Robustness of the exponential sequential probability ratio test (SPRT) when Weibull distributed failures are transformed using a “known” shape parameter

Abstract

Assumptions accompanying exponential failure models are often not met in the life-testing of many products. Several authors have suggested sequential life testing techniques that transform Weibull failure times to an exponential density using the “known” Weibull shape parameter. In practice, this parameter is never known and must be estimated. This paper demonstrates that procedures based on this transformation are extremely sensitive to mis-specification of the shape parameter. Furthermore, it is doubtful that the shape parameter may be estimated with enough precision to successfully implement these procedures. Using a Weibull sequential test without the transformation yields better results; however, sensitivity analysis to shape parameter mis-specification is recommended before any specific test is implemented.