Key Words: Reliability design, fractional factorial experiment, degradation, tolerance design ... extended to dynarmc fractional factorial experimental model.
Reliability Design Based on Dynamic
Factorial Experimenta1 MOdel* Kai Yang 0 Wayne State University 0 Detroit Jianan Xue 0 Wayne State University Detroit Key Words: Reliability design, fractional factorial experiment, degradation, tolerance design
SUMMARY & CONCLUSIONS This paper discusses how to apply the fractional factorial experiment method to degradation testing and reliability design. The static fractional factorial experimental model is extended to dynarmc fractional factorial experimental model. In data analysis, we suggest using degradation measure and safety margin function Z(t) as the response variable. Z(t) is similar to the signal-noise-ratio defined by Taguchi but has a clear relationship with reliability measure. Using the fractional factorial experimental models, we give a method for factorial parameter tolerance design from a product reliability requirement. An application example is given. 1. INTRODUCTION Reliability theory and technology are undergoing redirection and breakthrough. The current reliability technology, which puts the emphasis on reliability evaluation and safety analysis, fails to provide strong support to product design and manufacturing[l-6]. To satisfy the needs of concurrent engineering practice and a highly competitive world market, reliability technology must emphasize on product design and development in low cost and short period. To produce highly reliable products, the main efforts should be put on product design and manufacturing, because product reliability is mainly determined by its design and manufacturing. The current reliability design approach is based on life testing data, failure rate allocation, and system logical structure. For the systems of which the catastrophic failures are the major consideration in reliability analysis, this kind of reliability design method may work well. For most consumer products, however, this kind of reliability design method may not satisfy the design requirements. In designing consumer products, engineers usually need to connect product reliability to design parameters and their tolerances. Therefore, it is important to develop the methodology of reliability design based on design parameters and tolerances. A number of papers and books in the literature discuss how to apply fractional factorial experimental methods to reliability design [7-121. This paper will extend the static fractional factorial experimental model to a dynamic
fractional factorial experimental model, and establish the method for parameter design and tolerance design based on fractional factorial experiments. Notations: S: Aproduct; MI: A failure mode of product S; i=1,2, ...n y,: Failure indicator variable corresponding to MI, yI may be the function of time t; Y: (y1,y2,...yn)the failure indicator vector; x,: Product design parameter or environmental parameter; i=1,2,. ..,w; X: Design parameter vector. X=(x1,x2,...,x,); w: Number of the design parameters; w1: Number of the linear effect design parameters; E(t): Random variable corresponding to pure error in experimental models; (y(t), ER+}: Random process; cLy(t): Mean function of random process {y(t), tER+}; D;: The critical value of y,; o*,,(t): Variance function of random process { y(t), tER+}; cpd(t): parameter degradation capability function; Z(t): Safety margin function; ozx: variance of x,, i=1,2,. ..,n; 2 o m: Variance of IxJ; m2,: Variance corresponding to the main effect of x,; m2,,: Variance corresponding to the interaction effect of x, and x,. K,,(t): Interaction variance coefficient, the definition of K,, is in section IV. f: Continuous real function; SS: Sum-of-squares; T: Product design life. Nomenclature: Design parameters: The physical parameters of products which can be controlled in design and manufacturing process. Failure indicator parameter: The parameter which can represent the statue of the failure process. When this parameter pass over a pre-determined value, the failure will happen.
This research is supported by NSF, Grant No. DMI-9500126 0-7803-3783-2/97/$5.000 1997 IEEE 1997 PROCEEDINGS Annual RELIABILITY and MAINTAINABILITY Symposium 320 *
Failure critical value: A predetermined value which can be @ ( z i ~ )2)R*(T)'/" i=1,2, ...,n (7) used to distinguish the failure state and normal state. That is: Normal distribution random process: Random process z;(T) 2 &(R*(T)I'~) ,i=1,2,...,n (8) {y(t), teR+} is a normal distribution random process if at any The reliability requirement for product S can be expressed in time t, the random variable y(t) follows normal distribution. terms of the safety margin function: Zs(T) 2
