Estimation of system reliability for independent series components with Weibull life distributions

The reliability of a series system with independent components is estimated based on random samples from Weibull failure distributions with parameters θ_i and β_i. It is assumed that the β_i´s are known, which reduces the reliability of the system to a function, γg(θ), of θ=(θ₁, . . ., θ_p). An estimate of γ(θ) which is better than the MVUE of γ(θ) in terms of mean square error is determined. The predicted reliability and the percentage improvement for this estimator is computed and compared with the usual MVUE of γ(θ). The predicted reliability using the improved estimator is numerically closer to the true system reliability