QUALITY CONTROL AND LEARNING IN PRODUCTIVE SYSTEMS by

and especially Dave Kreps have significantly improved the quality of this work. The traditional view of quality is that it is costly-higher quality requires higher units costs. A recent, renewed interest in quality has led to another point of view, namely, that producing high quality products reduces unit costs. This point of view directly challenges the traditional assumed relationship between quality and cost. If valid, the "quality is free" hypothesis has significant implications for quality management. Specifically, if producing high quality output aids in cost reduction, then firms that ignore such an effect will suboptimize on their quality levels. The work in this paper links the previously disjoint literatures of quality control and learning curves in an attempt to explain why high quality and low costs need not be inconsistent. Toward this end, we introduce the idea of a quality-based learning curve. When costs are affected by a quality-based learning curve, product quality influences the rate of cost reduction due to experience or learning. More specifically, costs decline more rapidly with the experience of producing high quality products than with the experience of producing low quality products. We first provide a formulation of an economic conformance level model based on an exposition by Juran. This formulation serves as the base-case optimal quality control model. Next, we review briefly the formulation and some results of Spences's learning curve optimization model. His model solves for the optimal production paths when unit costs decline as a function of cumulative volume. These two models are knit together into the quality-based learning model. This model incorporates the cost tradeoffs inherent in choosing the optimal quality level as well as the cost decreases due to volume-based experience. The unique additional feature of the model is the assumption that producing high quality products generates extra cost-reducing learning benefits. We provide two formulations of the quality-based learning phenomemon. The first assumes that quality-based experience affects direct manufacturing costs. For this formulation, the optimal quality level is decreasing, but is always larger then the optimal base-case quality level. The optimal production quantity is constant if the interest rate is zero and increasing when the interest ratio is positive. The second formulation assumes that quality-based experience affects quality control costs. In this case, the optimal quality level is always increasing. The optimal quantity behavior is qualitatively similiar to the first formulation. One of the key features of the second model …