The reliability allocation topic studies how to determine the reliability of individual components in the system to ensure that the system reliability meets the design requirements. At the same time, this decision-making process needs to consider other constraints, such as the cost of improving component reliability and the feasibility of component reliability. From a mathematical point of view, this problem is a constrained optimization problem. Its task is to minimize the cost under the condition that the system reliability meets the standard. The author has seen that in existing software and literature, the methods for solving such problems usually assume that the cost equation is a smooth continuous equation for component reliability. The reason for this assumption is that the optimization algorithm they use requires the equation to be continuous and differentiable. However, such a continuous equation is either meaningless or difficult to obtain in practice. If such methods are adopted blindly, the user is actually solving the wrong problem. In this article, the author discusses a very acceptable cost equation. This cost equation may be very common. The author uses this cost equation to demonstrate how to use JMP to analyze the reliability allocation problem for two simple systems. Although the example is simple, the steps can be applied to complex systems or different but more realistic cost equations.
