# The Use of PPK to Determine If Confidence and Reliability Statement is met.

#### Desmond23

##### Registered
Im trying to get my head around the relationship between the PPK for continuous data and the ability to make a Confidence and reliability statement when using a certain amount of samples to perform your testing. As an example if you wanted to make a 95%/99% CR statement and you observed that a Pre-PQ observation was a PPK of 1.09, then as per a table this allows you to choose 80 samples and as long as you get a PPK of>= 0.92 you can then make 95/99 claim. The table gives several examples using a Pre_PQ observed value so you pick the One in the table which is closest to your observed value and lower (1.05 is close and lower than 1.09).

Ive being scouring the web to find an explanation of this but have had no luck. Can any of you point me in the right direction.?
Thank you.

 Pre-PQ observed Ppk (95% confidence lower bound) Sample Size Acceptance Criteria LTPD0.05 Ppk≥1.13 n=50 Ppk≥ 0.96, Pp≥ 1.02 ≤ 1% Ppk≥1.11 n=60 Ppk≥ 0.95, Pp≥ 1.01 ≤ 1% Ppk≥1.05 n=80 Ppk≥ 0.92, Pp≥ 0.99 ≤ 1% Ppk≥1.02) n=100 Ppk≥ 0.90, Pp≥ 0.97 ≤ 1%

#### Johnnymo62

##### Haste Makes Waste
I'm curious, what type of industry is your data from? All of your Ppk data would fail in automotive because the minimum is 1.33.

#### Desmond23

##### Registered
Medical device industry. Yes I've that very same query, to me if its below 1 then it cant be capable and you are producing rejects. I did question this and was told that its all about the confidence reliability statement. So if you test 100 units and get a PPK greater than 0.90 then you can make the 95/99 statement. I don't fully understand how this is which is in essence my question.

#### Bev D

##### Heretical Statistician
Super Moderator
I’m traveling so I’ll let @Miner and @Steve Prevette give the technical answer. But what you are experiencing is the power of magical thinking. Those who believe that math can magically overcome physics; they don’t want acknowledge the physical sleight of hand that Steps around the absolute requirements and assumptions of any statistical or mathematical formula. Read Donald Wheelers “the secret foundation of statistical inference” https://www.spcpress.com/pdf/DJW288.pdf

#### Tidge

Trusted Information Resource
Louis Lyons said:
Bayesians address the question everyone is interested in by using assumptions no-one believes, while Frequentists use impeccable logic to deal with an issue of no interest to anyone.

Confucius said:
By three methods we may learn wisdom:
1. By reflection, which is noblest;
2. By imitation, which is easiest;
3. By experience, which is the bitterest.

#### Miner

##### Forum Moderator
I was staying out of this because I am not familiar with the nuances of the medical device industry. I know there are a lot of aspects about this that would never be accepted in automotive. One is the use of Pp/Ppk instead of Cp/Cpk for Pre-PQ. Another is using a threshold less than 1.33 for Pp/Ppk or 1.67 for Cp/Cpk. The table gives values very close to the 95%/99% confidence intervals for the Pp/Ppk for those sample sizes.

#### Bev D

##### Heretical Statistician
Super Moderator
Ppk should never be used to predict a DEFECT rate as (1) too many processes are non-homogenous and are under sampled and not representative of the true variation (see sampling frame) and (2) most processes are NOT Normally distributed and even if they are bell shaped the distribution of actual real life data (NOT simulated data from a theoretical model) simple don’t exist beyond 3 sigma.

The whole confidence reliability calculation requires that (1) the sampling frame include the full range of allowable variation and (2) that the sample is actually random and not a convenience sample and (3) that the nonhomogeneity of the process is taken into account in the sampling scheme. This rarely happens in real life where statistical charletons are at work.

#### Steve Prevette

##### Deming Disciple
Super Moderator
Im trying to get my head around the relationship between the PPK for continuous data and the ability to make a Confidence and reliability statement when using a certain amount of samples to perform your testing. As an example if you wanted to make a 95%/99% CR statement and you observed that a Pre-PQ observation was a PPK of 1.09, then as per a table this allows you to choose 80 samples and as long as you get a PPK of>= 0.92 you can then make 95/99 claim. The table gives several examples using a Pre_PQ observed value so you pick the One in the table which is closest to your observed value and lower (1.05 is close and lower than 1.09).

Ive being scouring the web to find an explanation of this but have had no luck. Can any of you point me in the right direction.?
Thank you.

 Pre-PQ observed Ppk (95% confidence lower bound) Sample Size Acceptance Criteria LTPD0.05 Ppk≥1.13 n=50 Ppk≥ 0.96, Pp≥ 1.02 ≤ 1% Ppk≥1.11 n=60 Ppk≥ 0.95, Pp≥ 1.01 ≤ 1% Ppk≥1.05 n=80 Ppk≥ 0.92, Pp≥ 0.99 ≤ 1% Ppk≥1.02) n=100 Ppk≥ 0.90, Pp≥ 0.97 ≤ 1%
What does "Pre-PQ" mean? What does LTPD0.05 mean? I can guess, but best to know what the author of this table used. And what is the source of this table? That would help in answering the question.

The table does seem to behave similar to the Binomial. At a high Ppk (previous low probability of defect) you need less samples to show that the chance of failure with the new population is good. Similarly, with a low Ppk (previous high probability of defect) you need much larger sample sizes to show that the new population is good. This relationship could probably also be proven with Bayesian methods.

But again, we are dealing with a third order metric - taking an actual measurement, converting it to go no-go, and then manipulating it with the normal distribution. When it may not be normal. So I am with Bev in saying this is voodoo statistics, where we actually should be working with the real data and/or creating simulations to evaluate the sample sizes needed. Even better, use Statistical Process Control, again going be to the ground "truth" rather than manipulated data.

By the way, been traveling - my wife and I just got back from Japan.

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