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CHAPTER EIGHTEEN
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For a component or unit which forms part of a system mc ms ms where mc ms tc ts d tc ts mc d (1853) (1854)
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component MTBF in component operating hours component MTBF in system operating hours component operating hours system operating hours duty cycle (d tc / ts)
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The probability of both events x and y occurring Pxy is given by Pxy Px Py
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(1855) is given by (1856)
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And the probability of either event x or event y occurring Px Px where Px Py
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Px Py
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the probability of x occurring the probability of y occurring
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The following equations refer to series and parallel systems The symbols used are as above for reliability, unreliability, failure rate, etc, with the addition of appropriate subscripts as follows: Subscript s denotes series Subscript p denotes parallel Subscripts 1, 2, 3, etc denote components or subunits 1, 2, 3, etc Rs Qs Qs Rp Qp Qp Rs
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R1R2 Q1 1 R1 Q1Q2 1 e
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1 ( 1
(1857) Q2 Rs R2 R1R2 Q1Q2 (1858) (1859) (1860) (1861) (1862)
(1863) (1864) (1865)
ms Rs
(1866)
RELIABILITY, SYSTEMS, AND SAFETY ENGINEERING
n 1 n R1 R1 e e
(1867) (1868) R2 R2 e e
ms Rp Rp Rp Rp
R1R2 R3
(1869) R1R2 R2R3 R1R3 R1R2R3 (1870) (1871)
e e e 1
2 3)t
e mp mp 1
(1872) (1873)
1 2 3
(1874) 1 3 1 n (1875)
where n in Eqs (1867), (1868), and (1875) denotes the number of components or subunits having equal failure rates For a system, the utilization factor U is given by U operating time maintenance time idle time operating time (1876)
the availability (maximum utilization factor) A is given by A Umax operating time minimum maintenance time operating time (1877)
For any two sets of operating conditions denoted by x and m, respectively, the voltages Vx and Vm, temperatures tx and tm, and failure rates x and m are related by the equation
Vx Vm
(1878)
where n and K are constants over a limited range of conditions and may be determined by the equations
CHAPTER EIGHTEEN
K for a constant voltage test, and n for a constant temperature test
1 tx tm
(1879)
ln ( x / m) ln (Vm / Vx)
(1880)
SYSTEMS ENGINEERING*
SYSTEMS ENGINEERING
The design of a complex interconnection of many elements (a system) to maximize an agreed-upon measure of system performance is the basis of systems engineering Systems engineering, also referred to as system engineering, includes two parts: modeling, in which each element of the system and the criterion for measuring performance are described, and optimization, in which adjustable elements are set at values that give the best possible performance The systems approach can be applied to problems ranging from the very simple to those so complex that the human mind is unable to comprehend the reasons for system behavior A simple problem is the scheduling of the preparation of a family meal A much more complex system problem is the control of the timing of hundreds or thousands of traf c lights in a city The techniques of systems engineering have been applied to a tremendous range of current problems, from industrial automation to control of weapons and space vehicles Modeling refers to the determination of a quantitative picture of the important system characteristics This model may be in the form of collected data or analytical studies, or it may be a representation of the important system characteristics in a laboratory or computer simulation of the actual system A speci c and rather narrow systems problem is the control of traf c ow through a tunnel The designer has to maximize the number of cars permitted per hour through the tunnel To do this, the designer can vary the speed limit through the tunnel and control the number of cars within the tunnel (or the rate at which cars enter) Before a system design can be decided on, measurements are made of the way in which cars move under various speeds and degrees of congestion These data are combined with the known behavior characteristics of a driver On the basis of this quantitative information, a computer simulation of the system can be constructed from which the engineer can study the effects of different operating rules, the results of a breakdown in one lane of the tunnel, or the effect of a driver who stays below the minimum speed limit See the section Simulation below
* Excerpted from the McGraw-Hill Encyclopedia of Science and Technology Copyright 2003 by editors Used by permission of McGraw-Hill, Inc All rights reserved
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