A machine produced 20 defective articles in a batch of 400, then after an overhaul, it produced 10 defective in a batch of 300.. has the machine improved?

Question

kropot72 · Answer

Percentage of defectives before the overhaul is given by:
$$\large \frac{20}{400}\times100=you\ can\ calculate$$
Percentage of defectives after the overhaul is given by:
$$\large \frac{10}{300}\times100=you\ can\ calculate$$
When you have done the two calculations, you should then be able to see whether the machine has improved after the overhaul.

anonymous · Answer

ans please

kropot72 · Answer

We prefer to help people to solve questions rather than just give answers. Can you do the calculations?

abb0t · Answer

These are not hard to do problems. If you have a calculator, you can do them. Put some effort into it.

mrnood · Answer

I think this may be a more complex question.

The % calculations obviously show an improvement.

BUT this may be a question about sampling and probability. 

The question should be whether the apparent improvement is statistically significant. It is entirely possible that the changes did NOT actually improve the performance - and the results are within the typical variation in the samples.

I'm afraid my stats in not up to this - but you should be careful of using 'raw' data like this as proof of improvement.

kropot72 · Answer

@MrNood This question deals with whole batches and not with samples taken from batches. When the calculations are done, it can be seen that there is a 34% reduction in defectives. Both batches are reasonably large, 300 and 400 articles, so there is a strong indication of improvement.

mrnood · Answer

Each batch is a sample from the machine's capability.
There is no indication in the question if these are 'large batches'

As I said - my stats is limited here (although I understand machine capability fairly well) and I would like to see more assurance than "there is a strong indication " to be sure that an improvement was significant

kropot72 · Answer

As you probably know, control charts are an excellent method of monitoring machine performance. Without more data being supplied with the question (such as control charts taken before and after the overhaul) it is not possible to apply statistical methods to this question.

mrnood · Answer

I have just googled "are 2 samples from the same population" and it is a bag of worms which I cannot tackle right now!

I think I might post tis as a question to see if I can get any understanding on it.