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Question:

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.

Using the MS excel application; construct the Weibull Probability Plot for each of the ten components in the air conditioning and pressurization system. The cumulative distribution function may be estimated using the median rank method
Weibull Plots And Analysis

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 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

Table 2: Overtemp switch

 Over-Temp Switch 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

Table3: Duct temperature sensor

 Duct 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).

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.

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).

References

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

Cite This Work

My Assignment Help (2021) EAS437 Reliability Centred Maintenance [Online]. Available from: https://myassignmenthelp.com/free-samples/eas437-reliability-centred-maintenance/evaluation-criteria-for-reliability.html
[Accessed 02 December 2023].

My Assignment Help. 'EAS437 Reliability Centred Maintenance' (My Assignment Help, 2021) <https://myassignmenthelp.com/free-samples/eas437-reliability-centred-maintenance/evaluation-criteria-for-reliability.html> accessed 02 December 2023.

My Assignment Help. EAS437 Reliability Centred Maintenance [Internet]. My Assignment Help. 2021 [cited 02 December 2023]. Available from: https://myassignmenthelp.com/free-samples/eas437-reliability-centred-maintenance/evaluation-criteria-for-reliability.html.

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