Robust first-order rotatable lifetime improvement experimental designs

Abstract

Experimental designs are widely used in predicting the optimal operating conditions of the process parameters in lifetime improvement experiments. The most commonly observed lifetime distributions are log-normal, exponential, gamma and Weibull. In the present article, invariant robust first-order rotatable designs are derived for autocorrelated lifetime responses having log-normal, exponential, gamma and Weibull distributions. In the process, robust first-order D-optimal and rotatable conditions have been derived under these situations. For these lifetime distributions with correlated errors, it is shown that robust first-order D-optimal designs are always robust rotatable but the converse is not true. Moreover, it is observed that robust first-order D-optimal and rotatable designs depend on the respective error variance–covariance structure but are independent from these considered lifetime response distributions.

Keywords:

• correlated error
• lifetime distribution
• mean life
• response surface
• robust rotatability

Acknowledgments

The authors thank editor and the referees who have provided valuable comments to improve this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP)(No. 2011-0030810).