Double standards?

Measuring uncertainty in the manufacturing process

Measuring uncertainty has an effect on the clearance allowance in quality assurance and in the actual useful tolerance in in-house production and at the suppliers. There cannot be multiple interpretations of the tolerance on the drawing. However, there are two ways to deal with this situation.

Every measuring technician knows the so-called "golden rule" [1].  This states that the measurement uncertainty should ideally amount to at the most one tenth of the tolerance. At the time this rule was formulated it was considered that if this rule was adhered to the measurement uncertainty could be ignored. This way of looking at things is still widespread today.

A better understanding of the inter-relationships does however permit a differentiated means of proceeding. The analysis of the measurement uncertainty becomes an integral part of the measurement. In this way the increased requirements caused by the tolerances, which in an economic production are forever getting smaller, are taken into account. With newer standards, consideration of the measurement uncertainty with regard to the measurement result is already in place.

 

Taking measurement uncertainty into consideration

Every measurement contains a measurement uncertainty, U, by which the value reported might be too large or too small. The definition includes incidental as well as systematic deviations. Normally they are not distinguished from one another, but for simplicity's sake are only looked at in their total amount.

Despite ever smaller tolerances, the measuring uncertainty is all too often neglected. Especially, with the operation of coordinate measuring machines (CMM) the determination of the measuring uncertainty is not always easy. For each characteristic that is to be measured, such as e.g. the distance between two bores or an angle measurement, it must be separately determined. So it can be tempting to ignore the existence of the measuring uncertainty. In order to compensate for this, tolerances that are unnecessarily tight are chosen for safety by the design departments (nervous tolerances).   When measuring uncertainty is ignored, undefined technical problems in the assembly or functioning of the manufactured components can occur.

If approving parts which are in fact outside the tolerance limit is to be avoided the particular existing measuring uncertainty must be taken into consideration. The means of proceeding, which has been known for some time, has been dealt with in several articles [1, 2, 3]. But it was only the ISO-standard 14253-1 [4], which describes how the measurement uncertainty can be fixed into the pass/fail decision making, which led to intensive debate among experts.

Instead of the linear graphic representation in this ISO standard publication another graphic representation was proposed in many of the expert contributions. It represents the measurement uncertainty as triangles, depending on the characteristic to be measured or on the metrology being used.

For a better understanding, we should first consider the usual representation in somewhat modified form (Fig. 1).

By means of the triangles a variable measurement uncertainty is represented and through it the basic relationship between measurement uncertainty and tolerance is made clear. The gradual color tone should indicate that for the measurement uncertainty, which is always composed of many components, there is rarely an even distribution but rather a Gauss distribution is present.

In the upper part in illustration 1 the inter-relations for the determination of the manufacturing clearance tolerance are represented. As an example a ratio of tolerance (in this example 50µm) to measurement uncertainty of 5 to 1 was selected.  This can be quite realistic. The measurement uncertainty is represented in the illustration by the double arrows A. If it is to be avoided with certainty that parts, which are not within tolerance are approved, the clearance tolerance must be limited on both sides by the measuring uncertainty. With series parts this is best done with a preceding calculation of the measuring uncertainty for each characteristic and then alteration of the drawing tolerances in the measurement plans. In the numerical example in illustration 1, after deduction of the measurement uncertainty, the remaining clearance tolerance still amounts to 40µm.

With the borderline cases, the effects of the narrowed clearance tolerance are again made clear (illustration 1). Suppose that the measurement results were lying on the clearance tolerance limits B (in the illustration only represented on one side).  In the worst case, measurements could lie exactly on the specific tolerance limits or in the best case within the tolerance. That means: No parts outside the tolerance will be allowed. The more critical case comes about if the actual measurements as with C are laying within the measurement uncertainty triangles. They would then, in reality, be within the specified tolerance.  They would however, have to be rejected.

In the lower part of Fig.1 a further aspect is represented that must be taken into consideration with the measurement uncertainty.  This is only hinted at in the ISO standard [4] . It concerns the agreement between buyer and supplier. The buyer may not reject a product, which is only outside the tolerance by the value of the measurement uncertainty of his own incoming inspection equipment.  That means that the tolerance for the inspection must be increased on both sides by that measurement uncertainty. With a ratio of tolerance to measurement uncertainty of 1 to 10, that is a measurement uncertainty of 5µm.  The tolerance for the inspection is increased to 55µm.

This aspect has considerable consequences. With this means of proceeding the buyer has the choice of rejecting parts that are on the tolerance limit or of approving parts that are outside tolerance. Both of these fly in the face of economic trading and of conscientious quality assurance. The treatment of the measurement uncertainty between buyer and supplier must therefore be especially regulated.

 

Tolerance determination in the buyer - supplier relationship

Since the buyer cannot blame the supplier for the measurement uncertainty of the devices installed in his own incoming inspection department.  He can only complain if the tolerance value limits, which have been extended by his measurement uncertainty, have been exceeded. So, this procedure leads to a contradiction. There can not be double standards for the diagram tolerance. Two roads lead out of this situation:

"After an appropriate examination, the supplier earns a status of trust from the buyer. It is assumed that only parts that are within tolerance are delivered. The incoming inspection at the buyer's facility is dropped."

A contractual tolerance (5) is determined for the supplier, which also takes the measurement uncertainty of the buyer into consideration. Doing away with incoming inspection places the responsibility for the parts' quality and their effects on the end product entirely in the hands of the supplier. Here the clarification of questions of liability takes on a great importance.

The definition of contractual tolerance is shown in Fig. 2. Instead of variable measurement uncertainties, an example for a concrete characteristic on the use of each type of measurement device is simply explained here. The measurement uncertainty, UA, of the buyer and the measurement uncertainty, UZ, of the supplier are represented. The specified contractual tolerance for the supplier for each characteristic is limited by the measurement uncertainty of the buyer:

•    Contractual tolerance = specified tolerance - measurement uncertainty buyer
•    Clearance tolerance = supplier contractual tolerance - measurement certainty supplier

For the quality control at the supplier's, a further tightening of the tolerance by his own measurement uncertainty is required. Through the contractual tolerance, his clearance tolerance, is additionally limited by the measurement uncertainty of the buyer. Even if the measurement uncertainty of the buyer, as shown in the numerical example in illustration 2, is clearly less than that of the supplier, a reduction of the clearance tolerance to 34µm is the result. Once more we see that more accurate measuring can reduce the production costs.

The removal of the measurement uncertainty of the buyer leads to a linear addition of the two measurement uncertainties at the supplier's and is the same as in the worst case. If the measurement uncertainties were accepted as a normal distribution, a quadratic addition would be possible. This assumption cannot however be valid here, since an addition of uncertainties is not being carried out but rather a value limit is being formed from a value of the measurement uncertainty in order to create clear proportions for a contractual relationship.

If the supplier adheres to the contractual tolerance, this will not lead to verification in the test by the buyer, which in illustration 2 is lying in the ranges of A and would lead to a rejection.

Actually useable tolerance range

On account of the measuring uncertainty, unknown to the parties involved, the actual available tolerance range for the production is further reduced. Fig. 3 describes this effect on the example of the specified tolerance for your own production. These statements are also in principle valid for the case of a contractual tolerance. Fig. 3 is drawn to the same scale and with the same numerical values as Fig. 1 and 2. It contains three cases for the physically useable manufacturing tolerance. Case A shows the case of tightening once again by 2 U described in the literature [6].

Let us suppose here that the measuring uncertainty appears with negative or positive sign and is to be estimated on both sides with the particular unfavourable sign. If a measurement e.g. is lying on the left range limit in case A, by reason of the measuring uncertainty the indication can be lying exactly on the tightened tolerance limit. The case on the right hand side is analogous. If the manufacture produces measures according to this theory, which are lying once more by 2 U within the already tightened clearance tolerance then the measurement will always confirm the observance of the specified tolerance.

Even if it is in accordance with the definition this case is however somewhat unrealistic. On measuring the same characteristic a CMD will not even make use of the measuring uncertainty in negative and another time in positive direction unless the measuring uncertainty is exclusively of coincidental nature. This can be the case if through calibration the systematic deviation has been corrected. In these cases however the measuring uncertainty will clearly take on smaller values. For the more frequent case in practice it is assumed that the measuring uncertainty consists of a coincidental and a systematic part. Mathematically formulated the estimate comes to:

US = ± ( ± u + S )

With a numerical example it follows from that:

US = ± ( ± 2 + 8 ) µm.

That means that the measuring uncertainty estimated at 10µm consists as assumed here of an uncertainty portion of 2µm and a systematic measurement deviation of 8µm. It therefore takes on values between 6µm and 10µm. The sign of US can be positive or negative. In illustration 3 these two cases are referred to as B and C. The measuring uncertainty US with the systematic portion has a variable size on account of the incidental portion. The incidental portion always has the effect with regard to the limit value observation - as shown in the graphics- of the least favourable signs. It can be seen in both cases B and C that the actually usable range of the manufacturing tolerance is larger than in the case A. In the case of the too large indication (case B) it moves to the left nearer to the tolerance limit and more to the right in the other case. In the numerical example the usable range amounts in case A to 60µm and in the cases B and C to 76µm.

Conclusion

Dealing with measuring uncertainties and tolerances requires a critical examination of the attending influences. Since the effects of the tolerance and the measuring uncertainty of the testing processes are considerable on the manufacturing costs it would seem to be urgently advisable to give this topic more room in initial- and further training. This includes the correct determination of tolerances in the construction, the ensuring of stable manufacturing processes and the introduction of quality assuring processes with measurement uncertainty orientated toleration.

Literatur

[1] Berndt, G.; Hultzsch, E.; Weinhold, H.: Functional tolerance and measuring uncertainty. In: Scientific magazine of the Technical University Dresden, 17 (1968) 2

[2] Neumann, H. J. 1.: The influence of measuring uncertainty on the tolerance use in manufacture. In: CNC-Co-ordinates measuring technology,III. Neumann (edit., expert Verlag, Volume 172, 1988

[3] Neumann, H. 1.: Length measuring uncertainty in co-ordinates measuring technology. In: Co-ordinates measuring technology, Issue 1. Neumann (edit., expert

[4]DIN EN 150 14253-1: Testing of work pieces and measuring devices through measurements. Part 1: Decision rules for the determination of accordance and non-accordance with specifications, Beuth Verlag, Berlin 1999

[5] Christoph, R. and Neumann, H. J.: Multi-sensor co-ordinates measuring technology, Library of technology, Volume 248, mi Verlag, Landsberg 2003

[6] Weckenmann, A.; Gawande, B.: Chapter economic viability/process evaluation. In: Co-ordinates measuring technology, Carl Hanser verlag 1999

The authors of this contribution

Ralf Christoph PhD. (Eng.) habilitation, born 1955, studied precision engineering in Jena. In 1985 he obtained his doctorate in the area of the use of image sensors in optical co-ordinates measuring devices. His habilitation in the area of optical sensoring for geometrical measurement came about in 1989. Since 1990 Dr. Christoph has been working for Werth Messtechnik in Giessen, at the beginning as a development leader and since 1993 as managing director. For more than ten years he has been playing a decisive role with VDI and DIN in the creation of guidelines and standards in the area of co-ordinates measuring technology.

Hans Joachim Neumann B. Eng., born 1932, studied radio technology at the engineering school Mittweida (Saxony). After working for two years on opto-electronic development with Carl Zeiss, Jena he transferred in 1957 to CarI Zeiss, Oberkochen. There he was first of all working in leading positions in the areas of electronic development for telescopes and precision measuring devices, then later for software and application technology and finally as manager of marketing communication for the commercial area industrial measuring technology. Up to 2001 as a freelancer he was the representative of the company for standardisation and technical information and member in the ISO-committee for co-ordinates measuring technology. For eleven years he was chairman of the VDI/DIN common committee for co-ordinates measuring technology and for this was awarded an honorary badge by the VDI. He works as a specialist author.