Abstract: For one unit repairable system having a normal distribution of products quality failure,considering random shift,a joint economic design approach to Variable Sampling Size and Control Limits(VSSCL) X-bar control chart and preventive maintenance policies is discussed.Firstly,an integrated frame structure on VSSCL X-bar control chart and preventive maintenance policies is developed to reveal the running coupling mechanism between control chart and preventive maintenance policies.Secondly,for the integrated frame structure,probabilities models of four repair events which can lead to system renew are given based on VSSCL X-bar control chart and the system condition characteristic parameters.Then,a mathematical decision model on joint economic design for dynamic SPC and preventive maintenance policies is presented to find the minimization average cost per unit time according to renew theory and the law of total probability decomposition,and a comparison shows that the proposed joint economic design model has a lower average cost per unit time than previous independent economic design model.Finally,a sensitivity analysis for model parameters was conducted by using orthogonal regression design.

Key words: one unit repairable system, VSSCL X-bar control chart, preventive maintenance, joint economic design