LIFE TESTING IN VARIABLY SCALED ENVIRONMENTS

Typically, accelerated life-testing models postulate a specific functi onal relationship between the stress level at which an experiment is p erformed and the parameters of the assumed family of lifetime distribu tions. These models, and the statistical analyses that accompany them, are often criticized on the basis of the dubious validity of the assu med functional relationship and of the uncertainty involved in the ext rapolation of experimental results to low stress levels at which littl e or no data have been obtained. This study focuses on an exponential factorial model for accelerated life tests that postulates that the li fetime distributions of different component types tested under varying environmental conditions are linked via environmental or component-re lated scale changes. Necessary and sufficient conditions are given for the identifiability of model parameters. For both censored and comple te data, the derivation and properties of maximum likelihood estimates of these parameters are discussed in detail. Under the conditions tha t guarantee identifiability, the existence and the uniqueness of the m aximum likelihood estimators are demonstrated, and their computation a nd large-sample behavior are discussed. In the final section, the mode l is fitted to published data from an accelerated life-testing experim ent.