A new application of network reliability is proposed to help analyze a business process performance in usual business activities. This research is to construct an easy, formal and mathematical tool to probe the health of daily-run business activities. A business activity consists of a series of value-added tasks, which are carried out by their related attenders, to meet business objectives. Traditional management behaviors include practices and skills to sustain the plan, sanction, management, and analysis of business activities. However, the assessment of activity performance remains a weak gap in analytic requirements. The approach proposed in this paper is one of the expected tools to fill the gaps in traditional management practices. The paper is to provide managers several new visions of modeling and analysis, which are not easily derived by traditional management practices. A distributor process with several scenarios to explain the approach are explored, and discussed.