Question

1. If you followed Taguchi’s principles, and you wanted to investigate a design with five factors at two levels, how many experiments do you need? How many would you need if you used five factors at two levels in classical statistics with full factorial experiments? Some of the participants can try their own numbers such as three factors at two levels; two factors at two levels; two factors at three levels; three factors at three levels, etc.

2. If your company policy decided on a Cp = 1.33 design, what are the specification limits going to be equal to in terms of number of sigma? And what is the expected defect rate? Some of the participants can try their own numbers such as Cp = 1.67, Cp = 1, etc.

3. According to the example of taking the defect rate and translating it into a Cpk (assuming that the specification limits are two sided and the process average m = design nominal N), what is the equivalent Cpk for a defect rate of five units per 1000 tested? Some of the participants can try their own numbers such as six defect rate per 1000 tests, etc. Each participant should have a unique reject rate translated into Cpk.

Answer 1

1. Number of experiments needed as per Taguchi's principles:

No. of factors, F= 5

No. of levels, L = 2

No. of experiments, E = 1 + F*(L-1)

= 1 + 5*(2-1) = 1 + 5*1 = 6

Number of full factorial experiments needed as per classical statistics:

E = L^F

= 2^5

= 32

2. As per the formula,

Cp = (USL - LSL) / 6*SD

where USL = Upper specification limit

LSL = Lower specification limit

SD = Standard deviation or Sigma

So, Cp = (USL - LSL) / 6*Sigma

For Cp = 1.33, number of sigma is 4.

Defect rate for Cp = 1.33 is 63 parts per million.

3. For a defect rate of 5 units per 1000 tested, i.e. 5000 units per 1,000,000 tested, Cpk value is 1.36