Title :
Distribution of the lifetime of consecutive k-within-m -out-of-n:F systems
Author_Institution :
Dept. of Stat., Bombay Univ., India
fDate :
9/1/1992 12:00:00 AM
Abstract :
The distribution of the lifetime (MTTF) of any consecutive k -within-m-out-of-n:F system, with independent exponentially distributed component lifetimes, is shown to be a convex combination of the distributions (MTTFs) of several convolutions of independent random variables, where each convolution represents a distinct path in the evolution of the system´s history, and where in each convolution all but the last random variable is exponential. The last random variable in each convolution is either a zero lifetime or the lifetime of several disjoint consecutive ki within mi-out-of-n:F systems in series with each ki<k, each mi<m, and each ni<n. This enables the calculations to proceed recursively. Calculations are facilitated by the symmetric nature of the convex combination
Keywords :
failure analysis; reliability theory; MTTF; consecutive k-within-m-out-of-n:F systems; convolution; independent exponentially distributed component lifetimes; independent random variables; lifetime distribution; mean time to failure; reliability; Failure analysis; History; Independent component analysis; Probability; Random variables; Reliability theory;
Journal_Title :
Reliability, IEEE Transactions on