2 Reliability Problems - Have Answers, Need Formula

[Jgutierrez]

Hello everyone, can you tell me what formulas do I use to solve the following 2 problems:

1.- What is the reliability of a system at 850 hours, if the average usage on the system was 400 hours for 1650 items and the total number of failures was 145? Assume exponential distribution.

Answer should be 83%


2.- Component 1 has an exponential failure rate of 3 x 10 (raised up to -4) failures per hour. Component 2 is normally distributed with a mean of 600 hours and standard deviation of 200 hours. Assuming independence, calculate the reliability of the system after 200 hours. Components 1 and 2 are in series.


Answer should be 0.918


Thanks in advance

[Coury Ferguson]

Originally Posted by Jgutierrez

Hello everyone, can you tell me what formulas do I use to solve the following 2 problems:

1.- What is the reliability of a system at 850 hours, if the average usage on the system was 400 hours for 1650 items and the total number of failures was 145? Assume exponential distribution.

Answer should be 83%


2.- Component 1 has an exponential failure rate of 3 x 10 (raised up to -4) failures per hour. Component 2 is normally distributed with a mean of 600 hours and standard deviation of 200 hours. Assuming independence, calculate the reliability of the system after 200 hours. Components 1 and 2 are in series.


Answer should be 0.918


Thanks in advance

I am sorry I am unable to help you with these problems. This is not my forte. I know that there are covers that will be able to help you. Give it some time.

You may want to edit your title of the thread so that you may get more replies.

[Michael Walmsley]

See attached.

[Wes Bucey]

I'm curious as to the source of the two problems and the reason Jgutierrez needs the formulas to solve them. I adjusted the thread title to add " - have answers, need formula" for the benefit of search engines, but I'm open to better phrasing - any suggestions?

[Wesley Richardson]

Originally Posted by Jgutierrez

Hello everyone, can you tell me what formulas do I use to solve the following 2 problems:

1.- What is the reliability of a system at 850 hours, if the average usage on the system was 400 hours for 1650 items and the total number of failures was 145? Assume exponential distribution.

Answer should be 83%

2.- Component 1 has an exponential failure rate of 3 x 10 (raised up to -4) failures per hour. Component 2 is normally distributed with a mean of 600 hours and standard deviation of 200 hours. Assuming independence, calculate the reliability of the system after 200 hours. Components 1 and 2 are in series.

Answer should be 0.918


Thanks in advance

Question 1 is from the Quality Council of Indiana CQE Exam CD, question ID-86. This question is also CRE Exam CD, question ID-492. This was from 1980 ASQ published CRE question 49 and 1984 published CQE question 73, but was modified by QCI to the present question.

Question 2 is from the Quality Council of Indiana CQE Exam CD, question ID-553. This was from 1972 published CQE question, but was modified by QCI to the present question.

Note that explanations and equations are given on the CD.

Wes R.

[Michael Walmsley]

As a former proctor for the CRE exams, I recalled
many students/exam takers stumbling over them.

[Tim Folkerts]

A couple additional comments.

• I like Michaels approach of creating a spreadsheet and working through the numbers. it shows clearly where the numbers come from.
• For the first question, I took a slightly different approach and got a slightly different answer.
  Michael estimated lambda using (failures/total) / time
  = (145/1650) / 400 = 0.00022
  
  I rearranged the original equation and got - ln(reliability) / time
  = - ln(1505/1650) / 400 = 0.00023
  
  My approach lowers the reliablity estimate slightly from 0.830 to 0.822. I think my number is more accurate, since it correctly predicts the original failure rate observed at 400 hr.
  
  As long as the reliability is fairly high, the tow approaches will be almost identical. However, if only 10% had survived the testing, the two estimates of lambda would be quite different.
  
• For the second problem, I think the person writing the original solution was a little sloppy. If you apply the rule of thumb "95% of the data falls within 2 sigma", then you get the number listed in the original post. If you do it right - like a believe Michael did - then you get the "more correct" answer provided by Michael.

Tim F

[Michael Walmsley]

Thanks Tim (from one Physics guy to another)!