Estimation of renewal function under progressively censored data and its applications

Renewal function is an important tool used by researchers in the fields of applied probability such as reliability theory, risk analysis, inventory theory and warranty analysis etc. Estimation problem of this function under complete and right censored samples is well studied in the literature. However, there isn't any study dealing with the estimation problem of this function under progressive censoring which is used widely in survival and failure analyzes. In this study, estimation problem of renewal function as well as variance function of a renewal process under progressively censored data is considered. Some parametric plug-in estimators are proposed, and their statistical properties are investigated. Consistency and asymptotic unbiasedness of these estimators are established. Possible applications of the estimators in maintenance, warranty and spare parts analyzes are investigated. Numerical procedures are provided to compute renewal and variance functions and their plug-in estimators. Small sample performances of the estimators are evaluated by a simulation study. Finally, two real data sets are examined to exhibit applicability of the estimators in some reliability problems.