Random Sampling Theory in Clean Room Inspection Sampling Methods

Introduction

ISO 14644-1:1999 International Standard for Clean Rooms and Related Controlled Environments Part 1 "Air cleanliness classes" has been in use for five years since its release and is facing a time limit for re-examination. If it were not for this reason, the discussion about this standard might not be so intense.

Background of Standard Formulation

ISO/TC 209 is the technical committee responsible for the development of a series of international standards for "Clean Rooms and Related Controlled Environments". Its first working group is responsible for the drafting and review of iso 14644-1. As a member of this working group, I participated in the discussion of the revision of the standard. In the process, we found that there are some problems with the existing standard in theory and practical implementation.

Problems with the current standard

1. Inconsistency of confidence

The current standard ISO 14644-1 applies different confidence levels to clean rooms of different sizes. For example, the standard clearly stipulates that the confidence level of clean rooms with 2 to 9 sampling points is calculated as 15%. The confidence level of A Clean Room can be calculated by the number of sampling points. For example, the confidence level of a clean room with an area of 100 m² is only 67%. When the number of sampling points is 5 to 9, if the particle concentrations of all sampling points meet the standard and the average also meets the standard, the confidence level can reach 95%. At this time, the calculation of 95% confidence level is redundant.

2. Limitations of Sampling methods

The current standard sampling method does not allow "especially clean" areas in clean rooms. If the particle concentrations of some sampling points are abnormally low, the cleanliness of the entire clean room may not meet the standard. For example, in a clean room with 4 sampling points, if the particle concentrations are 950 particles/m³, 950 particles/m³, 250 particles/m³, and 200 particles/m³, respectively, although these values meet the ISO 4 cleanliness level, the calculated 95% confidence level does not meet the standard.

Although the standard allows to remove an abnormally low concentration value in the confidence calculation, this also brings two problems:

• For a clean room with only 3 sampling points, even if one point has an abnormally low concentration, it cannot be removed, otherwise the minimum number of sampling points will not be met.

• When there are multiple sampling points with abnormally low concentrations, after removing one low value, the 95% confidence calculation of the remaining concentration may still fail to meet the standard.

of the shortcomings of the current standard

The current sampling method has two main shortcomings: first, different confidence standards are implemented for clean rooms of different areas; second, the location with abnormally good cleanliness is not allowed in the clean room. The current standard assumes that the particle concentration in the clean room is normally distributed, emphasizes the uniform distribution sampling mode, and uses the average value as the judgment standard. However, the practical significance of this judgment method is worth discussing.

Discussion of the new sampling method

The new sampling method proposes a unified confidence level for clean rooms of various areas, that is, the confidence level of all clean rooms is 95%. This means that at a 95% confidence level, particle concentrations in at least 90% of the cleanroom area meet the standards. Such improvements are intended to address the inconsistencies and limitations of current standards and improve the efficiency of Cleanroom monitoring and management.

The new method shows the number of sampling points corresponding to clean rooms of various sizes in a table, which is clear, intuitive and convenient to use. And no matter how many sampling points there are, there is no need to calculate the confidence level. As can be seen from the table, compared with the old method, the number of sampling points of the new method starts to increase when the clean room area is 8 m2, and the two sides are close again when it reaches 500 m2. Among them, the gap between the two sides is the largest from more than 60 m2 to about 300 m2, and the number of sampling points of the new method is about 50% more than that of the old method. The new method is better than the old method in terms of confidence level and the minimum guaranteed area ratio. This also means that the sampling workload is increased, but the results are more reliable.

Calculating the number of sampling points with confidence level shows that the sampling method for clean room air cleanliness classification detection is based on probability theory, that is, a limited number of samples are used to reflect the characteristics of the whole or a certain proportion (such as 90%) of the whole according to a certain confidence level. But the randomness of the sample is the soul of this method. That is to say, all samples in the whole have an equal chance of being drawn and tested, and which one is drawn is just random. Regardless of the quality of the samples, they have an equal chance of being measured. This ensures the objectivity of the sampling and the reliability of the overall reflection. To apply this theory to Clean room Testing, we must first divide the clean room into several or more equal-area units with a certain unit area (for example, 4 m2) as the basic unit.  According to the area of the clean room, find the number of sampling points corresponding to the area in Table 1, and randomly select the number of units from the large number of equal-area units for testing. The specific test location is also randomly selected within the unit. Taking a 100 m2 clean room as an example, it can be divided into 25 units, each with 4 m2.

This random point selection process is not randomly selected by people, but is determined by selecting units with the same number based on the random numbers generated by the random number generator. The randomness of this method is the best, and the probability of units that have not been drawn being drawn each time is completely equal. Therefore, the drawn units will not be evenly or roughly evenly distributed in the clean room. This sampling method may leave large areas that have not been drawn in the clean room, and at the same time, some sampling points will appear relatively concentrated. The larger the area of the clean room. The more obvious this trend is.

So can this method reflect the full picture of the particle concentration in the clean room? The problem also starts with the analysis of the 4 m2 unit. According to the random Sampling theory, each sample has the same properties, is independent of each other, and does not affect each other. For example, in the random inspection of product quality, each product is produced with basically the same raw materials, the same machines, the same processes, and even the same workers. Their overall intrinsic quality should be basically the same. At this time, using random sampling methods to detect and find out unqualified products that may be mixed in them is a time-saving and labor-saving method.

But in the 4 m2 space in the clean room, each 4 m2 space may be different, such as under the vent, between the vents, or in the place without vents, their situations are also different. And because this small unit is not "isolated from the world", only in the empty vertical laminar flow clean room, this 4 m2 unit may be in the "most ideal" state. That is, the characteristics are roughly the same, various independent, without interference and influence. Regardless of which of the three occupancy states of the mixed flow clean room, or for the vertical laminar flow clean room in static or dynamic state, the unity and independence of its basic units are greatly discounted. Since the premise of random sampling is not so "pure", since this random sampling method may not reflect the full picture of the particle concentration distribution in the clean room, can we "improve" it? This is the so-called "semi-random" sampling.

It is to divide the clean room into uniform equal-area blocks according to the number of clean room samples listed in Table 1, and then select sampling points at random within each block for sampling. Let's take a 100m2 clean room as an example. The minimum number of sampling points for a 100 m2 clean room listed in Table 1 is 16. Divide this 100 m2 into 16 equal-sized areas.

According to this sampling method, each location has a chance to be sampled, but the chance to be sampled is only once. It overcomes the mechanical nature of the current method of sampling only in the center of each area, while taking into account the approximate uniformity of the distribution of sampling points. Avoid the occurrence of over-biased or concentrated sampling points. Since this method still has a certain degree of randomness, it still retains a random component in principle.

The "full random" sampling method is more in line with the requirements and conditions of random sampling theory, while the "semi-random" sampling method also takes into account the different characteristics of different locations in the clean room under various circumstances. The "semi-random" sampling method inherits the existing method of dividing the clean room into equal-area sampling areas, and is not limited to the "mechanical" sampling location of the center point of the sampling area. The existing method has been used internationally for more than ten years, and the new method also takes into account its inheritance.