Track: Quality Engineering, Control and Management

Abstract

The np control chart is used to monitor the number of nonconforming items in a sample. A new np control chart was introduced recently by utilizing the information on the past subgroups via the idea of multiple dependent state sampling. Unlike traditional control charts, this chart is known with two pairs of control limits. This paper proposes an economic model with statistical constraints based on Lorenzen & Vance cost function in order to determine best design parameters of the new np chart. Moreover, the model is extended under linear, quadratic, exponential, and inverted normal loss functions. Accordingly, the same magnitude of deviations from the target results in different quality costs. A solution procedure is presented for optimally specification of five design parameters. Based on numerical studies, the algorithm procedure is illustrated and some comparisons are made to evaluate the performances of economic design (ED) versus economic-statistical design (ESD). The sensitivity of the optimal cost and the chart parameters for different loss functions and input parameters is investigated. The results have indication of significant improvement in statistical performance for ESD despite a small increase in cost due to the statistical constraints added to ED