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productivity
Productivity is a measure of the efficiency of production. Productivity is a ratio of what is produced to what is required to produce it. Usually this ratio is in the form of an average, expressing the total output divided by the total input. Productivity is a measure of output from a production process, per unit of input.
At the national level, productivity growth raises living standards because more real income improves people's ability to purchase goods and services, enjoy leisure, improve housing and education and contribute to social and environmental programs. Productivity growth is important to the firm because it means that the firm can meet its (perhaps growing) obligations to customers, suppliers, workers, shareholders, and governments (taxes and regulation), and still remain competitive or even improve its competitiveness in the market place.[1]

INTRODUCTION
For years, quality and productivity have been viewed as two important indexes of company performance, especially in manufacturing industries. However, they are always emphasized separately. The main reason that quality and productivity are not emphasized simultaneously is that the objectives of quality management and productivity management are traditionally viewed as contradictory (Deming, 1986; Belcher, 1987; Hart and Hart, 1989; Darst, 1990; Kaydos, 1991; Omachonu and Ross, 1994). Recent research indicates that quality and productivity should have a positive relationship. However, this theory is primarily based on logical reasoning and not empirically tested models.

Few mathematical models regarding the relationship between quality and productivity have been proposed. Unfortunately, the existing models have major deficiencies. These deficiencies cause the existing models to not be applicable in the real world.
This article studies a mathematical relationship between quality and productivity. Since the definitions of quality and productivity are different, it is necessary to select a

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