Quantum mechanics

Linguistics

Phase (matter)

Negative binomial distribution

Engineering

Philosophy

Ecology

Biology

Statistics

Materials science

Stress (linguistics)

Applied mathematics

Poisson distribution

Systems engineering

Distribution (mathematics)

Power (physics)

Probability distribution

Beta-binomial distribution

Geology

Paleontology

Matrix (chemical analysis)

Type (biology)

Estimation

Physics

Organic chemistry

Mathematics

Binomial distribution

Geometric distribution

Mathematical analysis

Reliability (semiconductor)

Composite material

Chemistry

Maximum likelihood

Communication in Statistics- Theory and Methods

In this paper, the stress-strength reliability of single and multi-component systems are estimated assuming discrete phase type distribution for stress and strength components. The systems with strength following mixture of discrete phase type distributions is also considered. Matrix based expressions are obtained for stress-strength reliability and its maximum likelihood estimate is obtained using EM algorithm. The numerical illustration using various special cases of discrete phase type distribution like geometric, negative binomial, generalized negative binomial and different mixtures of discrete distributions are also carried out.

Estimation of stress-strength reliability using discrete phase type distribution