Patent Application
20180267521
The invention relates to the use of statistical indicators in an industrial setting, for example, in the aeronautics industry, in particular for facilitating monitoring and control of the manufacturing of parts.
The manufacture of parts, especially mechanical parts, in an industrial setting is met with two opposing constraints: specifically, the increase in manufacturing throughput and volumes on the one hand, and the increased quality requisites on the other, which is particularly true in the aeronautical field.
Today it is difficult to imagine performing quality control on all parts manufactured except to considerably impair manufacturing throughput. Statistical manufacturing indicators are therefore generally used, reliably deducing overall information on the quality of the set of parts manufactured from specific information on the quality of a finite number of parts taken as samples.
Apart from controls at the end of production, which can be done on samples having a limited number of parts, checks are generally also made during production to be able to optionally regulate production flow, that is, adjust manufacturing conditions to ensure that the parts made continue to respond to the required quality criteria. In some cases, these statistical controls during production can result in production stopping completely, especially if the parts produced present excessive quality defects and the manufacturing flow must be completely reinitialised.
Quality controls are performed in relation to a characteristic dimension of the parts that are manufactured. This characteristic dimension can be, for example, a particular side of the part, its mass, or any other measurable characteristic of said parts.
To perform statistical controls, several samples are taken successively, each sample comprising several parts of the manufacturing flow, and the characteristic dimensions of each part of the sample taken are then measured. The value of a statistical indicator selected previously to monitor the quality of the manufacturing flow is calculated from the different measurements of the characteristic dimension of the parts of the sample taken.
There are various statistical indicators, which can be used to monitor the evolution of a manufacturing flow of parts, each statistical indicator giving different information for adjusting the manufacturing conditions in one way or another.
Most statistical indicators used for monitoring an industrial manufacturing process are calculated from an average p and a standard deviation a of the measured characteristic dimension on several parts. More precisely, p corresponds to the average of the decentring measured for the characteristic dimension relative to the reference value for this characteristic dimension.
An example is the centring coefficient, noted Cc, which shows restraint imposed on the variations of the average p inside the tolerance interval IT. The tolerance interval IT is the deviation between the extreme admissible values of the characteristic dimension, therefore being calculated as the difference between the greater tolerance TS and the lesser tolerance TI of the measured characteristic dimension, or IT=TS−TI. The centring coefficient Cc is generally defined by the formula:
The manufacturing process can also be regulated by studying capability indices which characterise the real performance of the process relative to the preferred performance. Such indices in fact measure the capacity of the manufacturing process to make parts whereof the characteristic dimensions are included in the preferred tolerance interval IT.
Reference can be made for example to the process capability index Cp which represents the aptitude of a manufacturing process to produce parts precisely and repeatably. The larger the capability index Cp the more the parts made will be similar, whereas if the capability index Cp is low, the production will be dispersed. The process capability index Cp is defined generally by the formula:
The disadvantage of such a process capability index Cp is that a positive result (that is, high) can also correspond to production outside the limits of tolerance. In fact, the industrial conformity of a manufacturing flow depends on scope, that is not only its dispersion but also the position of its average relative to the tolerance interval IT. Another capability index used is therefore the capability index Cpk, which shows dispersion but also the centring of the production relative to the limits of tolerance. In this case, when the capability index Cpk is high, this means that production can be repeated and that it is also centred in the tolerance interval IT, that is, there will be less risk that parts are manufactured outside tolerances. The process capability index Cpk is defined generally by the formula:
There are of course other statistical indicators having specific properties, and, which can be used as a function of the needs to regulate the manufacturing process.
For reliable monitoring and regulating of the manufacturing process using such statistical indicators, these indicators are generally monitored on two time scales.
In fact, this can be based on a long-term scale defined with a minimum number of parts (in general at least 250 parts per sampling), on which it is possible to calculate statistical indicators such as the Cpk with a sufficiently good confidence interval to accord them a certain credibility.
This can also be based on a short-term scale which is defined as such relative to a time interval after which a sample is taken (generally each week); this enables a prompter reaction in case of rapid excess of production.
These methods of production monitoring are not satisfactory however when the manufacturing flow of parts is not substantial enough, that is, when the number of parts of the sample taken is too small and/or very different between two successive samplings.
For example, the production of turbine blades is often highly variable, where the sizes of samples can be extremely different from one week to the next (from 8 to 300 parts per period).
An aim of the present invention is to propose a manufacturing method of parts based on analysis of at least one effective statistical indicator for monitoring random production, with a number of variable parts to be sampled, and/or with small numbers of parts.
Another aim of the present invention is to propose a manufacturing method for parts based on analysis of at least one statistical indicator which is reactive to substantial variations in the manufacturing flow, and is sufficiently stabilised so as not to react to the least insignificant production deviation, also enabling overall vision of the manufacturing flow.
For this purpose, a method for manufacturing parts is proposed, based on analysis of at least one statistical indicator representative of a characteristic dimension of parts, according to which:
Each of the steps presented is preferably automated.
The measuring step of the characteristic dimension can be conducted with a measuring device, for example comprising sensors for performing automated measuring of specific dimensions of the part.
The calculation steps can be taken by any appropriate calculation device, such as for example processing computer data means, such as a computer.
The regulating step can be taken for example by a regulating device integrating processing means for integrating and processing data originating from the calculation steps in order to correct any deviation detected in production and correct production flow. In particular, the regulating device is provided to correct the input parameters of the production device from which parts originated.
The regulating device therefore preferably adjusts the regulating parameters of the manufacturing device used to make the parts for example in order to reduce the deviation between the value of the statistical indicator and the reference value
More generally, the aim is to optimise the deviation between the value of the statistical indicator and the reference value so that production of parts complies with requirements of the relevant specification. The production parameters are modified for modifying, or respectively correcting, the deviation identified between the value of the statistical indicator and the reference value. As a function of the statistical indicator used, optimising the deviation could for example consist of reducing the deviation identified.
Preferred, though non-limiting, aspects of this method, taken singly or in combination, are the following:
N
t+1
=λn
t+1+(1−λ)Nt
N
t+1
=kλn
t+1+(1−λ)Nt
M
t+1=λμt+1+(1−λ)Mt
S
t+1=√{square root over (λσt+12+(1−λ)St2+λ(1−λ)(μt+1−Mt)2)}
M
t+1=λ*μt+1+(1−λ)Mt
S
t+1=√{square root over (λ*σt+12+(1−λ)St2+λ*(1−λ)(μt+1−Mt)2)}
Other characteristics and advantages of the invention will emerge from the following description which is purely illustrative and nonlimiting and must be viewed with respect to the attached figures:
To respond to the restrictions of variability in production, which impacts not only on the average of the measured characteristic dimension during sampling, but also on the standard deviation of these measurements, it is proposed to calculate for each sample taken a weighted average and a weighted standard deviation of the characteristic dimension according to exponential weighting.
This calculation is preferably based on the average and the standard deviation of characteristic dimensions measured on the parts of the sample taken, as well as on the weighted averages and the weighted standard deviations of the characteristic dimension which have been calculated for samples taken previously.
For weighting of the average for example, the monitored index is a weighted average of the decentring of production to be noted as Mt, and which is calculated at the period t+1 as follows, as a function of decentring data of the period t+1 noted μt+1, and of the index calculated at the period t:
M
t+1=λμt+1+(1−λ)Mt
where λ∈[0; 1] λ∈[0; 1] is a weighting coefficient previously selected.
This corresponds to the mix of two populations of averages μt+1 and Mt in respective proportions λ and (1−λ).
The weighting is called exponential as developing the formula hereinabove gives:
M
t+1=λμt+1+λ(1−λ)μt+λ(1−λ)2μt−1+λ(1−λ)3μt−2+λ(1−λ)4μt−3+ . . .
Throughout the description, a value corresponding to a characteristic specifically linked to the sample taken at the period t is noted by a lowercase letter qualifying said characteristic followed by the index t. In contrast, a value of a characteristic which is not specifically linked to the sample taken at the period t but rather to all samples taken between the periods 0 and t is noted by an uppercase letter qualifying said characteristic followed by the index t.
So μt represents the average of decentring noted on the parts of the sample taken at the period t, whereas Mt represents the average of weighted decentring and calculated from all the samples taken between the periods 0 and t.
In the same way as for the average an indicator St of the standard deviation of a population can be constructed where a heavier weight is given to the last samples taken, and calculated as the standard deviation of the mix of two populations of standard deviations respective σt+1 (data of the period t+1) and St (index of the period t) in respective proportions λ and (1−λ), as follows:
S
t+1=√{square root over (λσt+12+(1−λ)St2+λ(1−λ)(μt+1−Mt)2)}
In reality, it is preferable to also consider variations of the size of samples.
A number of parts aggregated at the period t, noted Nt, can be defined and which is calculated recursively as a function of the size nt+1 of the sample at time t+1.
A possible aggregation formula is the following:
N
t+1
=λn
t+1+(1−λ)Nt
This aggregation formula of the number of parts gives an unaccumulated average: the sum of the coefficients allocated to the different samples is 1.
If focus is placed on a simple sum of size of samplings over a given number of weeks k (k=5 for example in the event where the sample considered accumulates measurements of the last five samplings), the sum of the weightings allocated to the samples would be k (and of course without this nothing at all changes calculation of the corrected averages and standard deviations).
The challenge of this sum of weightings is in the calculation of intervals of confidence for the capability indices Cpk: if the corrected size of the sample is calculated using the formula Nt+1=λnt+1+(1−λ)Nt with sampling sizes equal to 10 of 30 consecutive samples, the corrected size of the sample will always be 10, and the confidence interval on the calculated capability indices Cpk would be enormous, whereas if the focus were the cumulative size of the last five samplings (Nt+1=nt+1+nt+nt−1+nt−2+nt−3), the accumulated size of the sample would be permanently equal to 50, and the confidence interval on the capability indices Cpk would be much better.
So to further improve monitoring and regulating of the manufacturing flow, a partially cumulative formula will be used for calculating the corrected size of the sample, of the form:
N
t+1
=kλn
t+1+(1−λ)Nt
where k>1, and λ∈[0; 1] are fixed at the start of the manufacturing method by the user as a function of his requirement in terms of reactivity and accumulated samplings.
If a simple mix of two samples were done relative to their respective sizes n1 and n2, the average and the standard deviation of the mixture would be calculated by the formulas:
μ=γμ1+(1−γ)μ2
and
σ=√{square root over (γσ12+(1−γ)σ22+γ(1−γ)(μ1−μ2)2)}
with
The «virtual» population of size Nt+1=kλnt+1+(1−λ)Nt is in exactly the same way a clustered population, constituted by the mix of two subpopulations of respective sizes kλnt+1 and (1−λ)Nt.
The proportion of parts recently controlled in the mixture, to be noted can therefore be defined according to the formula:
As per another embodiment, the weighted average Mt+1 and the weighted standard deviation St+1 can be calculated by the formulas:
M
t+1=λ*μt+1+(1−λ*)Mt
and
S
t+1=√{square root over (λ*σt+12+(1−λ*)St2+λ*(1−λ*)(μt+1−Mt)2)}
Monitoring and regulating of manufacturing flows of parts is then done by using the usual statistical indicators based on an average and a standard deviation of the characteristic dimension measured on the parts of the sample, by substituting the weighted average Mt+1 for the average p, and the weighted standard deviation St+1 for the standard deviation in the formulas which define these statistical indicators.
Thus for example, the capability index Cpk will be calculated according to the formula:
The capability index Cp will be calculated according to the formula:
The centring coefficient Cc will be calculated according to the formula:
The example described below for
The graph of
This graphic shows that the indicator illustrated by the curve IH is reactive, but since intervals of confidence on samples of ten parts are considerable, it does not satisfactorily characterise the population produced. Its volatility also does not easily uncover patterns in production monitoring. In fact, it tends to display variations in sampling (noise or oscillations) which impair the legibility of its evolution, or else tends to be jubilant in an upswing or too pessimistic in a downturn.
The indicator illustrated by the curve IM accumulates data of four weeks, which lets it display a sample size of 40 parts, considered as sufficient in this example for characterising production satisfactorily. But it is evident that it has inertia which makes it minimally reactive to rapid variations in production.
The weighted indicator illustrated by the curve IP also displays an aggregated sample size of 40 parts, which makes it sufficiently “voluminous” to let the manufacturer characterise production with a level of confidence deemed satisfactory. Also, this large size is not accompanied by inertia as detrimental as that of the second indicator illustrated by the curve IM in the face of rapid excesses. When examined, it simply uncovers upward or downward trends in production cycles.
It is therefore evident that the weighted indicator accumulates the advantages of both other preexisting indicators, without having any of their disadvantages.
It simplifies reading of indicators and regulating of production and makes it become more relevant, as well as best characterising the population of a given period.
As emerges from the description above, combined use of a calculation formula weighted for averages and for standard deviations, drawn from an analogy with the formulas for population mix, best responds to production monitoring needs for which both the average and also the standard deviation must be considered as variables.
The introduction of an intermediate weighting coefficient noted λ* takes into account the variable sizes of samples taken. The value of this intermediate weighting coefficient reflects exactly the weight of parts controlled during the preceding period in the overall aggregated sample.
Finally, the introduction of a cumulative coefficient, noted k, accumulates measured samples so that the size of the aggregated sample is greater than the average size of samples taken (in the way as when monitoring is performed over five successive weeks, the size of the sample is equal to five times the size of weekly sampling).
The proposed method can be performed in a manufacturing chain of parts, which can be fully or partially automated, where controls during production regulate the manufacturing flow, that is, adjust the manufacturing conditions to ensure that the finished parts continue to respond to the required quality criteria.
In this automated production chain, parts are sampled when exiting the machining device to form a sample and sent to a measuring device which measures one or more characteristic dimensions of each part of the sample taken. Such a measuring device can for example be a three-dimensional measuring machine having sensors which automatically measure the preferred characteristic dimensions of each of the parts.
The measurement data coming from the measuring device are then sent to a calculation device which processes them to calculate one or more statistical indicators representative of one of the characteristic dimensions of the parts.
The calculated value of the statistical indicator is then compared to a reference instruction on the characteristic dimension in order to manage the manufacturing flow. More precisely, the results of this comparison optionally adjust the input parameters of the machining device.
If a deviation is evident, implying an error, for example if the value of the statistical indicator on the characteristic dimension is outside an acceptable range defined by the reference instruction, corrective measurements are determined by a corrector to adjust the input parameters of the machining device. The aim of modifications to the input parameters of the machining device is to correct the evident deviation so that the value of the statistical indicator on the characteristic dimension is back within an acceptable range.
| Number | Date | Country | Kind |
|---|---|---|---|
| 1461991 | Dec 2014 | FR | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/FR2015/053323 | 12/4/2015 | WO | 00 |
