Tolerance design deals with manufacturing uncertainties, while minimizing production cost. Various methods have been proposed for statistical analysis such as root-sum-squares (RSS) method, first-order reliability method (FORM), second-order reliability method (SORM), Monte-Carlo simulation and experimental design techniques. These methods have advantages and disadvantages in terms of accuracy, computational complexity and application scope. Experimental design techniques are one of popular choices and are taken up in this paper.
The design variables in a statistical tolerancing are assumed as distributed according to some probability distributions appropriate for such uncertainties. In usual statistical tolerance analyses, they are taken as normally distributed. There are cases, however, that the normal distribution is not reasonable enough. The experimental design technique in the literature, which has been limited only to normally distributed random variables, is extended to handle nonnormal cases. It is based on the three-level Taguchi method and optimum levels and weights to handle nonnormal distributions are derived. It is easy to implement and provides good results for the moments of system response functions compared with other traditional methods. The experimental design technique also needs no derivatives and little computation as opposed to the Monte-Carlo simulation. Although this method gives only estimates of the first four moments (mean, standard deviation, skewness, and kurtosis) of the system response function, the type of probability distribution can be determined by using the Pearson system.
For many tolerance design problems, it is required to consider several simultaneous and correlated system requirements. In this paper, the system reliability is approximated by using the Ditlevsen's bounds. The correlation coefficients between the system requirements can be obtained by the proposed experimental design technique. It is expected that the proposed procedure may give the system reliability with better accuracy than other traditional approximate methods since the probability of each failure function and correlation coefficients are calculated more accurately. This is illustrated in examples for tolerance analysis and synthesis. An approximate sensitivity analysis method using the experimental design technique is also proposed. This requires little computational efforts while obtaining good accuracy. This sensitivity analysis combined with the proposed reliability analysis is very suitable for probability based optimal design.
The proposed procedure of tolerance analysis and design is applied to some examples containing various nonnormal distributions. This shows that the proposed method is practicable with very good accuracy and efficiency, regardless of the type of distributions.
