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Answer the following questions: Part 1 (20 Points) Problem I:
The current reliability of Complex GA Aircraft Systems is unknown. The ability to gain insight into this unknown will provide the aviation community with a valuable benchmark that will assist in the development of reliability and safety requirements for future aircraft. This benchmark must be established in order to ensure that technology development, design guidelines, and work on certification standards progresses towards the effective goal of affordable technologies for small engine airplanes.
In order to provide relevant information regarding GA aircraft reliability that is conducive to the engineering goal of ensuring development of an affordable, advanced single pilot transportation aircraft, it is necessary to include airplanes that share many of the characteristics of future aircraft design. The proposed future aircraft design will consist of an aircraft with a cruise speed of 160 knots and a range of 700 nm. This aircraft is considered to be a single pilot, four-place, light-single engine piston aircraft with near all-weather capability.
Complex GA Aircraft have retractable landing gear, flaps, and a constant-speed propeller. The systems of the future aircraft will be very similar to current Complex GA Aircraft Systems and therefore, represent the population of GA aircraft used in this study. Where the futuristic airplane model did not provide guidance into design complexity or definition, typical Complex GA Aircraft architecture was assumed.
The approach used in performing the reliability study is to define the Complex GA Aircraft Systems and Subsystems for complex aircraft, collect failure data from a random sample of complex aircraft, and then analyze the data in order to determine reliability estimates. To accomplish this, Complex GA Aircraft were divided into the folloving four systems indicating primary function:
Airframe - any component or structure that is essential to the structural integrity of the aircraft.
Control - any component that controls the aircraft's attitude, heading, and altitude or changes the aerodynamic characteristics of the aircraft in the air or on the ground (excluding powerplant).
Electrical - the lighting system and any components involved in the source and distribution of electrical power.
Powerplant - any component or system that is essential to developing thrust for the aircraft.
After researching many data sources and collection methods, it is determined that failure data obtained from operational aircraft would provide a good benchmark of current system reliability and that logbooks of complex aircraft could provide the source of this failure data. The logbooks, required by law to be kept by aircraft owners, are reviewed by the Federal Aviation Administration (FAA) and cover the history of maintenance performed on the aircraft. Work performed on the aircraft is logged in these books and is signed by the mechanic vho performs the work. This provides a good source of historical data regarding airplane component failures and replacements.
The method selected for estimating the reliability of the GA Aircraft Systems is to first determine the proper distribution that models the collected failure data for each sub-system. This is accomplished by placing the failure data collected from the total number of aircraft sampled into a database and separating them according to the defined subsystems. By constructing probability plots for each subsystem, distributions that describe the failure process can then be obtained. This information can then be used to determine the probability distribution parameters.
Airframe has many components connected in series and if any of the components fails, airframe system fails. Here is the data for airframe failure times.
Given the following 20 failure times (hours):
131 325 630 1000
170 390 690 1065
223 440 725 1260
260 480 760 1320
300 540 820 1460
Assume failure times are distributed according to the two-parameter Weibull distribution.

a). By the graphic method or the method of least squares, find the Weibull parameters. The Weibull shape and scale parameters must be estimated using the Weibull probability plot paper. (2 points)
b). Determine the reliability of the Airframe at 300 hours. (2 points)
Aircraft Control system (ACS) also has numerous parts connected in series and if any Of the parts fails the aircraft control system fails. Assuming Weibull distribution, the failure times in hours data are given:
20 28 35 44 55
67 84 92 105 118
138 170 200 224 255
c). Find the Weibull parameters using the Weibull probability paper. (2 points)
d). Determine the reliability of Aircraft Control system at 300 hours. (2 points)
Powerplant system also has many components which are used to develop thrust for the aircraft. The failure times for the Powerplant system are in hours:
270
380 1220
1750
2620
3320
4060
5200
6450
e). Estimate the Weibull parameters using Weibull probability paper. (2 points)
f). Determine the reliability of the Powerplant system at 300 hours. (2 points)
Electrical system has five components involved in the source and distribution of electrical power. They are connected in mixed order (series and parallel mixed, as shown in the diagram below) and the failure times in hours are distributed as following:

Electrical System Diagram
Component 1 has been observed to follow a Normal distribution with a mean lifetime (p) of 400 hours and standard deviation (o) of 120 hours.
• Component 2 has been observed to follow an Exponential distribution and the mean time to failure (MTTF) is 450 hours.
• Component 3 has been observed to follow a Log-Norrnal distribution, and the mean value .
(p) of the natural logarithm of the life time of component is 6 and the standard deviation (o) is
1.5.
• Component 4 has demonstrated a Gamma failure distribution a = 4 and A = 0.003 (failures per hour).
• Component 5 has Nonnat failure distribution with a mean lifetime (p) of 330 hours and standard deviation (o) of 100 hours.
g. Determine the reliability of electrical system at 300 hours. (4 points)
h. Suppose the desired electrical system reliability is 99%. What improvements are needed in the electrical system design to increase the reliability to 99%? (2 points)
Further, Complex GA Aircraft's four systems indicating primary function are connected in series:

Systems Diagram
Determine the Reliability of Complex GA Aircraft system at 300 hours. (2 points)

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