# Application of statistical and related methods to new technology and product development process

**BS ISO 16337**:2021 pdf free.Application of statistical and related methods to new technology and product development process一Robust tolerance design (RTD).

If the absolute error of a design parameter is larger than the specified permissible difference , the variability in the product output cannot meet the designed performance and specifications.

RTD is used by the design section to set the optimum tolerance for each design parameter to achieve the designed performance, which is evaluated based on the total variance of the product output. The permissible difference of a design parameter is the maximum allowable error around the nominal value in the manufacturing process, and it Is closely related to the cost of manufacturing.

The optimum nominal values of the design parameters can be identified by robust parameter design (RPD) through robustness measure, signal-to-noise ratiol1). The selection of a robust product by setting the nominal values as the optimum values using RPD prior to RTD is highly recommended. RPD can optimize the target product by choosing the optimum combination of design parameter nominal values from the viewpoint of the variability of the product output without increasing the costiZi.

If RPD cannot achieve a target variability, RTD is used to identify possible tolerances for achieving the target variability even at a higher cost. Smaller tolerances result in smaller variability, but this requires upgrading the parts or elements of the product, which leads to higher manufacturing cost. RTD is used to investigate the balance between product quality and improvement cost.

Even if RPD achieves the target variance, RTD is used, in some cases, to identify larger tolerances than those considered in RPD. Larger tolerances mean larger variability, but if the increased variability satisfies the target variability, the larger tolerances are applicable as they lead to reduced cost of manufacturing the designed product.

The purpose of RTD Is to achieve the target variability by setting optimum tolerances from the viewpoints of robustness, performance, and cost. For this purpose, RTD estimates the total variance of the output of the designed product if the tolerance of a design parameter is changed. The total variance can be estimated based on the results of analysis of variance (ANOVA).

If the tolerance of a design parameter is reduced, that is, A<1, the magnitude of error of the design parameter becomes smaller, and the total output variance is reduced. A smaller tolerance means that an upgraded part or element is used, so the cost of producing the new design can be higher than that of the present design.

If the tolerance of a design parameter is enlarged, that is, A>1, the magnitude of error of the design parameter becomes larger, and the total output variance Is enlarged. A larger tolerance means that a down-graded part or element is used, so the cost of producing the new design can be smaller than that of the present design.

RTD comprises two steps, as follows.

1) RTD experimentation: Collect data on the designed product, and analyse the data to determine the dependence of the product output on the design parameters.

Tolerance determination: Estimate the total variance if a tolerance is changed, and compare the

effects in quality with the cost of the change to identify the optimum tolerance.

RTD experiments collect the output data of the designed product in which there are errors in the product design parameters, and estimate the total variance and its dependence on the design parameters. The experimental design plan is used to collect the data under the combination of design parameter errors. The ANOVA results show the effects of errors in the design parameters on the product output. The product output has a target variance from the viewpoints of robustness and performance.

In RTD experiments, the design parameters are taken as noise factors. A noise factor is an experimental factor which is taken into experiment for the purpose of estimating its variability. The variance in the linear effect of errors in the design parameters is estimated.

In RPD, on the other hand, the design parameters are taken as control factors. A control factor is an experimental factor which is taken into experiment for the purpose of selecting the optimum level of the factor. Designers can fix the nominal values of design parameters to the optimum RPD values. However, in actual manufacturing, the parts or elements of the product invariably have errors, so the designer cannot specify the error of a design parameter. The designer can set only the permissible difference i as an error limit.

Design parameter errors cause variability in product output. If the error of a design parameter has a linear effect on the product output, the output variance can be changed by resetting the tolerance of the design parameter. RTD experimentation is used to determine the contributions of the effects of errors in design parameters to the product output.

In the tolerance determination step of RTD, the change in the output variance due to resetting a tolerance is estimated, and the designer selects optimum tolerance for achieving the target output variance. The optimum tolerance can be determined by balancing the effect in quality due to a tolerance change against the cost of the tolerance changel3l.

4.2 RTD experimentation

4.2.1 Data generation

RTD experimentation is used to determine the design parameters’ linear effects for the designed product. The relationship between the output by the product and the errors in the design parameters is investigated. The output data can be generated in three ways:

1) by using a theoretical formula,

by experimentation with an actual product;

3) by simulation experimentation.

When the theoretical relationship between the product output and the design parameters is known, the output data can be directly calculated for various combination of the design parameter values. RTD offers multi-factor design as an experimental design for generating the output data in various combinations of the level of experimental factors, as shown in case study (1) in Clause S. ANOVA is used for analysing the dependence of the product output on the factors.

Mathematical analysis can be applied in this case. Mathematical analysis consists of using variance estimates for a system by. for example, propagating an input variance through the system via Taylor series expansions of moment generating functionsLl.

If an actual product can be constructed, it can be used for experimentation, and the data output can be collected using the actual experiment. However, in many cases, it is difficult to set the intended levels of the errors of design parameters in an actual product because the noise levels cannot be controlled within the error distribution of the design parameters. Simulation experimentation can be used in such cases. This is why simulation experiments are often used in RTIJ. A simulation program can provide the product output data, as shown in case study (2) in Clause 6.BS ISO 16337 pdf download.Application of statistical and related methods to new technology and product development process