Analysis of joint multiple failure mode and linear degradation data with renewals

Non-parametric estimators of various competing modes intensities and failure probabilities from linear degradation-failure time data with partial renewals are given. Decompositions of counting processes associated with degradation and failure moments are obtained. Some of these decompositions imply estimation procedures. Others are used to obtain asymptotic properties of estimators. Conditions for the uniform consistency of the estimators are given. The limit law of the estimators is obtained.