SKEDSOFT

Example:Write out a functional form which is a second order polynomial with two control factors and two noise factors and calculates the related c vector and C and D matrices assuming there is only one quality characteristic?

Answer:

Robust Design Based on Profit Maximization:

Robust Design based on Profit Maximization (RDPM) methods generally require all of the inputs that response surface methods (RSM) require. These include (1) an “experimental design”, Ds and (2) vectors that specify the highs, H, and lows, L, of each factor. In addition, they require (3) the declaration of which factors xc are control and which are noise z.

Algorithm Robust Design based on Profit Maximization:

Step 1:If models of the pr(xc) for all quality characteristics are available, go to Step 6. Otherwise continue.

Step 2:For each quality characteristic for which pr(xc) is not available, include the associated response index in the set S1 if the response is a quality characteristic. Include the response in the set S2 if the response is the fraction nonconforming with respect to at least one type of nonconformity. Also, identify the specification limits, LSLk and USLk, for the responses in the set S1.

Step 3:Apply a response surface method (all steps except the last, optimization step) to obtain an empirical model of all quality characteristics including the production rate, yest,r(x c,z) for r = 1,…,q.

Step 4:Estimate the expected value, μz,i, and standard deviation, σz,i, of all the noise

factors relevant under normal system operation for all i = 1, …, mn.

Step 5:Estimate the failure probabilities as a function of the control factors, pr(xc) for all quality characteristics, r ∈S1

Step 6:Obtain cost information in the form of revenue per unit, w0, and rework and/or scrap costs per defect or nonconformity of type wr for r = 1,…,q.

Step 7:Maximize the profit, Profit(x c), in Equation (14.3) as a function of xc.