A weather satelite has an expected life of 10 years from the time it is placed into earth orbit. Determine its probability of no wear – out before each of the following lengths of service . Assume the exponential distribution is appropriate.

a. 5 year b. 12year c. 20 years d. 30 years.

MTBF = 10 years

Question

A weather satelite has an expected life of 10 years from the time it is placed into earth orbit. Determine its probability of no wear – out before each of the following lengths of service . Assume the exponential distribution is appropriate.

a. 5 year b. 12year c. 20 years d. 30 years.

MTBF = 10 years

Accepted Answer

Compute the ratio T/MTBF for [latex]T = 5, 12, 20[/latex], and 30, and obtain the values of [latex]e^{-T/MTBF}[/latex] from Table 4S.1

TABLE 4S.1

Values of [latex]e^{- T / MTBF}[/latex]

T/MTBF	[latex]e^{-T/MTBF}[/latex]	T/MTBF	[latex]e^{-T/MTBF}[/latex]	T/MTBF	[latex]e^{-T/MTBF}[/latex]
0.1	0.9048	2.6	0.0743	5.1	0.061
0.2	0.8187	2.7	0.0672	5.2	0.0055
0.3	0.7408	2.8	0.0608	5.3	0.005
0.4	0.6703	2.9	0.055	5.4	0.0045
0.5	0.6065	3	0.0498	5.5	0.0041
0.6	0.5488	3.1	0.045	5.6	0.0037
0.7	0.4966	3.2	0.0408	5.7	0.033
0.8	0.4493	3.3	0.0369	5.8	0.003
0.9	0.4066	[latex]3.4[/latex]	[latex]0.0334[/latex]	[latex]5.90[/latex]	0.0027
1·00	0.3679	3.5	0.0302	6·00	0.0025
1.1	0.3329	3.6	0.0273	6.1	0.0022
1.2	0.3012	3.7	0.0247	6.2	0.002
1.3	0.2725	3.8	0.0224	6.3	0.0018
1.4	0.2466	3.9	0.0202	6.4	0.0017
1.5	0.2231	4·00	0.0183	6.5	0.0015
1.6	0.2019	4.1	0.0166	6.6	0.0014
1.7	0.1827	4.2	0.015	6.7	0.0012
1.8	0.1653	4.3	0.0136	6.8	0.0011
1.9	0.1496	4.4	0.0123	6.9	0.001
2·00	0.1353	4.5	0.0111	7·00	0.0009
2.1	0.1255	4.6	0.0101
2.2	0.1108	4.7	0.0091
2.3	0.1003	4.8	0.0082
2.4	0.0907	4.9	0.0074
2.5	0.0821	5·00	0.0067

The solutions are summarized in the following table:

T	MTBF	T/MTBF	[latex]e^{- T/MTBF}[/latex]
a. 5	10	0.5	0.6065
b. 12	10	1.2	0.3012
c. 20	10	2·00	0.1353
d. 30	10	3·00	0.0498

Question P.4.4: A weather satelite has an expected life of 10 years from the...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions