Reliability estimation from two types of accelerated testing data considering measurement error

Reliability testing is an indispensable tool for evaluating the lifetime of a product. However, for a highly reliable product, it is quite common that a large proportion of test units will be censored in a regular life test or even in accelerated life testing (ALT) when the total testing time is too short. As an alternative, accelerated degradation testing (ADT) can be conducted to collect degradation data of a highly reliable product under accelerated conditions. For a reliability practitioner, it will be very valuable to use both ALT and ADT data for reliability estimation. In practice, degradation data are often contaminated by measurement error, which may affect the accuracy of reliability estimation. Therefore, a statistical procedure is needed when using both ALT data and ADT data with measurement error for evaluating the reliability of a highly reliable product. In this paper, an Inverse Gaussian (IG) process is used to model the degradation process of a product considering measurement error. To incorporate the two types of accelerated testing data, a new expectation-maximization (EM) algorithm is developed to estimate the model parameters by taking advantage of the parameter structure. A simulation study and a case study on a hydraulic piston pump are presented to illustrate the practical value of the proposed method in improving the accuracy of reliability estimation for a highly reliable product.