Question

In a manufacturing process that laminates several ceramic layers, 1% of the assembles are defective. Assume that the assemblies are independent.
a) What is the mean number of assemblies that need to be checked to obtain 5 defective assemblies?
b) What is the standard deviation of the number of assemblies that need to be checked to obtain 5 defective assemblies?
X = number of assemblies needed to obtain 5 defectives.

Answer 1

@ybarrap

Answer 2

a) If 1% are defective and you want to know how many to check to get 5 defective ones, then 1% of X = 5 or
$$
.01X=5\\
\implies X=\cfrac{5}{.01}
$$
Round up to closest integer.

b) In a discrete uniform distribution, the variance \(\sigma\) is
$$
\sigma=\sqrt{\cfrac{n^2-1}{12}}
$$
Where n=X found above (must be integer).

http://en.wikipedia.org/wiki/Uniform_distribution_%28discrete%29

Answer 3

Correction:
*In b), the formula I have there is the standard deviation \(\sigma\), not the variance. Standard deviation is the square root of the variance.

Answer 4

what type of distribution is this : I mean binomial, geometrical Poisson
...

Answer 5

i guess it should be negative binomial distribution @ybarrap

Answer 6

We assume that errors are uniformly distributed. There is no justification for using another type: http://en.wikipedia.org/wiki/Maximum_entropy_probability_distribution#Uniform_and_piecewise_uniform_distributions

Answer 7

We assume the defects, not the errors, are uniformly distributed between 1 and X.

Answer 8

\[σ^{2}=\frac{ k(1-p) }{ p ^{2} }\]

Answer 9

k=5
p=0.01

Answer 10

So you are assuming a geometric distribution. That makes sense.

Answer 11

yas correct

Answer 12

So then the average number of trials for 1st defect = 1/.01 then for 5 defects, it would be X=5*(1/.01)=500.

Answer 13

And your variance above would be correct. Just need to take the square root for standard deviation.

Answer 14

yes , o got it and the standard deviation is the square root of variance

Answer 15

yes , i did ,,bye the way tnx a lot

Answer 16

good question. you're welcome