Design method of Cpm-index based on product performance and manufacturing cost

Recently, process capabilities of machining in industries have been increasing, and customer demand for product performance is also growing. These tendencies will continue in the future, so a new tolerance method should be developed based on the product performance. The product performance of each product usually varies because a machining and an assembling errors are inevitable. Statistical tolerance index, which specifies the limits of process capability indices such as Cp,Cpk,Cc and Cpm on design drawing, is gaining attention as the new method. Process capability index is usually used to evaluate a stable manufacturing process and is defined by process mean, standard deviation and target dimension. Therefore, the statistical tolerance index (STI) can limit the process mean and standard deviation at design stage. If probability density functions of respective parts dimensions are assumed to be normal distribution, STI can limit the probability density functions. Product is consisting of parts, and product performance or quality is usually depend on parts dimensions. The probability density function of parts should be limit to control product performance at design stage. Therefore, STI can be useful tool to control the product performance or quality in a mass production process. In order to specify a suitable STI in design process, stack-up and allocation problems of the STI should be studied. In this study, an allocation method of the Cpm using genetic algorithms is proposed. The objective function is set to a manufacturing cost, and the constraints are set to requirements for product performance and yield. The product performance of mass production is quantified as inner product of probability density function and performance-function depended on a functional dimension. To evaluate an effectiveness of the method, several case studies are conducted by numerical simulation using a virtual product model which is consisting of six parts and stacking-up linearly. The cost function is assumed as the square of specified value to Cpm. Although a performance-function depends on function of product, virtual performance-function is assumed as a test. As a result, the STI are suitably allocated based on the performance and yield constraints minimizing the manufacturing cost.