Analysis of batched service time data using Gaussian and semi-parametric kernel models

Batched data is a type of data where each observed data value is the sum of a number of grouped (batched) latent ones obtained under different conditions. Batched data arises in various practical backgrounds and is often found in social studies and management sector. The analysis of such data is analytically challenging due to its structural complexity. In this article, we describe how to analyze batched service time data, estimate the mean and variance of each batch that are latent. We in particular focus on the situation when the observed total time includes an unknown proportion of non-service time. To address this problem, we propose a Gaussian model for efficiency as well as a semi-parametric kernel density model for robustness. We evaluate the performance of both proposed methods through simulation studies and then applied our methods to analyze a batched data.