Failure Data Analysis using Weibull Probability Plot
The air conditioning and pressurisation (ATA 21) system on aircraft is an essential system that regulates the pressure and the temperature in the cabin as well as supplies continuous flow of fresh air to ensure the comfort of the passengers throughout a flight.
The system schematic diagram of a passenger transport aircraft is shown, while the failure data for the aircraft components collected from the aircraft fleet is compiled in
Table 1.
(a)Using the MS Excel application, construct the Weibull Probability Plot for each of the ten (10) components in the air conditioning and pressurisation system. The cumulative distribution function may be estimated using the median rank method.
(b)For each of the Weibull Probability Plots drawn in (a), construct the best-fit straight line(s) connecting failure data points, and estimate the shape parameter and scale parameter for each best-fit straight line(s).
(c)Comment on the failure patterns exhibited by each of the ten (10) components in the air conditioning and pressurisation system and estimate the MTBF values, where applicable. Appraise one usage of the MTBF data.
(d)Recommend the appropriate maintenance option for each of the ten (10) components in the air conditioning and pressurisation system. Note that some of these components may exhibit more than one failure pattern over its lifetime.
In the first column of the tables 1 to 10, i represents the rank of the observed failure, i is the failure hours, N is the rank of the last item observed, MR is Median Rank, Yi is the dependent variable derived by determining the natural logarithm of the natural logarithm of 1/1-MR and ln t is the natural logarithm of t (failure hours). Now, the median rank parameter is derived from the formula: MR= i-0.3/N+0.4 (standardized). Once this parameter is obtained by substituting i, and N appropriately, the other remaining columns can be filled using the formulae given. For example, to determine 1/1-MR in an excel program, we invoke the sum formula ensuring a negative is embedded, then raising this to the power of negative one (-1) as this is also mathematically equivalent to finding reciprocal of a number. It should be noted that once the first cell in each column is calculated, we simply replicate the rest by copy and pasting the 1st cell entry (the excel programme automatically generates the rest). The weibull probability plot entails a plot of Yi (vertical axis) against ln t.
Table 1: Cockpit temperature controller
|
Temperature |
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|
Controller |
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|
WEIBULL PLOT |
|
|
Failure Hours |
i |
ln t |
i-0.3 |
N+0.4 |
MR |
1-MR |
1/1-MR |
ln(1/1-MR) |
Yi, (ln2) |
|
lnt |
Yi |
|
250 |
1 |
5.521461 |
0.7 |
31.4 |
0.022293 |
0.977707 |
1.022801 |
0.022545 |
-3.79224 |
|
5.521461 |
-3.79224 |
|
300 |
2 |
5.703782 |
1.7 |
31.4 |
0.05414 |
0.94586 |
1.057239 |
0.055661 |
-2.88848 |
|
5.703782 |
-2.88848 |
|
320 |
3 |
5.768321 |
2.7 |
31.4 |
0.085987 |
0.914013 |
1.094076 |
0.08991 |
-2.40894 |
|
5.768321 |
-2.40894 |
|
760 |
5 |
6.633318 |
4.7 |
31.4 |
0.149681 |
0.850319 |
1.176029 |
0.162144 |
-1.81927 |
|
6.633318 |
-1.81927 |
|
860 |
6 |
6.756932 |
5.7 |
31.4 |
0.181528 |
0.818472 |
1.221789 |
0.200316 |
-1.60786 |
|
6.756932 |
-1.60786 |
|
920 |
7 |
6.824374 |
6.7 |
31.4 |
0.213375 |
0.786625 |
1.271254 |
0.240004 |
-1.4271 |
|
6.824374 |
-1.4271 |
|
1,000 |
8 |
6.907755 |
7.7 |
31.4 |
0.245222 |
0.754778 |
1.324893 |
0.281331 |
-1.26822 |
|
6.907755 |
-1.26822 |
|
1,090 |
9 |
6.993933 |
8.7 |
31.4 |
0.277069 |
0.722931 |
1.383258 |
0.324441 |
-1.12565 |
|
6.993933 |
-1.12565 |
|
1,990 |
10 |
7.59589 |
9.7 |
31.4 |
0.308916 |
0.691084 |
1.447002 |
0.369494 |
-0.99562 |
|
7.59589 |
-0.99562 |
|
1,990 |
11 |
7.59589 |
10.7 |
31.4 |
0.340763 |
0.659237 |
1.516905 |
0.416672 |
-0.87546 |
|
7.59589 |
-0.87546 |
|
2,040 |
12 |
7.620705 |
11.7 |
31.4 |
0.37261 |
0.62739 |
1.593905 |
0.466187 |
-0.76317 |
|
7.620705 |
-0.76317 |
|
2,810 |
13 |
7.94094 |
12.7 |
31.4 |
0.404457 |
0.595543 |
1.67914 |
0.518282 |
-0.65724 |
|
7.94094 |
-0.65724 |
|
2,980 |
14 |
7.999679 |
13.7 |
31.4 |
0.436304 |
0.563696 |
1.774006 |
0.57324 |
-0.55645 |
|
7.999679 |
-0.55645 |
|
3,540 |
15 |
8.171882 |
14.7 |
31.4 |
0.468151 |
0.531849 |
1.880233 |
0.631395 |
-0.45982 |
|
8.171882 |
-0.45982 |
|
3,680 |
16 |
8.210668 |
15.7 |
31.4 |
0.499998 |
0.500002 |
1.999992 |
0.693143 |
-0.36652 |
|
8.210668 |
-0.36652 |
|
4,990 |
17 |
8.515191 |
16.7 |
31.4 |
0.531845 |
0.468155 |
2.136044 |
0.758956 |
-0.27581 |
|
8.515191 |
-0.27581 |
|
5,320 |
18 |
8.579229 |
17.7 |
31.4 |
0.563692 |
0.436308 |
2.291958 |
0.829407 |
-0.18704 |
|
8.579229 |
-0.18704 |
|
8,010 |
19 |
8.988446 |
18.7 |
31.4 |
0.595539 |
0.404461 |
2.472426 |
0.9052 |
-0.0996 |
|
8.988446 |
-0.0996 |
|
8,600 |
20 |
9.059517 |
19.7 |
31.4 |
0.627386 |
0.372614 |
2.683742 |
0.987212 |
-0.01287 |
|
9.059517 |
-0.01287 |
|
8,930 |
21 |
9.097172 |
20.7 |
31.4 |
0.659233 |
0.340767 |
2.934556 |
1.076556 |
0.073767 |
|
9.097172 |
0.073767 |
|
10,280 |
22 |
9.237956 |
21.7 |
31.4 |
0.69108 |
0.30892 |
3.237083 |
1.174673 |
0.160989 |
|
9.237956 |
0.160989 |
|
10,570 |
23 |
9.265775 |
22.7 |
31.4 |
0.722927 |
0.277073 |
3.609156 |
1.283474 |
0.24957 |
|
9.265775 |
0.24957 |
|
10,690 |
24 |
9.277064 |
23.7 |
31.4 |
0.754774 |
0.245226 |
4.077869 |
1.405575 |
0.340446 |
|
9.277064 |
0.340446 |
|
12,150 |
25 |
9.405084 |
24.7 |
31.4 |
0.786621 |
0.213379 |
4.686495 |
1.544685 |
0.43482 |
|
9.405084 |
0.43482 |
|
12,690 |
26 |
9.44857 |
25.7 |
31.4 |
0.818468 |
0.181532 |
5.508668 |
1.706323 |
0.534341 |
|
9.44857 |
0.534341 |
|
15,060 |
27 |
9.619798 |
26.7 |
31.4 |
0.850315 |
0.149685 |
6.680692 |
1.899222 |
0.641444 |
|
9.619798 |
0.641444 |
|
19,670 |
28 |
9.88685 |
27.7 |
31.4 |
0.882162 |
0.117838 |
8.48622 |
2.138444 |
0.760078 |
|
9.88685 |
0.760078 |
|
19,830 |
29 |
9.894951 |
28.7 |
31.4 |
0.914009 |
0.085991 |
11.62911 |
2.453511 |
0.89752 |
|
9.894951 |
0.89752 |
|
20,880 |
30 |
9.946547 |
29.7 |
31.4 |
0.945856 |
0.054144 |
18.46923 |
2.916106 |
1.070249 |
|
9.946547 |
1.070249 |
|
22,850 |
31 |
10.03671 |
30.7 |
31.4 |
0.977703 |
0.022297 |
44.84888 |
3.803299 |
1.335869 |
|
10.03671 |
1.335869 |
|
|
N=31 |
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Table 2: Overtemp switch
|
Over-Temp Switch |
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|
WEIBULL PLOT |
|
|
|
Failure Hours |
i |
ln t |
i-0.3 |
N+0.4 |
MR |
1-MR |
1/1-MR |
ln(1/1-MR) |
Yi, (ln2) |
|
lnt |
Yi |
|
280 |
1 |
5.63479 |
0.7 |
30.4 |
0.02303 |
0.97697 |
1.02357 |
0.0232955 |
-3.75949 |
|
5.63479 |
-3.75949 |
|
930 |
2 |
6.83518 |
1.7 |
30.4 |
0.05592 |
0.94408 |
1.05923 |
0.0575454 |
-2.85518 |
|
6.835185 |
-2.85518 |
|
3,030 |
3 |
8.01632 |
2.7 |
30.4 |
0.08882 |
0.91118 |
1.09747 |
0.0930101 |
-2.37505 |
|
8.016318 |
-2.37505 |
|
3,340 |
4 |
8.11373 |
3.7 |
30.4 |
0.12171 |
0.87829 |
1.13858 |
0.1297789 |
-2.04192 |
|
8.113726 |
-2.04192 |
|
3,960 |
5 |
8.28400 |
4.7 |
30.4 |
0.15461 |
0.84539 |
1.18288 |
0.1679514 |
-1.78408 |
|
8.283999 |
-1.78408 |
|
4,810 |
6 |
8.47845 |
5.7 |
30.4 |
0.18750 |
0.81250 |
1.23077 |
0.2076391 |
-1.57195 |
|
8.478452 |
-1.57195 |
|
5,100 |
7 |
8.53700 |
6.7 |
30.4 |
0.22039 |
0.77961 |
1.28270 |
0.2489672 |
-1.39043 |
|
8.536996 |
-1.39043 |
|
5,780 |
8 |
8.66216 |
7.7 |
30.4 |
0.25329 |
0.74671 |
1.33921 |
0.2920773 |
-1.23074 |
|
8.662159 |
-1.23074 |
|
6,030 |
9 |
8.70450 |
8.7 |
30.4 |
0.28618 |
0.71382 |
1.40092 |
0.3371299 |
-1.08729 |
|
8.704502 |
-1.08729 |
|
7,070 |
10 |
8.86362 |
9.7 |
30.4 |
0.31908 |
0.68092 |
1.46860 |
0.3843084 |
-0.95631 |
|
8.863616 |
-0.95631 |
|
7,350 |
11 |
8.90246 |
10.7 |
30.4 |
0.35197 |
0.64803 |
1.54315 |
0.4338234 |
-0.83512 |
|
8.902456 |
-0.83512 |
|
7,780 |
12 |
8.95931 |
11.7 |
30.4 |
0.38487 |
0.61513 |
1.62567 |
0.4859184 |
-0.72171 |
|
8.959312 |
-0.72171 |
|
8,860 |
13 |
9.08930 |
12.7 |
30.4 |
0.41776 |
0.58224 |
1.71751 |
0.5408772 |
-0.61456 |
|
9.089302 |
-0.61456 |
|
8,960 |
14 |
9.10053 |
13.7 |
30.4 |
0.45066 |
0.54934 |
1.82036 |
0.599033 |
-0.51244 |
|
9.100526 |
-0.51244 |
|
9,570 |
15 |
9.16639 |
14.7 |
30.4 |
0.48355 |
0.51645 |
1.93630 |
0.6607808 |
-0.41433 |
|
9.166388 |
-0.41433 |
|
10,040 |
16 |
9.21433 |
15.7 |
30.4 |
0.51645 |
0.48355 |
2.06802 |
0.7265939 |
-0.31939 |
|
9.214332 |
-0.31939 |
|
12,290 |
17 |
9.41654 |
16.7 |
30.4 |
0.54934 |
0.45066 |
2.21898 |
0.7970454 |
-0.22684 |
|
9.416541 |
-0.22684 |
|
14,510 |
18 |
9.58259 |
17.7 |
30.4 |
0.58224 |
0.41776 |
2.39370 |
0.8728391 |
-0.136 |
|
9.582593 |
-0.136 |
|
15,430 |
19 |
9.64407 |
18.7 |
30.4 |
0.61513 |
0.38487 |
2.59829 |
0.954852 |
-0.0462 |
|
9.644069 |
-0.0462 |
|
17,910 |
20 |
9.79311 |
19.7 |
30.4 |
0.64803 |
0.35197 |
2.84112 |
1.0441968 |
0.043248 |
|
9.793114 |
0.043248 |
|
19,560 |
21 |
9.88124 |
20.7 |
30.4 |
0.68092 |
0.31908 |
3.13401 |
1.1423143 |
0.133056 |
|
9.881242 |
0.133056 |
|
20,090 |
22 |
9.90798 |
21.7 |
30.4 |
0.71381 |
0.28619 |
3.49424 |
1.2511168 |
0.224037 |
|
9.907977 |
0.224037 |
|
21,670 |
23 |
9.98368 |
22.7 |
30.4 |
0.74671 |
0.25329 |
3.94804 |
1.373219 |
0.317158 |
|
9.983684 |
0.317158 |
|
34,960 |
24 |
10.46196 |
23.7 |
30.4 |
0.77960 |
0.22040 |
4.53730 |
1.5123311 |
0.413652 |
|
10.46196 |
0.413652 |
|
36,420 |
25 |
10.50287 |
24.7 |
30.4 |
0.81250 |
0.18750 |
5.33331 |
1.6739716 |
0.515199 |
|
10.50287 |
0.515199 |
|
38,220 |
26 |
10.55111 |
25.7 |
30.4 |
0.84539 |
0.15461 |
6.46805 |
1.866874 |
0.624265 |
|
10.55111 |
0.624265 |
|
38,840 |
27 |
10.56721 |
26.7 |
30.4 |
0.87829 |
0.12171 |
8.21615 |
2.1061017 |
0.744839 |
|
10.56721 |
0.744839 |
|
44,410 |
28 |
10.70122 |
27.7 |
30.4 |
0.91118 |
0.08882 |
11.25913 |
2.4211793 |
0.884255 |
|
10.70122 |
0.884255 |
|
54,280 |
29 |
10.90191 |
28.7 |
30.4 |
0.94408 |
0.05592 |
17.88201 |
2.8837954 |
1.059107 |
|
10.90191 |
1.059107 |
|
70,570 |
30 |
11.16436 |
29.7 |
30.4 |
0.97697 |
0.02303 |
43.42651 |
3.77107 |
1.327359 |
|
11.16436 |
1.327359 |
|
TOTAL |
|
|
|
|
|
|
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|
|
|
|
|
Table3: Duct temperature sensor
|
Duct |
|
|
|
|
|
|
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|
|
|
|
|
Temperature |
|
|
|
|
|
|
|
|
|
|
|
|
|
Sensor |
|
|
|
|
|
|
|
|
|
|
WEIBULL PLOT |
|
|
Failure Hours |
i |
ln t |
i-0.3 |
N+0.4 |
MR |
1-MR |
1/1-MR |
ln(1/1-MR) |
Yi, (ln2) |
|
lnt |
Yi |
|
600 |
1 |
6.39693 |
0.7 |
30.4 |
0.02303 |
0.97697 |
1.02357 |
0.023296 |
-3.75949 |
|
6.39693 |
-3.75949 |
|
1,000 |
2 |
6.907755 |
1.7 |
30.4 |
0.05592 |
0.94408 |
1.05923 |
0.057545 |
-2.85518 |
|
6.907755 |
-2.85518 |
|
1,600 |
3 |
7.377759 |
2.7 |
30.4 |
0.08882 |
0.91118 |
1.09747 |
0.09301 |
-2.37505 |
|
7.377759 |
-2.37505 |
|
1,600 |
4 |
7.377759 |
3.7 |
30.4 |
0.12171 |
0.87829 |
1.13858 |
0.129779 |
-2.04192 |
|
7.377759 |
-2.04192 |
|
1,800 |
5 |
7.495542 |
4.7 |
30.4 |
0.15461 |
0.84539 |
1.18288 |
0.167951 |
-1.78408 |
|
7.495542 |
-1.78408 |
|
2,140 |
6 |
7.668561 |
5.7 |
30.4 |
0.18750 |
0.81250 |
1.23077 |
0.207639 |
-1.57195 |
|
7.668561 |
-1.57195 |
|
2,200 |
7 |
7.696213 |
6.7 |
30.4 |
0.22039 |
0.77961 |
1.28270 |
0.248967 |
-1.39043 |
|
7.696213 |
-1.39043 |
|
2,460 |
8 |
7.807917 |
7.7 |
30.4 |
0.25329 |
0.74671 |
1.33921 |
0.292077 |
-1.23074 |
|
7.807917 |
-1.23074 |
|
3,320 |
9 |
8.10772 |
8.7 |
30.4 |
0.28618 |
0.71382 |
1.40092 |
0.33713 |
-1.08729 |
|
8.10772 |
-1.08729 |
|
3,330 |
10 |
8.110728 |
9.7 |
30.4 |
0.31908 |
0.68092 |
1.46860 |
0.384308 |
-0.95631 |
|
8.110728 |
-0.95631 |
|
3,590 |
11 |
8.185907 |
10.7 |
30.4 |
0.35197 |
0.64803 |
1.54315 |
0.433823 |
-0.83512 |
|
8.185907 |
-0.83512 |
|
3,860 |
12 |
8.258422 |
11.7 |
30.4 |
0.38487 |
0.61513 |
1.62567 |
0.485918 |
-0.72171 |
|
8.258422 |
-0.72171 |
|
4,250 |
13 |
8.354674 |
12.7 |
30.4 |
0.41776 |
0.58224 |
1.71751 |
0.540877 |
-0.61456 |
|
8.354674 |
-0.61456 |
|
5,240 |
14 |
8.564077 |
13.7 |
30.4 |
0.45066 |
0.54934 |
1.82036 |
0.599033 |
-0.51244 |
|
8.564077 |
-0.51244 |
|
5,480 |
15 |
8.60886 |
14.7 |
30.4 |
0.48355 |
0.51645 |
1.93630 |
0.660781 |
-0.41433 |
|
8.60886 |
-0.41433 |
|
5,590 |
16 |
8.628735 |
15.7 |
30.4 |
0.51645 |
0.48355 |
2.06802 |
0.726594 |
-0.31939 |
|
8.628735 |
-0.31939 |
|
9,090 |
17 |
9.11493 |
16.7 |
30.4 |
0.54934 |
0.45066 |
2.21898 |
0.797045 |
-0.22684 |
|
9.11493 |
-0.22684 |
|
9,570 |
18 |
9.166388 |
17.7 |
30.4 |
0.58224 |
0.41776 |
2.39370 |
0.872839 |
-0.136 |
|
9.166388 |
-0.136 |
|
11,110 |
19 |
9.315601 |
18.7 |
30.4 |
0.61513 |
0.38487 |
2.59829 |
0.954852 |
-0.0462 |
|
9.315601 |
-0.0462 |
|
14,110 |
20 |
9.554639 |
19.7 |
30.4 |
0.64803 |
0.35197 |
2.84112 |
1.044197 |
0.043248 |
|
9.554639 |
0.043248 |
|
14,840 |
21 |
9.605082 |
20.7 |
30.4 |
0.68092 |
0.31908 |
3.13401 |
1.142314 |
0.133056 |
|
9.605082 |
0.133056 |
|
17,310 |
22 |
9.75904 |
21.7 |
30.4 |
0.71381 |
0.28619 |
3.49424 |
1.251117 |
0.224037 |
|
9.75904 |
0.224037 |
|
17,980 |
23 |
9.797015 |
22.7 |
30.4 |
0.74671 |
0.25329 |
3.94804 |
1.373219 |
0.317158 |
|
9.797015 |
0.317158 |
|
23,150 |
24 |
10.04975 |
23.7 |
30.4 |
0.77960 |
0.22040 |
4.53730 |
1.512331 |
0.413652 |
|
10.04975 |
0.413652 |
|
23,180 |
25 |
10.05105 |
24.7 |
30.4 |
0.81250 |
0.18750 |
5.33331 |
1.673972 |
0.515199 |
|
10.05105 |
0.515199 |
|
28,690 |
26 |
10.2643 |
25.7 |
30.4 |
0.84539 |
0.15461 |
6.46805 |
1.866874 |
0.624265 |
|
10.2643 |
0.624265 |
|
30,670 |
27 |
10.33104 |
26.7 |
30.4 |
0.87829 |
0.12171 |
8.21615 |
2.106102 |
0.744839 |
|
10.33104 |
0.744839 |
|
36,780 |
28 |
10.51271 |
27.7 |
30.4 |
0.91118 |
0.08882 |
11.25913 |
2.421179 |
0.884255 |
|
10.51271 |
0.884255 |
|
36,790 |
29 |
10.51298 |
28.7 |
30.4 |
0.94408 |
0.05592 |
17.88201 |
2.883795 |
1.059107 |
|
10.51298 |
1.059107 |
|
98,830 |
30 |
11.50116 |
29.7 |
30.4 |
0.97697 |
0.02303 |
43.42651 |
3.77107 |
1.327359 |
|
11.50116 |
1.327359 |
|
TOTAL |
|
|
|
|
|
|
|
|
|
|
|
|
Duct temperature sensor
Table 4: Control System shut off valve SOV
|
Environmental Pressure Regulating |
|
|
|
|
|
|
|
|
|
|
|
|
|
Control System Shut-off Valve |
|
|
|
|
|
|
|
|
|
|
|
|
|
(ECS) (SOV) |
|
|
|
|
|
|
|
|
|
WEIBULL PLOT |
|
|
|
Failure Hours |
i |
ln t |
i-0.3 |
N+0.4 |
MR |
1-MR |
1/1-MR |
ln(1/1-MR) |
Yi, (ln2) |
|
lnt |
Yi |
|
930 |
1 |
6.835185 |
0.7 |
30.4 |
0.02303 |
0.97697 |
1.02357 |
0.023296 |
-3.75949 |
|
6.835185 |
-3.75949 |
|
1,000 |
2 |
6.907755 |
1.7 |
30.4 |
0.05592 |
0.94408 |
1.05923 |
0.057545 |
-2.85518 |
|
6.907755 |
-2.85518 |
|
1,110 |
3 |
7.012115 |
2.7 |
30.4 |
0.08882 |
0.91118 |
1.09747 |
0.09301 |
-2.37505 |
|
7.012115 |
-2.37505 |
|
1,980 |
4 |
7.590852 |
3.7 |
30.4 |
0.12171 |
0.87829 |
1.13858 |
0.129779 |
-2.04192 |
|
7.590852 |
-2.04192 |
|
2,240 |
5 |
7.714231 |
4.7 |
30.4 |
0.15461 |
0.84539 |
1.18288 |
0.167951 |
-1.78408 |
|
7.714231 |
-1.78408 |
|
2,470 |
6 |
7.811973 |
5.7 |
30.4 |
0.18750 |
0.81250 |
1.23077 |
0.207639 |
-1.57195 |
|
7.811973 |
-1.57195 |
|
4,150 |
7 |
8.330864 |
6.7 |
30.4 |
0.22039 |
0.77961 |
1.28270 |
0.248967 |
-1.39043 |
|
8.330864 |
-1.39043 |
|
4,830 |
8 |
8.482602 |
7.7 |
30.4 |
0.25329 |
0.74671 |
1.33921 |
0.292077 |
-1.23074 |
|
8.482602 |
-1.23074 |
|
5,340 |
9 |
8.582981 |
8.7 |
30.4 |
0.28618 |
0.71382 |
1.40092 |
0.33713 |
-1.08729 |
|
8.582981 |
-1.08729 |
|
6,160 |
10 |
8.725832 |
9.7 |
30.4 |
0.31908 |
0.68092 |
1.46860 |
0.384308 |
-0.95631 |
|
8.725832 |
-0.95631 |
|
6,650 |
11 |
8.802372 |
10.7 |
30.4 |
0.35197 |
0.64803 |
1.54315 |
0.433823 |
-0.83512 |
|
8.802372 |
-0.83512 |
|
6,830 |
12 |
8.82908 |
11.7 |
30.4 |
0.38487 |
0.61513 |
1.62567 |
0.485918 |
-0.72171 |
|
8.82908 |
-0.72171 |
|
7,500 |
13 |
8.922658 |
12.7 |
30.4 |
0.41776 |
0.58224 |
1.71751 |
0.540877 |
-0.61456 |
|
8.922658 |
-0.61456 |
|
8,140 |
14 |
9.004545 |
13.7 |
30.4 |
0.45066 |
0.54934 |
1.82036 |
0.599033 |
-0.51244 |
|
9.004545 |
-0.51244 |
|
9,320 |
15 |
9.139918 |
14.7 |
30.4 |
0.48355 |
0.51645 |
1.93630 |
0.660781 |
-0.41433 |
|
9.139918 |
-0.41433 |
|
9,740 |
16 |
9.183996 |
15.7 |
30.4 |
0.51645 |
0.48355 |
2.06802 |
0.726594 |
-0.31939 |
|
9.183996 |
-0.31939 |
|
9,940 |
17 |
9.204322 |
16.7 |
30.4 |
0.54934 |
0.45066 |
2.21898 |
0.797045 |
-0.22684 |
|
9.204322 |
-0.22684 |
|
14,080 |
18 |
9.552511 |
17.7 |
30.4 |
0.58224 |
0.41776 |
2.39370 |
0.872839 |
-0.136 |
|
9.552511 |
-0.136 |
|
15,550 |
19 |
9.651816 |
18.7 |
30.4 |
0.61513 |
0.38487 |
2.59829 |
0.954852 |
-0.0462 |
|
9.651816 |
-0.0462 |
|
18,210 |
20 |
9.809726 |
19.7 |
30.4 |
0.64803 |
0.35197 |
2.84112 |
1.044197 |
0.043248 |
|
9.809726 |
0.043248 |
|
21,270 |
21 |
9.965053 |
20.7 |
30.4 |
0.68092 |
0.31908 |
3.13401 |
1.142314 |
0.133056 |
|
9.965053 |
0.133056 |
|
22,390 |
22 |
10.01637 |
21.7 |
30.4 |
0.71381 |
0.28619 |
3.49424 |
1.251117 |
0.224037 |
|
10.01637 |
0.224037 |
|
26,100 |
23 |
10.16969 |
22.7 |
30.4 |
0.74671 |
0.25329 |
3.94804 |
1.373219 |
0.317158 |
|
10.16969 |
0.317158 |
|
27,950 |
24 |
10.23817 |
23.7 |
30.4 |
0.77960 |
0.22040 |
4.53730 |
1.512331 |
0.413652 |
|
10.23817 |
0.413652 |
|
33,220 |
25 |
10.41091 |
24.7 |
30.4 |
0.81250 |
0.18750 |
5.33331 |
1.673972 |
0.515199 |
|
10.41091 |
0.515199 |
|
37,760 |
26 |
10.53901 |
25.7 |
30.4 |
0.84539 |
0.15461 |
6.46805 |
1.866874 |
0.624265 |
|
10.53901 |
0.624265 |
|
42,910 |
27 |
10.66686 |
26.7 |
30.4 |
0.87829 |
0.12171 |
8.21615 |
2.106102 |
0.744839 |
|
10.66686 |
0.744839 |
|
47,820 |
28 |
10.7752 |
27.7 |
30.4 |
0.91118 |
0.08882 |
11.25913 |
2.421179 |
0.884255 |
|
10.7752 |
0.884255 |
|
64,060 |
29 |
11.06758 |
28.7 |
30.4 |
0.94408 |
0.05592 |
17.88201 |
2.883795 |
1.059107 |
|
11.06758 |
1.059107 |
|
66,680 |
30 |
11.10766 |
29.7 |
30.4 |
0.97697 |
0.02303 |
43.42651 |
3.77107 |
1.327359 |
|
11.10766 |
1.327359 |
|
TOTAL |
|
|
|
|
|
|
|
|
|
|
|
|
Control system shut off valve
Table 5
|
Environmental Pressure Regulating |
|
|
|
|
|
|
|
|
|
|
|
|
|
Control System Shut-off Valve |
|
|
|
|
|
|
|
|
|
|
|
|
|
(ECS) (SOV) |
|
|
|
|
|
|
|
|
|
WEIBULL PLOT |
|
|
|
Failure Hours |
i |
ln t |
i-0.3 |
N+0.4 |
MR |
1-MR |
1/1-MR |
ln(1/1-MR) |
Yi, (ln2) |
|
lnt |
Yi |
|
2,220 |
1 |
7.705262 |
0.7 |
10.4 |
0.067308 |
0.932692 |
1.072165 |
0.0696799 |
-2.66384 |
|
7.705262 |
-2.66384 |
|
2,320 |
2 |
7.749322 |
1.7 |
10.4 |
0.163461 |
0.836539 |
1.195402 |
0.1784827 |
-1.72326 |
|
7.749322 |
-1.72326 |
|
2,330 |
3 |
7.753624 |
2.7 |
10.4 |
0.259615 |
0.740385 |
1.350649 |
0.3005853 |
-1.20202 |
|
7.753624 |
-1.20202 |
|
2,940 |
4 |
7.986165 |
3.7 |
10.4 |
0.355769 |
0.644231 |
1.552238 |
0.439698 |
-0.82167 |
|
7.986165 |
-0.82167 |
|
3,140 |
5 |
8.051978 |
4.7 |
10.4 |
0.451923 |
0.548077 |
1.824561 |
0.6013392 |
-0.5086 |
|
8.051978 |
-0.5086 |
|
3,600 |
6 |
8.188689 |
5.7 |
10.4 |
0.548077 |
0.451923 |
2.212765 |
0.7942427 |
-0.23037 |
|
8.188689 |
-0.23037 |
|
4,500 |
7 |
8.411833 |
6.7 |
10.4 |
0.64423 |
0.35577 |
2.810808 |
1.0334721 |
0.032924 |
|
8.411833 |
0.032924 |
|
4,660 |
8 |
8.446771 |
7.7 |
10.4 |
0.740384 |
0.259616 |
3.851847 |
1.3485527 |
0.299032 |
|
8.446771 |
0.299032 |
|
4,700 |
9 |
8.455318 |
8.7 |
10.4 |
0.836538 |
0.163462 |
6.117632 |
1.8111751 |
0.593976 |
|
8.455318 |
0.593976 |
|
4,750 |
10 |
8.4659 |
9.7 |
10.4 |
0.932692 |
0.067308 |
14.85704 |
2.6984741 |
0.992686 |
|
8.4659 |
0.992686 |
|
TOTAL |
10 |
|
|
|
|
|
|
|
|
|
|
|
Table 6: Temperature modulating valve
|
Temperature Modulating Valve |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
WEIBULL PLOT |
|
|
|
Failure Hours |
i |
ln t |
i-0.3 |
N+0.4 |
MR |
1-MR |
1/1-MR |
ln(1/1-MR) |
Yi, (ln2) |
|
lnt |
Yi |
|
1,950 |
1 |
7.575585 |
0.7 |
15.4 |
0.045455 |
0.954546 |
1.047619 |
0.04652 |
-3.06787 |
|
7.575585 |
-3.06787 |
|
2,300 |
2 |
7.740664 |
1.7 |
15.4 |
0.11039 |
0.889611 |
1.124087 |
0.116972 |
-2.14582 |
|
7.740664 |
-2.14582 |
|
2,400 |
3 |
7.783224 |
2.7 |
15.4 |
0.175325 |
0.824676 |
1.212598 |
0.192765 |
-1.64628 |
|
7.783224 |
-1.64628 |
|
2,430 |
4 |
7.795647 |
3.7 |
15.4 |
0.24026 |
0.759741 |
1.316239 |
0.274778 |
-1.29179 |
|
7.795647 |
-1.29179 |
|
2,500 |
5 |
7.824046 |
4.7 |
15.4 |
0.305195 |
0.694806 |
1.439252 |
0.364123 |
-1.01026 |
|
7.824046 |
-1.01026 |
|
2,890 |
6 |
7.969012 |
5.7 |
15.4 |
0.37013 |
0.629871 |
1.587628 |
0.462241 |
-0.77167 |
|
7.969012 |
-0.77167 |
|
3,000 |
7 |
8.006368 |
6.7 |
15.4 |
0.435065 |
0.564936 |
1.770114 |
0.571044 |
-0.56029 |
|
8.006368 |
-0.56029 |
|
3,010 |
8 |
8.009695 |
7.7 |
15.4 |
0.5 |
0.500001 |
1.999998 |
0.693146 |
-0.36651 |
|
8.009695 |
-0.36651 |
|
3,020 |
9 |
8.013012 |
8.7 |
15.4 |
0.564935 |
0.435066 |
2.298504 |
0.832259 |
-0.18361 |
|
8.013012 |
-0.18361 |
|
3,190 |
10 |
8.067776 |
9.7 |
15.4 |
0.62987 |
0.370131 |
2.70175 |
0.9939 |
-0.00612 |
|
8.067776 |
-0.00612 |
|
3,500 |
11 |
8.160518 |
10.7 |
15.4 |
0.694805 |
0.305196 |
3.276588 |
1.186803 |
0.171263 |
|
8.160518 |
0.171263 |
|
3,500 |
12 |
8.160518 |
11.7 |
15.4 |
0.75974 |
0.240261 |
4.162149 |
1.426032 |
0.354895 |
|
8.160518 |
0.354895 |
|
3,550 |
13 |
8.174703 |
12.7 |
15.4 |
0.824675 |
0.175326 |
5.703677 |
1.741111 |
0.554523 |
|
8.174703 |
0.554523 |
|
4,450 |
14 |
8.400659 |
13.7 |
15.4 |
0.88961 |
0.110391 |
9.058751 |
2.203731 |
0.790152 |
|
8.400659 |
0.790152 |
|
4,550 |
15 |
8.422883 |
14.7 |
15.4 |
0.954545 |
0.045456 |
21.99954 |
3.091021 |
1.128502 |
|
8.422883 |
1.128502 |
|
TOTAL |
15 |
|
|
|
|
|
|
|
|
|
|
|
Table 7: Non-return valve
|
Non-Return Valve |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
WEIBULL PLOT |
|
|
|
Failure Hours |
i |
ln t |
i-0.3 |
N+0.4 |
MR |
1-MR |
1/1-MR |
ln(1/1-MR) |
Yi, (ln2) |
|
lnt |
Yi |
|
20 |
1 |
2.995732 |
0.7 |
19.4 |
0.036082 |
0.963918 |
1.037433 |
0.036749 |
-3.30364 |
|
2.995732 |
-3.30364 |
|
70 |
2 |
4.248495 |
1.7 |
19.4 |
0.087628 |
0.912372 |
1.096044 |
0.091708 |
-2.38915 |
|
4.248495 |
-2.38915 |
|
250 |
3 |
5.521461 |
2.7 |
19.4 |
0.139174 |
0.860826 |
1.161675 |
0.149863 |
-1.89803 |
|
5.521461 |
-1.89803 |
|
320 |
4 |
5.768321 |
3.7 |
19.4 |
0.19072 |
0.80928 |
1.235667 |
0.211611 |
-1.55301 |
|
5.768321 |
-1.55301 |
|
350 |
5 |
5.857933 |
4.7 |
19.4 |
0.242266 |
0.757734 |
1.319725 |
0.277423 |
-1.28221 |
|
5.857933 |
-1.28221 |
|
360 |
6 |
5.886104 |
5.7 |
19.4 |
0.293812 |
0.706188 |
1.416054 |
0.347874 |
-1.05591 |
|
5.886104 |
-1.05591 |
|
440 |
7 |
6.086775 |
6.7 |
19.4 |
0.345358 |
0.654642 |
1.527553 |
0.423667 |
-0.85881 |
|
6.086775 |
-0.85881 |
|
480 |
8 |
6.173786 |
7.7 |
19.4 |
0.396904 |
0.603096 |
1.658111 |
0.505679 |
-0.68185 |
|
6.173786 |
-0.68185 |
|
730 |
9 |
6.593045 |
8.7 |
19.4 |
0.44845 |
0.55155 |
1.813073 |
0.595023 |
-0.51915 |
|
6.593045 |
-0.51915 |
|
800 |
10 |
6.684612 |
9.7 |
19.4 |
0.499996 |
0.500004 |
1.999985 |
0.69314 |
-0.36652 |
|
6.684612 |
-0.36652 |
|
950 |
11 |
6.856462 |
10.7 |
19.4 |
0.551542 |
0.448458 |
2.229864 |
0.801941 |
-0.22072 |
|
6.856462 |
-0.22072 |
|
1,050 |
12 |
6.956545 |
11.7 |
19.4 |
0.603088 |
0.396912 |
2.519451 |
0.924041 |
-0.079 |
|
6.956545 |
-0.079 |
|
1,100 |
13 |
7.003065 |
12.7 |
19.4 |
0.654634 |
0.345366 |
2.895481 |
1.063151 |
0.061237 |
|
7.003065 |
0.061237 |
|
1,520 |
14 |
7.326466 |
13.7 |
19.4 |
0.70618 |
0.29382 |
3.403447 |
1.224789 |
0.202768 |
|
7.326466 |
0.202768 |
|
1,580 |
15 |
7.36518 |
14.7 |
19.4 |
0.757726 |
0.242274 |
4.127561 |
1.417687 |
0.349027 |
|
7.36518 |
0.349027 |
|
1,640 |
16 |
7.402452 |
15.7 |
19.4 |
0.809272 |
0.190728 |
5.243074 |
1.656908 |
0.504953 |
|
7.402452 |
0.504953 |
|
1,830 |
17 |
7.512071 |
16.7 |
19.4 |
0.860818 |
0.139182 |
7.184847 |
1.971974 |
0.679035 |
|
7.512071 |
0.679035 |
|
1,850 |
18 |
7.522941 |
17.7 |
19.4 |
0.912364 |
0.087636 |
11.41086 |
2.434566 |
0.889768 |
|
7.522941 |
0.889768 |
|
1,900 |
19 |
7.549609 |
18.7 |
19.4 |
0.96391 |
0.03609 |
27.70866 |
3.321745 |
1.20049 |
|
7.549609 |
1.20049 |
|
TOTAL |
N=19 |
|
|
|
|
|
|
|
|
|
|
|
Table 8: Shutoff valve
|
Shut-off Valve (SOV) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
WEIBULL PLOT |
|
|
|
Failure Hours |
I |
ln t |
i-0.3 |
N+0.4 |
MR |
1-MR |
1/1-MR |
ln(1/1-MR) |
Yi, (ln2) |
|
lnt |
Yi |
|
220 |
1 |
5.393628 |
0.7 |
20.4 |
0.034314 |
0.965686 |
1.035533 |
0.034916 |
-3.3548 |
|
5.393628 |
-3.3548 |
|
280 |
2 |
5.63479 |
1.7 |
20.4 |
0.083333 |
0.916667 |
1.090909 |
0.087011 |
-2.44172 |
|
5.63479 |
-2.44172 |
|
440 |
3 |
6.086775 |
2.7 |
20.4 |
0.132353 |
0.867647 |
1.152542 |
0.14197 |
-1.95214 |
|
6.086775 |
-1.95214 |
|
800 |
4 |
6.684612 |
3.7 |
20.4 |
0.181373 |
0.818627 |
1.221557 |
0.200126 |
-1.60881 |
|
6.684612 |
-1.60881 |
|
1,660 |
5 |
7.414573 |
4.7 |
20.4 |
0.230392 |
0.769608 |
1.299363 |
0.261874 |
-1.33989 |
|
7.414573 |
-1.33989 |
|
1,840 |
6 |
7.517521 |
5.7 |
20.4 |
0.279412 |
0.720588 |
1.387755 |
0.327687 |
-1.1157 |
|
7.517521 |
-1.1157 |
|
1,900 |
7 |
7.549609 |
6.7 |
20.4 |
0.328431 |
0.671569 |
1.489051 |
0.398139 |
-0.92095 |
|
7.549609 |
-0.92095 |
|
2,120 |
8 |
7.659171 |
7.7 |
20.4 |
0.377451 |
0.622549 |
1.606299 |
0.473933 |
-0.74669 |
|
7.659171 |
-0.74669 |
|
2,620 |
9 |
7.87093 |
8.7 |
20.4 |
0.426471 |
0.573529 |
1.74359 |
0.555946 |
-0.58708 |
|
7.87093 |
-0.58708 |
|
2,720 |
10 |
7.908387 |
9.7 |
20.4 |
0.47549 |
0.52451 |
1.906542 |
0.645291 |
-0.43805 |
|
7.908387 |
-0.43805 |
|
2,820 |
11 |
7.944492 |
10.7 |
20.4 |
0.52451 |
0.47549 |
2.103092 |
0.743409 |
-0.29651 |
|
7.944492 |
-0.29651 |
|
2,840 |
12 |
7.951559 |
11.7 |
20.4 |
0.573529 |
0.426471 |
2.344827 |
0.852212 |
-0.15992 |
|
7.951559 |
-0.15992 |
|
3,480 |
13 |
8.154788 |
12.7 |
20.4 |
0.622549 |
0.377451 |
2.64935 |
0.974314 |
-0.02602 |
|
8.154788 |
-0.02602 |
|
4,240 |
14 |
8.352319 |
13.7 |
20.4 |
0.671569 |
0.328431 |
3.044775 |
1.113427 |
0.107443 |
|
8.352319 |
0.107443 |
|
4,540 |
15 |
8.420682 |
14.7 |
20.4 |
0.720588 |
0.279412 |
3.578946 |
1.275068 |
0.243 |
|
8.420682 |
0.243 |
|
5,460 |
16 |
8.605204 |
15.7 |
20.4 |
0.769608 |
0.230392 |
4.340423 |
1.467972 |
0.383882 |
|
8.605204 |
0.383882 |
|
5,840 |
17 |
8.672486 |
16.7 |
20.4 |
0.818627 |
0.181373 |
5.51351 |
1.707201 |
0.534855 |
|
8.672486 |
0.534855 |
|
5,940 |
18 |
8.689464 |
17.7 |
20.4 |
0.867647 |
0.132353 |
7.555548 |
2.022282 |
0.704227 |
|
8.689464 |
0.704227 |
|
6,760 |
19 |
8.818778 |
18.7 |
20.4 |
0.916667 |
0.083333 |
11.99998 |
2.484905 |
0.910234 |
|
8.818778 |
0.910234 |
|
7,640 |
20 |
8.941153 |
19.7 |
20.4 |
0.965686 |
0.034314 |
29.14273 |
3.372205 |
1.215567 |
|
8.941153 |
1.215567 |
|
TOTAL |
20 |
|
|
|
|
|
|
|
|
|
|
|
Table 9: Cabin temperature controller
|
Cabin |
|
|
|
|
|
|
|
|
|
|
|
|
|
Temperature |
|
|
|
|
|
|
|
|
|
|
|
|
|
Controller |
|
|
|
|
|
|
|
|
|
|
WEIBULL PLOT |
|
|
Failure Hours |
i |
ln t |
i-0.3 |
N+0.4 |
MR |
1-MR |
1/1-MR |
ln(1/1-MR) |
Yi, (ln2) |
|
lnt |
Yi |
|
270 |
1 |
5.598422 |
0.7 |
30.4 |
0.02303 |
0.97697 |
1.02357 |
0.023296 |
-3.75949 |
|
5.598422 |
-3.75949 |
|
340 |
2 |
5.828946 |
1.7 |
30.4 |
0.05592 |
0.94408 |
1.05923 |
0.057545 |
-2.85518 |
|
5.828946 |
-2.85518 |
|
910 |
3 |
6.813445 |
2.7 |
30.4 |
0.08882 |
0.91118 |
1.09747 |
0.09301 |
-2.37505 |
|
6.813445 |
-2.37505 |
|
1,510 |
4 |
7.319865 |
3.7 |
30.4 |
0.12171 |
0.87829 |
1.13858 |
0.129779 |
-2.04192 |
|
7.319865 |
-2.04192 |
|
1,630 |
5 |
7.396335 |
4.7 |
30.4 |
0.15461 |
0.84539 |
1.18288 |
0.167951 |
-1.78408 |
|
7.396335 |
-1.78408 |
|
1,800 |
6 |
7.495542 |
5.7 |
30.4 |
0.18750 |
0.81250 |
1.23077 |
0.207639 |
-1.57195 |
|
7.495542 |
-1.57195 |
|
1,960 |
7 |
7.5807 |
6.7 |
30.4 |
0.22039 |
0.77961 |
1.28270 |
0.248967 |
-1.39043 |
|
7.5807 |
-1.39043 |
|
2,350 |
8 |
7.762171 |
7.7 |
30.4 |
0.25329 |
0.74671 |
1.33921 |
0.292077 |
-1.23074 |
|
7.762171 |
-1.23074 |
|
2,600 |
9 |
7.863267 |
8.7 |
30.4 |
0.28618 |
0.71382 |
1.40092 |
0.33713 |
-1.08729 |
|
7.863267 |
-1.08729 |
|
2,630 |
10 |
7.874739 |
9.7 |
30.4 |
0.31908 |
0.68092 |
1.46860 |
0.384308 |
-0.95631 |
|
7.874739 |
-0.95631 |
|
2,720 |
11 |
7.908387 |
10.7 |
30.4 |
0.35197 |
0.64803 |
1.54315 |
0.433823 |
-0.83512 |
|
7.908387 |
-0.83512 |
|
2,840 |
12 |
7.951559 |
11.7 |
30.4 |
0.38487 |
0.61513 |
1.62567 |
0.485918 |
-0.72171 |
|
7.951559 |
-0.72171 |
|
3,120 |
13 |
8.045588 |
12.7 |
30.4 |
0.41776 |
0.58224 |
1.71751 |
0.540877 |
-0.61456 |
|
8.045588 |
-0.61456 |
|
4,550 |
14 |
8.422883 |
13.7 |
30.4 |
0.45066 |
0.54934 |
1.82036 |
0.599033 |
-0.51244 |
|
8.422883 |
-0.51244 |
|
5,210 |
15 |
8.558335 |
14.7 |
30.4 |
0.48355 |
0.51645 |
1.93630 |
0.660781 |
-0.41433 |
|
8.558335 |
-0.41433 |
|
5,630 |
16 |
8.635865 |
15.7 |
30.4 |
0.51645 |
0.48355 |
2.06802 |
0.726594 |
-0.31939 |
|
8.635865 |
-0.31939 |
|
5,820 |
17 |
8.669056 |
16.7 |
30.4 |
0.54934 |
0.45066 |
2.21898 |
0.797045 |
-0.22684 |
|
8.669056 |
-0.22684 |
|
6,230 |
18 |
8.737132 |
17.7 |
30.4 |
0.58224 |
0.41776 |
2.39370 |
0.872839 |
-0.136 |
|
8.737132 |
-0.136 |
|
7,020 |
19 |
8.856518 |
18.7 |
30.4 |
0.61513 |
0.38487 |
2.59829 |
0.954852 |
-0.0462 |
|
8.856518 |
-0.0462 |
|
8,890 |
20 |
9.092682 |
19.7 |
30.4 |
0.64803 |
0.35197 |
2.84112 |
1.044197 |
0.043248 |
|
9.092682 |
0.043248 |
|
9,570 |
21 |
9.166388 |
20.7 |
30.4 |
0.68092 |
0.31908 |
3.13401 |
1.142314 |
0.133056 |
|
9.166388 |
0.133056 |
|
10,000 |
22 |
9.21034 |
21.7 |
30.4 |
0.71381 |
0.28619 |
3.49424 |
1.251117 |
0.224037 |
|
9.21034 |
0.224037 |
|
10,940 |
23 |
9.300181 |
22.7 |
30.4 |
0.74671 |
0.25329 |
3.94804 |
1.373219 |
0.317158 |
|
9.300181 |
0.317158 |
|
11,360 |
24 |
9.337854 |
23.7 |
30.4 |
0.77960 |
0.22040 |
4.53730 |
1.512331 |
0.413652 |
|
9.337854 |
0.413652 |
|
13,970 |
25 |
9.544667 |
24.7 |
30.4 |
0.81250 |
0.18750 |
5.33331 |
1.673972 |
0.515199 |
|
9.544667 |
0.515199 |
|
17,460 |
26 |
9.767668 |
25.7 |
30.4 |
0.84539 |
0.15461 |
6.46805 |
1.866874 |
0.624265 |
|
9.767668 |
0.624265 |
|
21,110 |
27 |
9.957502 |
26.7 |
30.4 |
0.87829 |
0.12171 |
8.21615 |
2.106102 |
0.744839 |
|
9.957502 |
0.744839 |
|
21,960 |
28 |
9.996978 |
27.7 |
30.4 |
0.91118 |
0.08882 |
11.25913 |
2.421179 |
0.884255 |
|
9.996978 |
0.884255 |
|
26,750 |
29 |
10.19429 |
28.7 |
30.4 |
0.94408 |
0.05592 |
17.88201 |
2.883795 |
1.059107 |
|
10.19429 |
1.059107 |
|
31,030 |
30 |
10.34271 |
29.7 |
30.4 |
0.97697 |
0.02303 |
43.42651 |
3.77107 |
1.327359 |
|
10.34271 |
1.327359 |
Table 10: Cockpit temperature controller
|
Cockpit |
|
|
|
|
|
|
|
|
|
|
|
|
|
Temperature |
|
|
|
|
|
|
|
|
|
|
|
|
|
Controller |
|
|
|
|
|
|
|
|
|
|
WEIBULL PLOT |
|
|
Failure Hours |
i |
ln t |
i-0.3 |
N+0.4 |
MR |
1-MR |
1/1-MR |
ln(1/1-MR) |
Yi, (ln2) |
|
lnt |
Yi |
|
250 |
1 |
5.521461 |
0.7 |
31.4 |
0.022293 |
0.977707 |
1.022801 |
0.022545 |
-3.79224 |
|
5.521461 |
-3.79224 |
|
300 |
2 |
5.703782 |
1.7 |
31.4 |
0.05414 |
0.94586 |
1.057239 |
0.055661 |
-2.88848 |
|
5.703782 |
-2.88848 |
|
320 |
3 |
5.768321 |
2.7 |
31.4 |
0.085987 |
0.914013 |
1.094076 |
0.08991 |
-2.40894 |
|
5.768321 |
-2.40894 |
|
760 |
5 |
6.633318 |
4.7 |
31.4 |
0.149681 |
0.850319 |
1.176029 |
0.162144 |
-1.81927 |
|
6.633318 |
-1.81927 |
|
860 |
6 |
6.756932 |
5.7 |
31.4 |
0.181528 |
0.818472 |
1.221789 |
0.200316 |
-1.60786 |
|
6.756932 |
-1.60786 |
|
920 |
7 |
6.824374 |
6.7 |
31.4 |
0.213375 |
0.786625 |
1.271254 |
0.240004 |
-1.4271 |
|
6.824374 |
-1.4271 |
|
1,000 |
8 |
6.907755 |
7.7 |
31.4 |
0.245222 |
0.754778 |
1.324893 |
0.281331 |
-1.26822 |
|
6.907755 |
-1.26822 |
|
1,090 |
9 |
6.993933 |
8.7 |
31.4 |
0.277069 |
0.722931 |
1.383258 |
0.324441 |
-1.12565 |
|
6.993933 |
-1.12565 |
|
1,990 |
10 |
7.59589 |
9.7 |
31.4 |
0.308916 |
0.691084 |
1.447002 |
0.369494 |
-0.99562 |
|
7.59589 |
-0.99562 |
|
1,990 |
11 |
7.59589 |
10.7 |
31.4 |
0.340763 |
0.659237 |
1.516905 |
0.416672 |
-0.87546 |
|
7.59589 |
-0.87546 |
|
2,040 |
12 |
7.620705 |
11.7 |
31.4 |
0.37261 |
0.62739 |
1.593905 |
0.466187 |
-0.76317 |
|
7.620705 |
-0.76317 |
|
2,810 |
13 |
7.94094 |
12.7 |
31.4 |
0.404457 |
0.595543 |
1.67914 |
0.518282 |
-0.65724 |
|
7.94094 |
-0.65724 |
|
2,980 |
14 |
7.999679 |
13.7 |
31.4 |
0.436304 |
0.563696 |
1.774006 |
0.57324 |
-0.55645 |
|
7.999679 |
-0.55645 |
|
3,540 |
15 |
8.171882 |
14.7 |
31.4 |
0.468151 |
0.531849 |
1.880233 |
0.631395 |
-0.45982 |
|
8.171882 |
-0.45982 |
|
3,680 |
16 |
8.210668 |
15.7 |
31.4 |
0.499998 |
0.500002 |
1.999992 |
0.693143 |
-0.36652 |
|
8.210668 |
-0.36652 |
|
4,990 |
17 |
8.515191 |
16.7 |
31.4 |
0.531845 |
0.468155 |
2.136044 |
0.758956 |
-0.27581 |
|
8.515191 |
-0.27581 |
|
5,320 |
18 |
8.579229 |
17.7 |
31.4 |
0.563692 |
0.436308 |
2.291958 |
0.829407 |
-0.18704 |
|
8.579229 |
-0.18704 |
|
8,010 |
19 |
8.988446 |
18.7 |
31.4 |
0.595539 |
0.404461 |
2.472426 |
0.9052 |
-0.0996 |
|
8.988446 |
-0.0996 |
|
8,600 |
20 |
9.059517 |
19.7 |
31.4 |
0.627386 |
0.372614 |
2.683742 |
0.987212 |
-0.01287 |
|
9.059517 |
-0.01287 |
|
8,930 |
21 |
9.097172 |
20.7 |
31.4 |
0.659233 |
0.340767 |
2.934556 |
1.076556 |
0.073767 |
|
9.097172 |
0.073767 |
|
10,280 |
22 |
9.237956 |
21.7 |
31.4 |
0.69108 |
0.30892 |
3.237083 |
1.174673 |
0.160989 |
|
9.237956 |
0.160989 |
|
10,570 |
23 |
9.265775 |
22.7 |
31.4 |
0.722927 |
0.277073 |
3.609156 |
1.283474 |
0.24957 |
|
9.265775 |
0.24957 |
|
10,690 |
24 |
9.277064 |
23.7 |
31.4 |
0.754774 |
0.245226 |
4.077869 |
1.405575 |
0.340446 |
|
9.277064 |
0.340446 |
|
12,150 |
25 |
9.405084 |
24.7 |
31.4 |
0.786621 |
0.213379 |
4.686495 |
1.544685 |
0.43482 |
|
9.405084 |
0.43482 |
|
12,690 |
26 |
9.44857 |
25.7 |
31.4 |
0.818468 |
0.181532 |
5.508668 |
1.706323 |
0.534341 |
|
9.44857 |
0.534341 |
|
15,060 |
27 |
9.619798 |
26.7 |
31.4 |
0.850315 |
0.149685 |
6.680692 |
1.899222 |
0.641444 |
|
9.619798 |
0.641444 |
|
19,670 |
28 |
9.88685 |
27.7 |
31.4 |
0.882162 |
0.117838 |
8.48622 |
2.138444 |
0.760078 |
|
9.88685 |
0.760078 |
|
19,830 |
29 |
9.894951 |
28.7 |
31.4 |
0.914009 |
0.085991 |
11.62911 |
2.453511 |
0.89752 |
|
9.894951 |
0.89752 |
|
20,880 |
30 |
9.946547 |
29.7 |
31.4 |
0.945856 |
0.054144 |
18.46923 |
2.916106 |
1.070249 |
|
9.946547 |
1.070249 |
|
22,850 |
31 |
10.03671 |
30.7 |
31.4 |
0.977703 |
0.022297 |
44.84888 |
3.803299 |
1.335869 |
|
10.03671 |
1.335869 |
|
|
N=31 |
|
|
|
|
|
|
|
|
|
|
|
Temperature controller
- For each of the Weibull Probability Plots drawn in (a), construct the best-fit straight line(s) connecting failure data points, and estimate the shape parameter and scale parameter for each best-fit straight line(s).
ANSWERS
For the best-fit straight lines, check the figures (from fig 1 to 10).
The shape parameter is the slope of the best-fit straight line and is determined as follows:
Shape parameter= change in Yi/change in ln t
Hence : shape parameter 1: (0—2)/8.5-6= 0.76923 { Note that the points (8.5,0) and (6,-2) can be deduced from figure 1 in the line of best-fit. To get shape parameter, use the gradient formula, that is: change in Y/change in X and substitute the points above); repeat the same for all figures 2 to 10}
The scale parameter is derived from the intersection of the 63.2% of the y-axis range of data with the weibull distribution plot. {In other words, we determine the 63.2% of the total distance in the Y axis, then mark off the point on the Y axis, next draw a horizontal line that is parallel to the x axis and perpendicular to the Y axis crossing at the marked point, that is, the 63.2% of the total distance. Also note that, in order to get the 63.2% mark point, we must add it to the smallest data point. Note that the total distance is the difference between the largest data point and the smallest data point, and this is the range. In this case, from all figures, it can be seen that the smallest data point is negative hence the range will be just addition as shown below, therefore, the intersection of the horizontal line and the line of best-fit tracing it downwards to the X axis gives the value of scale parameter}.
This is done as follows:
In the first graph, the range is 6 , that is :(2—4)= 6 hence : 0.632 x 6 = 3.792
Then drawing the line (check figure 1), y= 3.792 + -4 = -0.208
Hence scale parameter is x= 8.5 (note that this is just but estimation as the graphs could not locate decimals)
Shape parameter 2: (0—2)/9.5-8= 1.3333
For this case, repeat the procedure in figure 1 above hence:
Range= 4+1.5 = 5.5
0.632x 5.5 = 3.476
Y= 3.476-4 = -0.524
Hence X= 9.5
Shape parameter 3: (0—3.5)/9.5-6 = 1.000
Scale parameter3: Range = 4+1 = 5
0.632 x5= 3.16
Y= 3.16+-4= -0.84
X= 9
Shape parameter 4: (0—3.5)/10-6= 0.875
Scale parameter 4: range= 4+1.2 = 5.2
0.632x5.2 = 3.286
Y= 3.286-4= -0.714
X= 9.0
Shape parameter 5: (6—1.5)/2-0= 3.75
Scale parameter 5: range= 1+2.5= 3.5
0.632x3.5= 2.212
Y= 2.212-1= 1.212
Hence x= 8.5
Shape parameter 6: 0.75—1.75/8-2=0.41667
Scale parameter 6: range = 3+1.5 = 4.5
0.632 x 4.5= 2.844
Y= 2.844+ -3= -0.156
X= 8.02 (refer to figure 7)
Shape parameter 7: (0—2.5)/7-5= 1.25
Scale parameter 7: range= 3.5+1.5= 5.0
0.632x5.0= 3.16
Y= 3.16-3.5 = -0.34
X= 6.5 (refer to figure 7)
Shape parameter 8: 0—2/8.2-7= 1.6667
Scale parameter 8: range= 1.2+3.5 = 4.7
0.632x4.7= 2.9704
Y= 2.9704-3.5 = -0.5296
X= 7.9 (refer to figure 8)
Shape parameter 9: 6.5-0/9—3=0.54167
Scale parameter 9: 1.5+4= 5.5
0.632x5.5= 3.476
Y= 3.476-4= -0.524
X= 8.5 (refer to figure 9)
Shape parameter 10: 1—3/10-5.5= 0.8889
Scale parameter 10: range = 1.2+4= 5.2
0.632x5.2= 3.2864
Y= 3.2864-4= -0.7136
Hence x= 8.1 (refer to figure 10)
- Comment on the failure patterns exhibited by each of the ten (10) components in the air conditioning and pressurisation system and estimate the MTBF values, where applicable. Appraise one usage of the MTBF data.
ANSWERS
The graphs above exhibit a generally uniform failure pattern. Therefore, in selecting the maintenance option for each case will a bit simple as one strategy can fit all (of course with slight modifications) (SAE JA, 2002). The failure is almost linearly distributed as shown in the plots. Admittedly, the best approach would be preventive maintenance where failure is predicted before it occurs and necessary action is taken such as replacements, lubrication among others (NAVAIR, 2005). However in specific terms the following strategies shall be adopted:
MTBF is often used in predicting the subsequent failures by checking at the patterns of failure henc effective maintenance strategy can be drafted. The MTBF values are obtained via finding the antilog of the respective scale parameters:
The failure pattern exhibited by each is described as follows:
|
Graphs |
PATTERN EXHIBITED |
scale parameter |
MTBF |
|
1 |
Infant mortality since there is constant wear rate |
8.5 |
4969.101 |
|
2 |
Similar pattern exhibited |
9.5 |
13524.9 |
|
3 |
Similar pattern exhibited |
9 |
8197.962 |
|
4 |
Similar pattern exhibited |
9 |
8197.962 |
|
5 |
Similar pattern exhibited |
8.5 |
4969.101 |
|
6 |
Similar pattern exhibited |
8.02 |
3072.888 |
|
7 |
Similar pattern exhibited |
6.5 |
670.7572 |
|
8 |
Similar pattern exhibited |
7.9 |
2724.985 |
|
9 |
Similar pattern exhibited |
8.5 |
4969.101 |
|
10 |
Similar pattern exhibited |
8.1 |
3329.165 |
- Recommend the appropriate maintenance option for each of the ten (10) components in the air conditioning and pressurization system. Note that some of these components may exhibit more than one failure pattern over its lifetime.
The air conditioning and pressurization system is one of the most essential subsystems in the aircraft. Failure of one component, either hidden or exposed, can have irreparable damage on the aircraft performance in the long run. It is therefore necessary that aircraft engineers stay abreast with the functioning state of each component. Reliability centred maintenance approach is one of the methods used to study the failure patterns of these components (SAE JA1011, 1999). Therefore, the report hereinafter provides an analysis of the failure patterns of these components using Weibull distribution method. Reliability centered maintenance analysis of the aircraft pressure control system was done via Weibull distribution for each part as illustrated in tables 1 to 10.
The table illustrates more specifically the maintenance strategies to adopted:
|
COMPONENT |
MAINTENANCE STRATEGY |
|
Cockpit temperature controller |
Replacements since preventive maintenance would be cheaper to undertake and for safety reasons |
|
Cabin temperature controller |
Replacements is the best option due to cost effectiveness |
|
SOV 2 |
Condition monitoring on a regular basis , it is a safety risk |
|
Pressure SOV |
Condition monitoring on a regular basis, it is a safety risk |
|
Cockpit temperature modulating valve |
Prior fault finding as a preventive inspection method |
|
ECS |
Replacements is most necessary |
|
Cabin duct temp sensor |
Condition monitoring is the best option since it is a safety risk |
|
Cockpit overtemp S/W |
Replacements is the best strategy in this case |
|
Cabin temp controller |
Regular inspection and servicing is necea |
|
Cabin temp sensor |
|
As illustrated above, failure of one component may lead to failure of the entire system. It is therefore crucial that the engineer develops an effective program to either prevent or minimize failure. Although preventive maintenance is costly to implement, however, in the long run it ensures operational stability and safety is maintained which then translates to better working conditions and increased profitability (SAE JA., 2000).
NAVAIR 00-25-403. (2005) “Guidelines for the Naval Aviation Reliability-Centered Maintenance Process,”
SAE JA1011. (1999). “Evaluation Criteria for Reliability-Centered Maintenance (RCM) Processes,”
SAE JA1012. (2002) “A Guide to the Reliability-Centered Maintenance (RCM) Standard,”
SAE JA. (2000).Defence Standard 02-45 (NES 45)
SAE JA. (2000). Requirements for the Application of Reliability-Centred Maintenance Techniques to HM Ships, Submarines, Royal Fleet Auxiliaries and other Naval Auxiliary Vessels
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