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2007-03-19 14:32:14 · 2 answers · asked by Anonymous in Education & Reference Homework Help

2 answers

"Lean Manufacturing " refers to a factory's production of an item 'at the highest quality that's possible, while attempting to keep the cost(s) of the produced item at a minimun "

Null and Alternate Hypothesis
Every statistical test tests the null hypothesis H0 against the alternate hypothesis H1. Null means "nothing," and the null hypothesis is that nothing is present. The process change or treatment makes no difference, or the process is operating properly. The null hypothesis is like presumption of innocence.
"Accepting the null hypothesis" is like acquitting a defendant. It does NOT prove that the null hypothesis is true, or that the defendant is innocent. It means there is a reasonable doubt about the defendant's guilt. In statistical testing, the significance level, Type I risk, or alpha risk is the "reasonable doubt." It is the chance of wrongly rejecting the null hypothesis when it is true. In acceptance sampling, it is the producer's risk, or risk of wrongly rejecting a lot that meets requirements.

The alternate hypothesis is that the process change or treatment has an effect, or something is wrong with the process. The Type II risk is the chance of accepting the null hypothesis when it is false. The "consumer's risk" is the Type II risk for an acceptance sampling plan. It is the chance of passing a lot that does not meet the requirements. If the Type I risk is the chance of crying wolf, the Type II risk is the chance of not seeing a real wolf. The following table explains hypothesis testing and risks.

State of nature (actual situation) Decide that there is a problem Decide that there is no problem
There isn't a problem; the situation is as it should be. False alarm risk (alpha) or Type I risk
The risk of crying wolf when there isn't one
Risk of convicting an innocent defendant
Quality acceptance sampling; risk of rejecting a good lot
SPC; risk of calling the process out of control when it is in control
Design of experiments (DOE or DOX); risk of concluding that there is a difference between the treatments when there isn't
100% - alpha
Chance of acquitting an innocent defendant
Quality acceptance sampling; chance of accepting a good lot
SPC: chance of calling the process in control when it is
DOE: conclude that there is no difference between the treatments when there isn't.

There is a problem; the situation requires adjustment Power (gamma)
A test's ability to detect a real problem, or difference
Chance of seeing the wolf
Chance of convicting a guilty defendant
Quality acceptance sampling; chance of rejecting a bad lot
SPC: chance of calling the process out of control when it is
DOE: chance of detecting a difference between the treatments
Risk of missing the problem: Type II risk (beta)
Risk of not seeing the wolf·
Risk of acquitting a guilty defendant·
Quality acceptance sampling; risk of shipping a bad lot·
SPC; risk of calling the process in control when it is out of control
DOE: chance of missing a difference between the treatments



Significance level
This is among the more confusing terms. "Does a 5 percent significance level mean there is only a 5% chance that my results are significant?" The significance level is actually the alpha, or Type I risk. If the null hypothesis is true, there is a 5 percent chance of rejecting it because of random variation (luck).
Statisitical tables also can be confusing. The significance level (Type I risk, alpha risk) is the UPPER tail of the distribution (for the F and chi square distributions). The figure shows a chi square distribution with 6 degrees of freedom. 12.59 is the 95th percentile of the distribution. If we run an experiment whose result follows a chi square distribution with 6 degrees of freedom, and the null hypothesis is true, we expect to get chi square =< 12.59 95 times out of 100. If chi square > 12.59, there is only a 5 percent chance that it's just luck or variation, and we can be 95 percent sure that the null hypothesis is false. We can "convict the defendant (the null hypothesis) beyond a reasonable doubt." In statistics, we can quantify this "doubt" as the significance lev

Power
A test's power improves with sample size. Tests also become more powerful as the situation gets worse. As the wolf gets closer, the shepherd is more likely to see it. In statistical process control (SPC), the only way to improve the chart's power without increasing the false alarm rate is to use a bigger sample.
In SPC, the average run length (ARL) is the average number of samples that we will take before we detect an out of control condition. It is the reciprocal of the power. If there is a 10 percent chance that a point will be outside a control limit (because the process has shifted) we will, on average, take ten samples before this happens.

* Some people say that a control chart is not a hypothesis test. The original philosophy was that +/- 3 sigma control limits will capture most (~99.73 percent) of the random variation in any process, even one that does not follow a normal distribution. Modern computers, however, can characterize even highly nonnormal processes (e.g. gamma distributions, common when there is a one-sided specification, especially impurities). We can, therefore, characterize a nonnormal process and set appropriate control limits for it. In any event, when we start talking about average run lengths, and a control chart's false alarm risks, this implies a hypothesis test. "It looks like a duck, walks like a duck, and quacks like a duck..."

2007-03-19 18:07:47 · answer #1 · answered by shitstainz 6 · 0 0

A hypothesis is once you advise a given situation which does no longer definitely exist. All you're doing is putting ahead your ideas on the placement. you should provide someone a hypothetical situation to purpose to describe your perspective. you should hypothesize that waste administration should be more advantageous powerful managed if individual people recycled more advantageous, or that they used the waste products to fireside furnaces that could be used to warmth cities. They attempt this in Calgary in Canada. or possibly the position land fill web pages are placed, you should hypothesize that they retrieve powerful metals from used products that were buried in those web pages, and the money from the sale of those metals should be used to re-plant timber. there are various parts open to you to come across any of those avenues.

2016-11-26 23:39:19 · answer #2 · answered by sebring 4 · 0 0

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