Life Probability Distribution Model of Products with the Bathtub-shaped Failure Rate Changing Rule

For the products with bathtub-shaped failure rate changing rule, the characteristics of bathtub-shaped failure rate curve is analyzed and the factors affecting the failure rate change in the different stages are also studied. According to the probability distribution characteristics reflected by the bathtub-shaped failure rate changing rule, the probability distribution model of products is developed, and the corresponding models of reliability, failure rate and mean time to failure are derived. Then, the effect of parameters including the ratio parameter, the first scale parameter, the first shape parameter, the second scale parameter and the second shape parameter on the probability distribution characteristics is studied. As an example, the life probability distribution characteristics of component with bathtub-shaped failure rate changing rule is fitted with the probability model proposed. The results show that the probability model developed can be used to describe the life probability distribution chara