Weibull Distribution Of The Reliability Of The Approximate Confidence Limits And Bathtub-shaped Failure Rate Function And Its Statistical Analysis

The failure rate function is an important quantity charactrzing life phenomena. Many products'failure rate function exhibit bathtub shape.However,nearly none of the rate function of known distributions is bathtub shape.In this paper,a improved method of the exact joint confidence region of the two-parameter Weibull distribution is produced before a summary of bathtub-shaped failure rate which is proposed in recent years.further, A new three-parameter lifetime distribution with bathtub shape or increasing failure rate is proposed with stastical analysis ,which is simple and has the scale parameter with it to depict the failure data from most failure bathtub-shaped mechanism.So it has certain practical value.