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This paper describes a novel approach based on "proportional imputation" whenidentical units produced in a batch have random but independent installationand failure times. The current problem is motivated by a real life industrialproduction-delivery supply chain where identical units are shipped afterproduction to a third party warehouse and then sold at a future date forpossible installation. Due to practical limitations, at any given time point,the exact installation as well as the failure times are known for only thoseunits which have failed within that time frame after the installation. Hence,in-house reliability engineers are presented with a very limited, as well aspartial, data to estimate different model parameters related to installationand failure distributions. In reality, other units in the batch are generallynot utilized due to lack of proper statistical methodology, leading to grossmisspecification. In this paper we have introduced a likelihood basedparametric and computationally efficient solution to overcome this problem.

An imputation-based approach for parameter estimation in the presence of ambiguous censoring with application in industrial supply chain