The mean time between failures (MTBF) is a common metric used to measure the performance of manufacturing systems. MTBF is the elapsed time between failures of a system during normal operations. The failures could be caused by broken machines or computer errors, among other failures. Suppose that the MTBF for a new automated manufacturing system follows an exponential distribution with a mean of 12.8 hours. (a) What is the probability that the automated manufacturing system runs for more than 17 hours without a failure? 0.281 x (b) What is the probability that the automated manufacturing system runs for 7 or fewer hours before failure? 0.401 X (c) What is the probability that the automated manufacturing system runs for more than 6 hours but less than 11 hours before failure? 0.258 x

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
The mean time between failures (MTBF) is a common metric used to measure the performance of manufacturing systems. MTBF is the elapsed time between failures of a system during normal operations. The failures could be caused by
broken machines or computer errors, among other failures. Suppose that the MTBF for a new automated manufacturing system follows an exponential distribution with a mean of 12.8 hours.
(a) What is the probability that the automated manufacturing system runs for more than 17 hours without a failure?
0.281
X
(b) What is the probability that the automated manufacturing system runs for 7 or fewer hours before failure?
0.401
(c) What is the probability that the automated manufacturing system runs for more than 6 hours but less than 11 hours before a failure?
0.258
Transcribed Image Text:The mean time between failures (MTBF) is a common metric used to measure the performance of manufacturing systems. MTBF is the elapsed time between failures of a system during normal operations. The failures could be caused by broken machines or computer errors, among other failures. Suppose that the MTBF for a new automated manufacturing system follows an exponential distribution with a mean of 12.8 hours. (a) What is the probability that the automated manufacturing system runs for more than 17 hours without a failure? 0.281 X (b) What is the probability that the automated manufacturing system runs for 7 or fewer hours before failure? 0.401 (c) What is the probability that the automated manufacturing system runs for more than 6 hours but less than 11 hours before a failure? 0.258
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman