Upside-Down Bathtub Failure Rate from Diversity in Usage Rate

摘要

Lab tests often suggest an increasing failure rate for a product. However, failure rate from warranty data analysis is often upside-down bathtub or N-shape. Motivated by a real problem, this paper explains the discrepancies between lab test results and field return data by random customer usage rate. By supposing that lifetime of a product follows a Weibull distribution under design usage rate, we show that the field failure rate can be either decreasing, increasing, upside-down bathtub, or even N-shape, depending on the usage rate distribution and the corresponding parameters. These results are then applied to solve the motivating problem.