A reliability test-plan for series systems with components having stochastic failure rates

This paper proposes a reliability test plan for a series system, by considering the parameter λ_j of the exponential distribution to be a random variable having uniform distribution over [0, θ_j], j = 1, 2,..., n. Explicit expressions are obtained for the optimal values of the t_j, when the number of components in the system is 2. The general solution, albeit implicit, has also been obtained when the number of components in a given system is ⩾3. Mathematical programming is used to find the optimal solution and to illustrate it with numerical results