Cost-quality trade-offs are required when manufacturing industries seek to minimize cost and maximize product quality or reliability. We report a challenging cost-quality tradeoff problem for a consumer goods industry where both cost and quality are modeled together. First we present a 10-step systems engineering methodology for quality improvement of manufacturing systems and comprehensively discuss the cost of quality step. The methodology investigates in detail inspection strategies of the manufacturing systems by exploring four alternative strategies. Key elements in this investigation consists of modeling the appraisal costs that involve costs to detect a non-conformed unit through inspection or testing, and failure costs that involve costs of rework, scrap, warranty claims and loss of goodwill and sales. Among the main findings of the research is that optimum inspection strategy can be achieved by modeling the cost savings from each strategy and plotting against non-conforming rates shipped to the customer and additional external failure premium.