M Greenaway said:

I am now thinking that it is of one or more components is defective then the assembly fails, hence we need to OR all the possible combinations of ANDs.

So the assembly fails if we have one defective component, or two, or three, or four, or five, or six (all).

Which would be 0.14 + 0.14^2 + 0.14^3 + 0.14^4 + 0.14^5 + 0.14^6

Right idea, but not quite complete.

The odds of all six being bad are indeed

0.14^6

The odds of one being good and five bad are

(0.86) * (0.14^5) * 6.

*(The 0.86 is the odds that the first is good; the 0.14^5 are the odds that the next five are all bad; the 6 is for 6 choices for which one is bad.)*
The odds of two good and four bad are

(0.86)^2 * (0.14)^4 * (6*5/2)

The odds of three good and three bad are

(0.86)^3 * (0.14)^3 * (6*5*4/2/3)

The odds of four good and two bad are

(0.86)^4 * (0.14)^2 * (6*5*4*3/2/3/4)

The odds of five good and one bad are

(0.86)^5 * (0.14)^1 * (6*5*4*3*2/2/3/4/5)

Then, as you say, we need to add up the five terms. Plug it into excel and you get a total of 59.5% bad, which is what I got before .

NOTE: using the same formula, the odds of all sixe being good are

(0.86)^6 * (0.14)^0 * (6*5*4*3*2*1/2/3/4/5/6)

= (0.86)^6 *1 * 1

(again in agreement with my previous calculations).

Tim