c|c|c} Temp \ F & 55 & 65 & 70 & 85 & 95 & 105 \\ \hline Failure \ rate \ 10^6 & 1.90 & 1.93 & 1.97 & 2.00 & 2.01 & 2.01 \\ . & 1.94 & 1.95 & 1.97 & 2.02 & 2.02 & 2.04 \\ \end{array}$

i) Obtain desired least square line
ii) Obtain predicted failure rate at $\displaystyle 70^{\cdot} F$

2. Originally Posted by zorro
Question : The failure rate of a certain electronic device is suspended to increase linearly with its temparature. Fit a least squares linear line through the data (two measurements were taken for each given temparature)
$\displaystyle \begin{array}{c|c|c|c|c|c|c} Temp \ F & 55 & 65 & 70 & 85 & 95 & 105 \\ \hline Failure \ rate \ 10^6 & 1.90 & 1.93 & 1.97 & 2.00 & 2.01 & 2.01 \\ . & 1.94 & 1.95 & 1.97 & 2.02 & 2.02 & 2.04 \\ \end{array}$

i) Obtain desired least square line
ii) Obtain predicted failure rate at $\displaystyle 70^{\cdot} F$
See: least squares

CB

3. ## Issues

Originally Posted by CaptainBlack

In the table there are 2 reading provided for frequency so how should i incorporate it in the formula.............please advice

4. I would take the average of the two values.

5. ## Is this correct?

Originally Posted by ANDS!
I would take the average of the two values.

that means the for example for the first reading the value is as below:

$\displaystyle \frac{1.90 + 1.94}{2}$ = $\displaystyle 1.92$

6. Originally Posted by zorro
In the table there are 2 reading provided for frequency so how should i incorporate it in the formula.............please advice
You have 12 data points, the equations do not care that some are for the same independent variable value.

CB

7. Originally Posted by zorro
that means the for example for the first reading the value is as below:

$\displaystyle \frac{1.90 + 1.94}{2}$ = $\displaystyle 1.92$
That will work but is unnecessary, see previous post.

CB

8. Originally Posted by ANDS!
I would take the average of the two values.
Why would you want to do that? The regression equations work without any assumptions about non-repeating independent variable values. In this case there are 12 data points some of which have the same y values.

CB

9. ## Thank you CaptainBlack

Originally Posted by CaptainBlack
Why would you want to do that? The regression equations work without any assumptions about non-repeating independent variable values. In this case there are 12 data points some of which have the same y values.

CB

Thankyou CaptainBlack for helping me
cheer mite