A Novel Method to Estimate Mean Lifetime with Censoring in the Context of Reliability Improvement with Design of Experiments

Design of experiments has been widely applied to improve product quality and reliability. When the objective is to improve the reliability, the response of experiments is usually a life observation, and experiment is often stopped at a pre-specified time (i.e., type-I censoring) so that the gathered life data are incomplete. In this case, the traditional methods such as the Taguchi and response surface methods cannot be applied, and some assumptions have to be made so that the data can be analyzed using those methods. A typical assumption is that a right-censored time is treated as a failure time. This assumption is obviously unrealistic. To address this issue, this paper proposes a novel method to estimate mean lifetime with censoring of a right-censored time, which is used to replace the censored time. The proposed method first sorts the data in ascending order. Then, a weighted least squares method is used to fit the ordered data to a power-law model of the order number. Finally, the fitted model is used to extrapolate the mean lifetime with censoring. Three examples are included to illustrate the appropriateness and usefulness of the proposed method.