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>>p = 0.01*[13 37 12 56 33 71 22 43 57 31];>>k = [2 5 7];>>P = ikn(p,k)
P = 0.1401 0.1845 0.0225 % individual probabilities>>Pc = ckn(p,k)
Pc = 0.9516 0.2921 0.0266 % cumulative probabilities Reliability of systems with independent components
Suppose a system has n components which fail independently. Let E i be the event the i th component survives the designated time period. Then is defined to be the reliability of that component. The reliability R of the complete system is a function of the component reliabilities. There are three basic configurations.General systems may be decomposed into subsystems of these types. The subsystems become components in the larger configuration. The three fundamental configurationsare:
MATLAB solution . Put the component reliabilities in matrix
>>R = prod(RC) % prod is a built in MATLAB function >>R = parallel(RC) % parallel is a user defined function >>R = ckn(RC,k) % ckn is a user defined function (in file ckn.m). There are eight components, numbered 1 through 8. Component 1 is in series with a parallel combination of components 2 and 3, followed bya 3 of 5 combination of components 4 through 8 (see Figure 1 for a schematic representation). Probabilities of the components in order are
The second and third probabilities are for the parallel pair, and the last five probabilities are for the 3 of 5 combination.
>>RC = 0.01*[95 90 92 80 83 91 85 85]; % Component reliabilities>>Ra = RC(1)*parallel(RC(2:3))*ckn(RC(4:8),3) % Solution
Ra = 0.9172 
>>RC = 0.01*[95 90 92 80 83 91 85 85]; % Component reliabilities 1--8>>Rb = prod(RC(1:2))*parallel([RC(3),ckn(RC(4:8),3)]) % SolutionRb = 0.8532 
A test for independence
It is difficult to look at a list of minterm probabilities and determine whether or not the generating events form an independent class.The m-function imintest has as argument a vector of minterm probabilities. It checks for feasible size, determines the number of variables, and performs acheck for independence.
>>pm = 0.01*[15 5 2 18 25 5 18 12]; % An arbitrary class>>disp(imintest(pm))
The class is NOT independentMinterms for which the product rule fails
1 11 0
1 1 1 0 >>pm = [0.10 0.15 0.20 0.25 0.30]: %An improper number of probabilities>>disp(imintest(pm))
The number of minterm probabilities incorrect >>pm = minprob([0.5 0.3 0.7]);>>disp(imintest(pm))
The class is independent 
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