# What is the 95 x 95 Inspection Level? Either an attribute or variables type plan

R

#### rschoi

One is the so-called 95/95 requirement;
the other a 95% confidence interval on an average result.
A 95/95 type requirement may be met by either an attribute or variables type plan ;
the confidence interval on an average is met by a variables plan.

95/95 - Variables
We wish to be 95% sure that at least 95% (of the items being sampled) fall within the tolerance. To do this we project a frequency distribution and observe that it falls well within the required tolerance.
Tolerance limits which are a function of the sample size, sample average, and standard deviation are calcuated. These tolerance limits must be within the specification limits for acceptance.
Acceptance calculations are made as follows. For the sample size an appropriate " K-factor" is found in a table. (An except from a table is shown below.)
n k
5 5.079
6 4.414
7 4.007
8 3.732
9 3.532
10 3.379
Let us assume that we are sampling 10 items to evaluate against a specification of 100 ¡¾10 pounds. An average of 104 pounds and a standard deviation of 2 pounds is calculated. The 95/95 limits are x-bar ¡¾Ks, or 104¡¾ (3.379) x (2) or 104¡¾6.758. The limits are 110.758 and 97.242 pounds. Since the 110.758 value is greater than the maximum requirement of 110, we would reject the lot.
As I know, The 95 limit is the confidence interval on an average.
The 95/95 limits are ......?

Thank you very much.

[This message has been edited by rschoi (edited 10 April 2000).]

D

#### Don Winton

I know the 95% confidence level. But I don't know the 95% x 95% confidence level.

Frankly, I need more info. I have never heard of a 95% x 95% confidence interval.

Regards,

Don

#### Marc

##### Hunkered Down for the Duration
Staff member
This is an 'Oldie', but has anyone heard of a 95 x 95 Inspection Level?

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Marc said:
This is an 'Oldie', but has anyone heard of a 95 x 95 Inspection Level?
I have heard that in the context of "I am 95% confident that 95% of the parts being inspected are acceptable". Which is more of an attribute sample rather than a variable.

L

#### Lauren

Marc said:
This is an 'Oldie', but has anyone heard of a 95 x 95 Inspection Level?
The sampling standards, are generally based on 95% confidence interval (that is why we cannot use them for some critical applications, such as Class III medical devices that might require the CI to be 99% or even higher!). That means that we accept the fact, that the sampling distribution is not exactly reflecting the populationand the mean of the sampling distribution may differ from the mean of the population up to 5%. At the same time the Type 1 (alpha) error, also known as producer risk and Type II (beta) error, also known as consumer risk need to be taken into consideration. The majority of scientific sampling plans are constructed with the assumption, that the producer risk (alpha) is 5% and it means that there is 95% probability that good product will be accepted and 5% probability that good product might be rejected by using the sampling plan. The 95% mean confidence interval and 95% probability of acceptance of good product by using the sampling plan is providing the 95X95 inspection plan, by using either ANSI/ASQ plans for attribute inspection, or C=0 plans, etc.. By the way, the sampling plans assume the consumer risk (beta) to be 10%, which means that 10% of bad product might be accepted by using the sampling plan
Hope it helps.

Lauren.

D

#### Dave Strouse

Not so.

Lauren -

You said
"By the way, the sampling plans assume the consumer risk (beta) to be 10%, which means that 10% of bad product might be accepted by using the sampling plan
Hope it helps."

Sorry, but if you are talking about ANSI Z1.4 plans and AQL this is an absoulutely incorrect statement.

Look at the OC curves.

#### Tim Folkerts

Super Moderator
Lauren,

95% chace of acceptance is a good rule of thumb, but when I looked closely, I discovered that even within a specific plan (e.g. Normal, Level II, AQL=1), the chance of accepting a lot can vary considerably (from around 99% down to around 90%, depending on the lot size). Tightening tends to increase the risk of rejecting a good lot but also increases the odds of rejecting a bad lot; reduced sampling tends to reduce the risk of rejecting a good lot, but also increases the odds of accepting a bad lot.

That is one reason I have a couple of times in small ways advoacted getting rid of table-based plans like Z1.4 (or MIL-STD-105, or any of the others) and simply creating a software-based standard where you could specify probabilities instead of such vagaries as Inspection Level and Type. You would instead state someing like "Sample using a plan with alpha = 0.05 for lots with 1% defective, and beta = 5% for lots with 5% defective." You plug it into the computer and it spits out a sample size, an accept number and a reject number.

You could even borrow some of the old language, so that "Normal" might mean
alpha = beta =0.05, AQL would become the % defective associated with alpha, "Level II" would relate to the % defective associated with beta. The only drawback might be that people would actually see how big of risks they are taking and get scared away from sampling -- then again, maybe thats not a bad thing !

It just seems in the era when everyone has a computer that could instantly calculate the sampling plan to go with any parameters you could desire, using a printed table is so old-fashioned. But that is just my little soapbox

Tim F

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