# Validation Sampling for Variable Data...

## Information & Training. | SPC and Statistical Methods for Process Improvement.

Looking at the PQ (Process Qualification) element of a process validation, our objective is to minimize the risk of failing the PQ portion of a validation when the actual process output meets the specification requirements.

**A validation sampling plan is designed by determining a sampling rate where the LTPD (or RQL) is equal to the Spec-AQL.**

Note:

LTPD = Lot Tolerance Percent Defective

AQL = Acceptable Quality Level

Spec-AQL = the AQL a product or process must meet and is called out by specification.

RQL = Rejectable Quality Level

Validation sampling plans, unlike routine inspection plans, provide high confidence in meeting the Spec-AQL when the sampling plan is passed.

When (say) an RQL-05 is used, the probability of passing a validation sampling plan when the true defective rate is above the Spec-AQL does not exceed 5%. The probability of passing a validation sampling plan, when the true quality is equal to the Spec-AQL, is only 5%.

A key point, is that validation sampling plans are conservative by design. They provide high power at the Spec-AQL, meaning there is only a small chance of passing the PQ when the true process defective rate exceeds the Spec-AQL. However, validation sampling plans tend to reject processes that truly meet Spec-AQL requirements.

In order to routinely pass a validation sampling plan, the true defective rate of the product or process must be well below the Spec-AQL. Assuming this to be the case, a carefully designed sampling scheme can provide better odds in passing the PQ when the product or process truly meets specifications.

**Application of a Variable Sampling Plan.**

A common approach to PQ is to run the PQ over several independent “runs” or “shifts”, whereby the process is independently reset each time. Three independent runs or shifts appear to be the generally accepted practice. This provides evidence that the process is reproducible. In the world of attribute sampling, it is easy to break-up the sampling plan over three runs. For example, assume the SPEC-AQL is 1% defective. One possible sampling plan providing high confidence in meeting the Spec-AQL when passed would be: n=300, a=0.

One approach would be to conduct three runs of 100 units each. Finding zero defects, across the three runs would provide 95% confidence that the process meets the Spec-AQL. If three runs were conducted whereby 300 units were collected each time, this would be the equivalent to passing the sampling plan, n=900, a=0. In comparing the AQL’s of these two plans, the actual process for the latter must be three time better. (1/3 the level of defects) to have the same chance as passing n=300,a=0. In fact, the AQL for the plan n=900, a=0 is 0.0057% which is 175 times below the Spec-AQL of 1%. In contrast, the AQL for the sampling plan: n=300, a=0 is 0.017% or only 60 times below the Spec-AQL of 1%.

There is one primary challenge when trying to apply this same approach to variable data. Because the process is reset each time between runs, the average will most likely have a different aim. This would tend to inflate the overall variation. To properly evaluate the variable sampling plan, all data must be combined. Combining the data from the three independent runs results in the distribution being labelled “overall process”.

While it is possible for each run to have the same aim, it is highly probably that the aims of each run differ to some degree. It is clear to see that the capability of the distribution for the combined runs would generally be slightly to dramatically lower than the capability of the individual runs.

Alternatively the same sampling plan could be run and independently evaluated three times. While this eliminates the inflated variation issue, this approach brings up issues similar to the one stated in the attribute case. For example, assume the Spec AQL=1% and we have a one sided specification only. One possible variable sampling plan would be, n=125, k=2.63. Running the plan three times would bring similar issues to that of the attribute case n=900, a=0. While the chances of passing this sampling scheme is better than in the attribute case (primarily because we are working with variable data), the chance of passing is, much reduced over running the sampling plan just one time.

A superior approach would be to find a sampling plan such that passing it three times provides 95% confidence that the product or process is good. We know that 95% is equivalent to saying the probability of passing the sampling plan, if the true defect rate were equal to the Spec-AQL, is 5%. Therefore we want to develop a variable sampling plan, whereby passing it three times provides 95% confidence at the Spec-AQL. We can represent this in equation form. Passing this sampling plan three times provides 95% confidence that the true defective rate does not exceed 1% defective.

Therefore we must find a sampling plan, having approximately a 36% chance of passing on its own (i.e. a sampling plan having 64% confidence). If we perform and evaluate three independent runs using this plan and pass each time, we can say we are 95% confident that the true defect rate does not exceed the Spec-AQL.

**Attribute Validation Sampling Plans.**

Spec-AQL n a Confidence Level

1% 300 0 95% *

1% 100 0 64% **

* Three runs provide a 99.9% confidence level which is too high in a practical perspective.

** Three runs provide 95% confidence, confidence level is appropriate.

**Variable Validation Sampling Plans.**

Spec-AQL n a Confidence Level

1% 125 2.63 95% *

1% 50 2.45 64% **

* Three runs provide a 99.9% confidence level which is too high in a practical perspective.

** Three runs provide 95% confidence, confidence level is appropriate.

**Comment.**

64% confidence implies a 36% chance of passing when the actual process defective level is at the Spec-AQL.

95% confidence implies a 5% chance of passing when the actual process defective level is at the Spec-AQL.

**Summary.**

The above provides a simple sampling strategy to reduce the risk of rejecting a good validation (i.e. failing the sampling plan when the product or process truly meets performance specifications) when dealing with variable data.

## Information & Training.

## SPC & Statistical Methods for Process Improvement.

- Process Capability. Variability Reduction. Statistical Process Control.
- Pre-Control. R&R Studies.
- Process capability indices Cp, Cpk, Cpm, Capability ratio.
- Performance indices Pp and Ppk.
- Variable Control Charts.
- Attribute Charts.
- Pareto Charts.
- Individual – X Charts.
- Histograms / Process Capability Analysis.
- Scatter Diagrams.
- Etc. … Etc. …
**Information & Training presentation >>>**