The Annals of Applied Statistics

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

Samiran Ghosh

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This paper describes a novel approach based on “proportional imputation” when identical units produced in a batch have random but independent installation and failure times. The current problem is motivated by a real life industrial production–delivery supply chain where identical units are shipped after production to a third party warehouse and then sold at a future date for possible installation. Due to practical limitations, at any given time point, the exact installation as well as the failure times are known for only those units which have failed within that time frame after the installation. Hence, in-house reliability engineers are presented with a very limited, as well as partial, data to estimate different model parameters related to installation and failure distributions. In reality, other units in the batch are generally not utilized due to lack of proper statistical methodology, leading to gross misspecification. In this paper we have introduced a likelihood based parametric and computationally efficient solution to overcome this problem.

Article information

Ann. Appl. Stat., Volume 4, Number 4 (2010), 1976-1999.

First available in Project Euclid: 4 January 2011

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Censoring imputation maximum likelihood estimation proportional sampling reliability


Ghosh, Samiran. An imputation-based approach for parameter estimation in the presence of ambiguous censoring with application in industrial supply chain. Ann. Appl. Stat. 4 (2010), no. 4, 1976--1999. doi:10.1214/10-AOAS348.

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Supplemental materials

  • Supplementary material: Furnace Data Set and R Code for Furnace Data as well as Simulation for all Models Considered in the Paper. R code is used for the simulation as well as real data analysis. Supplementary material has five files: 1. Furnace data in MS Excel format (data.xls). 2. Code for analyzing furnace data (code_furn.doc). 3. Code for the Exponential–Exponential model (new_code_Exp(2).doc). 4. Code for the Exponential–Weibull model (new_code_ExpWeb.doc). 5. Code for the Weibull–Exponential model (new_code_WebExp.doc). For the simulation examples data sets are generated on the fly at the beginning of the code. No special R package is required to run the codes. All the codes are commented for the ease of understanding.