A novel approach to modeling steady‐state process‐time with smooth transition from repetitive to semi‐repetitive to non‐repetitive (memoryless) processes

Abstract

Defining properly the time distribution of a steady‐state process is crucial to its management. A common practice is to assume that process‐time is normally distributed for repetitive processes (process has constant work‐content), and exponentially for non‐repetitive processes (memoryless; no characteristic work‐content). This dichotomous distinction ignores the majority of processes, residing in between the two extreme scenarios, the semi‐repetitive ones. These processes own a characteristic duration time (as reflected in the mode), yet part of work‐content (“process identity”) randomly varies between cycles. In this paper, we develop a unified platform to model process‐time, comprising all three types of processes. The effects of work‐content instability on shape characteristics of process‐time distribution are studied, and process repetitiveness measure, possibly to be used to monitor work‐content instability, is defined. The generalized gamma distribution is employed to approximate the (unknown) distribution of process‐time sample mean, becoming exact for the two extreme scenarios (repetitive and non‐repetitive processes).