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# Consumer's risk

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## Question

Short Answer Flash Question 1 - With respect to hypothesis testing, whenever consumer's risk is decreased, producer's risk will increase. Explain if the statement is always true, conditionally true or always false (with justification).

This is a flash short answer question, open only for four hours - till 7:30 PM India time on 11th December 2018. The question needs to be answered in less than hundred words.

Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.

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Type 2 error or consumer risk error is very useful in determining sample size. Power and sample size are important and are widely used in our lives. If the pharmaceutical company wants to prove that the medicine is right they have to determine the sample size. Suppose anyone is down with fever and the doctor tells you that the medicine is 99.9% effective, you may ask doctor as to how many patients were considered in the experiment and at what confidence interval. So both the consumer and producer risk can be reduced by increasing sample size. (Obviously increasing sample size will increase the cost of inspection and this is not easy many times).

So it is not always true that reducing consumers risk will increase producers risk.

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"Whenever the consumer risk is decreased, the producer risk increases" -  this statement is always true. Risk of making an error is proportional to the tolerance that we are prepared to allow for the test. A tolerance of 5% means a confidence of 95%. Let us go with the null hypothesis that all the samples are of good quality, and set the alpha at 5%. Now, if we increase alpha to 10%, it means the customer would need less evidence to prove that the product is bad, implying his risk has decreased. Conversely, the producer’s risk has increased.

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The statement is conditionally true.

Condition being “rest of the thing remain the same”

Producer’s risk:- It is the probability of rejecting a true null hypothesis.

It is also called Alpha error or Type 1 Error or False alarms or overkill.

A Significance level of 5%, means there is 5% probability that we will reject a good product.

Consumers risk:- It is probability of failing to reject a false null hyphothesis.

It is also called as Beta error or Type 2 error or Misdetection or underkill.

A power or sensitivity of 10%, means there is 10% probability that a bad product is accepted.

Now when we try to decrease consumers risk. i.e we try to reduce bad product going to customer and  rest of the things remain the same than Producer’s risk is increased.

Analogy

Producer’s risk:- A good person is declared a criminal.

Consumer’s risk:- A Criminal is actually released.

To avoid a good person being punished, we need to check so many proofs, that because of lack of proofs sometimes a criminal is also released.

In addition, the inverse true, if we want to reduce consumers’ risk, probability of a good person getting punished increases.

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Conditionaly True

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Conditionally true.

As in the case of a zero defect organization, there will be near 100% risk free operation and production so both the risks of producer and the consumer will be in an equilibrium

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Producer's /type I/ alpha Risk(a) : when error is occurring and null hypothesis rejected then this risk occurs.

Consumer /Type II / Bita Risk(b): when error is occurring and alternate hypothesis is accepted.

In general we take it as a = 1 - b. But it depends upon which field/example we took. A famous jury case study if we consider a innocent person is getting convicted or a type II error - freeing a guilty person.

Now

Jury     =>     can be    =>    severy           =>  Some type I                No type two

Jury     =>     can be    =>    Kind              =>  No type I                     Some type two

Jury     =>     can be    =>    Normal         =>  Some type I                Some type two

Jury     =>     can be    =>    Perfect         =>  NO ERROR

When we increase the testing quality upto a certain portion Type I & Type II both gets reduced. The better the jury, the better the judgement will be.

In judiciary Type I has given more importance - so if there is doubt the person gets released - which is actually leading to increase Type II error

Concerning Bonferroni: it controls the probability of false positives only, which actually increase the probability of false negative resulting reding the statistical power again this can result a large critical values when testing large number of hypothesis.

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3 hours ago, Vishwadeep Khatri said:

Short Answer Flash Question 1 - With respect to hypothesis testing, whenever consumer's risk is decreased, producer's risk will increase. Explain if the statement is always true, conditionally true or always false (with justification).

This is a flash short answer question, open only for four hours - till 7:30 PM India time on 11th December 2018. The question needs to be answered in less than hundred words.

All rewards are mentioned here - https://www.benchmarksixsigma.com/forum/excellence-ambassador-rewards/

All questions so far can be seen here - https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/

The producer risk or type I error occurs when a true null hypothesis is rejected whereas the consumer risk or type II error occurs when a false null hypothesis is not rejected.Increase or decrease of one type error affects inversely on other type.But to control both together depends on sample size which is sometimes difficult to increase or decrease for a given situation.

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Producer's risk -  Good lot rejected due to sampling error.(Type I Error)

Consumer's risk - bad lot accepted thinking it is good.(Type II Error)

Rule : if d<=c, accept lot, else reject lot(c- acceptance number, d- defectives in sample)

In summary, type I error is falsely inferring that something is there, when it is not present  and type II is vice versa.

As per the question, when the consumer rejects the bad lot, the producer's risk will  increase.  Its true. When the correct decision is not made on rejecting or accepting the lot, the consumer might be in risk if he selects a bad lot or producer will be in risk if the right lot is rejected.

Eg. Type 1 - blood test wrongly detecting a disease when patient is actually not having.

Type II - Blood test fails to detect when the patient is suffering.

in another scenario, if the bad lot is selected by the consumer and gets affected, then the product in the market will lose its quality, brand name and its position. Hence the consumer's risk increases which also increases producer's risk.

thanks

Kavitha

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