Economic design of an chart for short-run production

The aim of this paper is to present an economical design of an X chart for a short-run production. The process mean starts equal to μ₀ (in-control, State I) and in a random time it shifts to μ₁>μ₀ (out-of-control, State II). The monitoring procedure consists of inspecting a single item at every m produced ones. If the measurement of the quality characteristic does not meet the control limits, the process is stopped, adjusted, and additional (r-1) items are inspected retrospectively. The probabilistic model was developed considering only shifts in the process mean. A direct search technique is applied to find the optimum parameters which minimizes the expected cost function. Numerical examples illustrate the proposed procedure.