Hypothesis Testing and Confidence Intervals for Products and Quotients of Poisson Parameters with Applications to Reliability

X1 X2, ···, Xk1, Y1, Y2, ···, Yk2 are k1 + k2 mutually independent Poisson random variables with parameters λ1, λ2, ···, λk1, μ1, μ2, ···, μk2, respectively. Confidence intervals and tests of hypotheses for the parameter θ = λ1λ2 ··· λk1 / μ1μ2 ··· μk2 are obtained. Under suitable conditions these procedures may be used to obtain approximate confidence intervals and tests of hypotheses of the parameter ρ = ρ1ρ2 ··· ρk1/ρk1+1ρk1+2 ··· ρk1+k2, where the ρi's, i = 1, 2, ···, k1 + k2 are binomial parameters. This problem is of importance in reliability analysis and some applications to reliability analysis are exhibited.