Parameters determination for adaptive bathtub-shaped curve using artificial fish swarm algorithm

The bathtub-shaped curve is essential in interpreting the failure rate function for the reliability analysis, and its parameters determine the representation of the bathtub-shaped function. This paper introduces a parameterised bathtub curve that provides an adaptive bathtub-shaped failure rate function (ABF) modelling approach which can be also easily utilised as a universal objective for further optimisation studies. Inspired by the swarm intelligence of the fish schooling behaviours, the artificial fish swarm algorithm (AFSA) is an artificial intelligence algorithm which firstly simulates the behaviour of an individual artificial fish (AF) and then constructs an AF schooling. Each AF in the school searches its own local optimal solution and passes on information in its self-organised system and finally achieves the global optimal solution. In this context the AFSA is employed as the optimiser, where the fitness function of coefficient of determination (R²) is defined as a quantity for the quantitative analysis, which measures the proportion of total components for the parameters determination. A case study for a complementary metal-oxide-semiconductor (CMOS) device acceleration test has been devised and the results have shown that the proposed method can work valuably for the potential applications of bathtub-shaped failure rate function modelling and optimising.