Question

Failures of a critical machine part due to cyclical vibration has a gamma distribution with a shape parameter of 2.3 and a scale parameter of 2000 operating hours. Find:

(a) the MTTF

(b) the standard deviation of the time to failure

(c) the probability that a machine part will exceed a lifetime of 1500 hours.

PLEASE SHOW HAND CALCULATIONS/MINITAB WORK!

Answer #1

It is known that if X~Gamma(shape=a,scale=b)
then E(X)=ab and Var(X)=ab^{2}

^{a) Here a=2.3 and b=2000. Then}

^{MTTF=E(X)=2.3*2000=4600}

b) SD=square root of (2.3*2000*2000) =3033.15

c) P(a machine part will exceed a lifetime of 1500 hours)=P(X>1500)=1-P(X<=1500)=1- 0.115651=0.884349

A machine has a high number of failures due to complexity.
Failures are measured in terms of number of cycles. The time to
failure is modeled as a lognormal with s = 1.25. Suppose that a
reliability of 0.95 is required at 1000 cycles.
(a) Find the other parameter of the lognormal distribution.
(b) Find the MTTF and the standard deviation.
(c) If the machine is still working after 1000 cycles, what is
its reliability for the next 1000
cycles?...

What tools could AA leaders have used to increase their
awareness of internal and external issues?
???ALASKA AIRLINES: NAVIGATING CHANGE
In the autumn of 2007, Alaska Airlines executives adjourned at
the end of a long and stressful day in the
midst of a multi-day strategic planning session. Most headed
outside to relax, unwind and enjoy a bonfire
on the shore of Semiahmoo Spit, outside the meeting venue in
Blaine, a seaport town in northwest
Washington state.
Meanwhile, several members of...

Delta airlines case study
Global strategy. Describe the current global
strategy and provide evidence about how the firms resources
incompetencies support the given pressures regarding costs and
local responsiveness. Describe entry modes have they usually used,
and whether they are appropriate for the given strategy. Any key
issues in their global strategy?
casestudy:
Atlanta, June 17, 2014. Sea of Delta employees and their
families swarmed between food trucks, amusement park booths, and
entertainment venues that were scattered throughout what would...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 36 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago