Integrated models and methodologies for parameter and tolerance designs

Most products are mixtures or assemblies of multiple components. These components require determining the means (nominal values) and acceptable tolerances of their relevant quality characteristics. The process of setting the means and tolerances of the components characteristics is called parameter and tolerance designs. These designs are found to be most effective when conducted simultaneously (integrated designs). In the classical models of integrated parameter and tolerance designs, the objective is to minimize the total costs while meeting the customer requirements and expectations using available technological capabilities. Total costs can be divided into two categories. The first category is the manufacturing costs, which include production and internal failure costs, i.e. costs incurred before the product is shipped to the customer. The second category is the quality losses or external failure costs, which include warranty costs, loss of market share, etc., i.e. costs incurred after the product is shipped to the customer. The major limitation of most existing integrated parameter and tolerance designs models is the use of the quadratic loss function. It is used to capture all external failure costs incurred by the manufacturer, customer, and the society as a whole as a function of the deviation of the product’s quality characteristic from its ideal value using a single proportionality constant. Despite the merits of its idea, the quadratic loss function suffers from its simplistic form and the difficulty of estimating its proportionality constant.;In this research, integrated parameter and tolerance designs models are proposed that use warranty costs instead of the quadratic loss function for estimating external failure costs. The advantage of using warranty costs is that they are related to product reliability, which can be modeled fairly accurately using empirical product failure data. However, since warranty costs are only part of the external failure costs, the first set of proposed integrated models run the risk of underestimating the external failure costs and jeopardizing the accuracy of the models results. This issue is addressed by proposing a second set of integrated parameter and tolerance designs models, which incorporate in them microeconomic and marketing concepts, such as pricing and demand functions. In these integrated models, instead of listing and estimating all external failure costs other than the warranty costs, these external failure costs are modeled as part of the customer’s decision of the amount he or she is willing to pay for the product. That is, the customer sets the purchase price based on a tradeoff between the amount of gained satisfaction and the perceived risk of using the product. As a result, the objective of these integrated models is to maximize the profit, which is the difference between the selling price and the total cost of the product, as opposed to minimizing total cost. After surveying pricing and demand models from the microeconomic and marketing literature, it is found that most pricing models use product manufacturing and quality costs in a very crude manner. Therefore, not only do the proposed integrated parameter and tolerance designs models provide a better representation of the external failure costs, but they also provide a better representation of manufacturing and quality costs of the product in the microeconomic and marketing decisions models. That is, the proposed integrated models bridge the gap between marketing and manufacturing operations and decisions by eliminating unnecessary assumptions and poor links from both areas.;Several numerical examples are presented to validate the proposed models and show their flexibility and applicability to a wide range of problems. For the first set of integrated models, in which microeconomic and marketing decisions are not considered, the examples include the cases of linear and nonlinear relationships between the product’s main quality characteristic and the quality characteristics of its components as well as the case of finite manufacturing processes. For the second set of integrated models, in which microeconomic and marketing decisions are considered, the numerical examples include the cases of static market analysis approach for a general demand function, a monopoly, and a duopoly competition as well as the case of a dynamic market analysis approach. In the different numerical examples, a variety of optimization and analysis techniques, such as nonlinear programming, integer programming, response surface methodology, simulation, and sensitivity analysis, are employed to show the methodology of handling the different design problems.