Integration of SPC and performance maintenance for supply chain system

In this paper, a supply chain system is viewed as a maintainable system, and the economic-statistical design of a likelihood ratio control chart with a maintenance application is considered for this system. The supply chain system is described by a three-state: normal state, warning state and failure state. A likelihood ratio control chart is used to monitor the system given that only categorical observations can be obtained. When the chart signals, a full inspection is performed to determine the actual system state (normal or warning), and preventive maintenance is immediately performed in the warning state. In addition, the supply chain system must be corrected upon failure (i.e. corrective maintenance), and should be maintained in a scheduled time (i.e. planned maintenance). A mathematical model is developed for the joint optimisation of the control chart parameters and planned maintenance time based on renewal theory. An example is presented to illustrate how to determine the optimal design parameters. We also investigate the effect of coefficients and statistical constraints on the decision variables and the expected cost.