A mathematical model is developed in this paper torepresent a deteriorating process that has multipledependent quality characteristics. The deterioration isassumed to be the combined effect of a drift and a shiftresulting from the random occurrence of assignablecauses. Consequently, the process moves into an out-ofcontrolstate where the proportion of defective itemsincreases and affects the production cost. The proposedmodel jointly determines the optimal process parameterssuch as initial process mean and the production run in thisstate which incurs minimum production cost. The jointeffect of a drift and a shift was not considered in theexisting models of the literature. Additionally, most of themodels assumed that the process has a single qualitycharacteristic. A few researchers considered a processwith multiple quality characteristics; however, theyassumed that the process has independent qualitycharacteristics. This assumption is being relaxed in theproposed model and thereby helps management to makedecisions on process adjustment based on an economiccriteria.