By R. D. Leitch
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Extra info for Basic Reliability Engineering Analysis
85/? 80/? 87/? 05/? 01/?! 02/? 85 ρ J= 0 J or (M - I)/? = 0 where I is the 3 x 3 identity matrix (with ones in the main diagonal, and zeroes elsewhere). e. Pi + Pi + P3 = 1 This gives four equations in just three unknowns. e. we can discard one without losing any information (the three equations sum to zero). Solving the equations in this case gives /?! e. 5 % of the time. There is other information that can be obtained from the transition matrix. F o r example, the time spent in each state is exponentially distributed.
The operator types in the coefficients of the transition matrix, the program subtracts one from the diagonal elements, asks the operator which of the equations is to be omitted, adds the equation expressing the fact that the probabilities sum to one, and solves these equations. The operator has the option of asking for the equations to be resolved with another equation omitted as a check, as the solution should be unchanged, entering new data, or quitting the program. The program itself has a number of checks.
5 % of the time. There is other information that can be obtained from the transition matrix. F o r example, the time spent in each state is exponentially distributed. The mean of this distribution is one over the sum of the rates at which the system goes into the other states. 18 h It is now possible to ask such questions as, what is the probability of the system being completely unavailable for longer than 1 h should it go down? 43 using the exponential distribution. 3 solves the equations using Gaussian elimination.