GB1573304A - Apparatus for calculating standard deviation of a propertyof articles - Google Patents

Description

(54) APPARATUS FOR CALCULATING STANDARD DEVIATION OF A PROPERTY OF ARTICLES (71) We, MOLINS LIMITED, a British Company, of 2 Evelyn Street, Deptford, London, SE8 5DH, do hereby declare this invention for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the followng statement: This invention relates to apparatus for calculating standard deviation of a property of articles, and is an improvement in or modification of the invention of our Patent No. 1,406,218. The apparatus is especially useful when employed in association with a machine which is continuously producing the articles in question, e.g. a continuousrod cigarette-making machine.

Standard deviation is a recognized statistical measure of the consistency of any measurable property of an article, and may validly be employed for various purposes as long as any non-random sources of variation in the property are eliminated so that the distribution of specific values of the property under consideration among the "population" of articles concerned is a random (Gaussian) distribution. The standard deviation is calculated in any particular case by taking the square root of the average of the squares of the errors for all the articles (error being the difference between the actual value of the property being considered for each article and the mean value of that property for all the articles). The fraction of the total number of articles for which the error in the measured property exceeds a defined value has a fixed relationship to the defined value of the error, e.g. if the defined value of error equals twice the standard deviation, then 4.56% of the total number of articles will have errors exceeding the defined value, and this 4.56% of the articles will include equal numbers of articles in which the error is positive and of articles in which the error is negative.

A calculating apparatus for this purpose is described in our British Patent Specification No. 1,406,218. In that specification, a preferred form of apparatus is disclosed (hereinafter termed "our prior apparatus") in which a succession of articles are fed past a measuring device providing an electric signal which indicates the value of the property for each article, comparing means receives said signal from the measuring device and emits a resultant pulse whenever said signal represents a value of the property beyond a limit represented as a reference voltage fed to said comparing means and count means produces a succession of count pulses in synchronism with articles being fed past the measuring device, each count pulse representing a preselected number (greater than 1) of articles. A digital counter is connected to receive both the resultant pulses and the count pulses at two separate inputs and is such that each pulse received at one of said inputs causes an increase by one of the number registered by said counter while each pulse received at the other of said inputs causes a reduction by one of said number, and a digital-to-analogue converter is connected to said counter so as to produce an analogue voltage which at all times represents the number registered in said counter, said converter being connected to deliver said output to the comparing means so as to control the reference voltage thereof.

The preselected number of which the count means operates must be correctly related to the reference level of the comparing means. For example, in a normal (Gaussian) distribution of the relevant property for a plurality of articles, if the reference level is set at a value of the property which is lower than the mean value for all the articles by 1.53 times the standard deviation than in one-sixteenth of the total number of articles the value of that property will be below the limit. Accordingly if, with the reference level so set, the count means is arranged to deliver one count pulse for every sixteen articles passing the measuring device, then over a period the counter receives equal numbers of resultant pulses and of count pulses, hence the number registered by the counter will not change (except for transient changes, rarely of more than one unit, due to the fact that the inputs receive discrete pulses) so the reference voltage of the comparing means will remain constant.

A change of standard deviation will however cause the number of resultant pulses in a period to be more or less than the number of count pulses, so the number registered by the counter will increase or decrease until the resulting variations of the output of the digital-to-analogue converter brings the reference voltage to a new level at which the number of resultant pulses in a period is again equal to the number of count pulses. Hence there is a different value of reference voltage for every value of standard deviation so that the reference voltage in fact is indicative of the prevailing standard deviation.

In our prior apparatus there is also means for correcting the indication of standard deviation produced, to allow for variation of the mean value of the relevant property of the articles. This correcting means is similar in general layout to that for indicating standard deviation as defined above, having a further digital counter with two inputs as before, but the arrangement is such that the counter receives a pulse at one or other of its inputs for every article passing the measuring device. A comparing means supplied with a reference voltage controlled by the number of registered in the further counter, through another digital-toanalogue converter, determines which of the counter inputs receives the pulse for each article according to the value of the property for that article being above or below the value represented by the reference voltage. The correcting means therefore achieves balanced condition in which the number registered in the counter remains constant (apart from transient increases or decreases) when the reference voltage is at a level representing the prevailing mean value of the property, as with this level of reference voltage equal numbers of pulses are received by the two counter inputs.

It is an object of the present invention to provide apparatus for calculating standard deviation of a property of articles, embodying the invention disclosed and claimed in Claim 1 of our aforesaid British Patent Specification No. 1,406,218 and providing a sufficiently accurate indication of standard deviation although without the correcting means of our prior apparatus.

It is a further object of the invention to improve on the indication accuracy of our prior apparatus, in circumstances where, as well as a random short-term variation in the property of which the standard deviation is to be derived, there is a much longer-term variation, i.e. a slow oscillation of the mean value of that property. Long-term variations of this character are not uncommon in properties of machine-made articles.

According to the present invention we provide apparatus according to Claim 1 of Patent No. 1,406,218 for producing an electrical indication of standard deviation of a property of articles while a succession of such articles are being fed past a measuring device adapted to provide an electric signal indicating the value of said property for each article, in which the comparing means is arranged to emit a resultant pulse whenever said electric signal represents a value of said property which is outside a range defined by upper and lower limits represented by at least one reference voltage fed to said comparing means.

The comparing means, in apparatus embodying the present invention, thus produces a resultant pulse whenever the value of the relevant property of an article is above or below the upper or lower limit respectively while in our prior apparatus resultant pulses are produced by the comparing means only when the value of the relevant property is beyond a single limit, i.e. the comparing means operates in one sense only. In our prior apparatus therefore any change of mean value immediately affects the indicated standard deviation directly, and correction is needed, but in apparatus embodying the present invention there is a measure of compensation as a change in the mean value of the property causes an increase in the frequency of resultant pulses due to the measured value being outside the defined range in one sense, but at the same time there is a decrease in the frequency of resultant pulses due to the measured value being outside the range in the other sense.

In apparatus embodying the present invention it will be noted that the fact that the comparing means produces resultant pulses whenver the measured value varies too much from the desired mean in either sense requires a different setting of the count means. As exemplified in our aforesaid specification, if the limit is set at 1.53 times standard deviation from the mean, the count means is set to produce one count pulse for each sixteen articles as with a normal distribution there is one article in every sixteen with a value of the relevant property beyond this limit. However, with apparatus embodying the present invention, to allow for the fact that such an error in either sense will cause a resultant pulse to be produced, if the amount by which the property may differ from the desired means before production of a resultant pulse is the same, i.e. 1.53 times standard deviation, then the count means must produce a count pulse for every eight articles past the measuring device.

The compensation obtained by taking account of the number of articles in which the relevant property is outside limits in either sense does not give complete accuracy, but can give a very close approximation to the correct standard deviation. (The correct standard deviation, in circumstances where the random short-term variation is accompanied by a much longer-term variation of the mean value, is equal to the square root of the sum of the mean squares of the errors due to the short-term and to the long-term components.) It can be shown by calculation that the error varies with the mean value and with the choice of reference level, i.e. of the upper and lower limits mentioned above. If the latter are so selected that each count pulse has to represent six articles, it is found that a mean value variation of up to two standard deviations gives an error in the indicated standard deviation not exceeding 1%.

The comparing means may take various forms but we prefer to employ two summing integrators of the type disclosed and claimed in our British Patent Specification No.

1,406,219 each delivering its output to a comparator and both comparators having their outputs linked via a common gate to the appropriate input of the counter; both integrators are fed with the same reference voltage, but while one integrator receives the signal from the measuring device direct, the other integrator is connected to the measuring device via an inverter.

In order that the invention may be well understood, a preferred embodiment thereof will now be described in more detail, referring to the accompanying drawings, in which: Figure I is a schematic block diagram of a preferred form of apparatus embodying the present invention Figures 2A, 2B and 2C show three distribution curves, annotated to assist in explanation of the operation of the apparatus of Figure 1; Figure 3 is a graphical illustration of the accuracy of the apparatus of Figure 1; and Figure 4 is a schematic diagram of an integrator used in the apparatus of Figure 1.

As shown in Figure 1, the preferred apparatus has a signal input terminal 1 connected directly to one input of a first integrator unit 2 and connected through an inverter 20 to one input of a second integrator unit 22. The outputs of the integrator units 2, 22 are respectively connected to inputs of two comparator units 3, 23 and the outputs of both the latter are connected to separate inputs of a gate 25. A synchronising input terminal 10 is connected to a divider unit 4 and to a third input of the gate 25 and a reset input terminal 11 is connected to a second input of each of the integrator units 2, 22.

The gate 25 has is output connected to one input of a digital counter 5; a second unit of said counter is connected to the output of the divider unit 4, and a digital-toanalogue converter 6 is connected to receive a digital output from the counter 5 and deliver a corresponding analogue voltage to a third input of each of the integrator units 2, 22. Each of the comparator units 3, 23 has a second input connected to earth.

The apparatus of Figure 1 is intended for use with a continuous-rod cigarette-making machine fitted with a Beta-ray device for measuring continuously the mass of tobacco in the rod before said rod is cut into individual cigarettes. During operation of the machine, the input terminal 1 will receive a continuously-varying voltage indicating tobacco mass, while terminal 10 receives a series of pulses so synchronised with operation of the cigarette making machine that a pulse appears at terminal 10 whenever a portion of the cigarette rod which will later be cut is subject to the beam of the Beta-ray device. Hence the pulses at terminal 10 are termed "end-of-cigarette pulses" and it will be understood that the portion of the continuously-varying voltage appearing at terminal 1 in the time period between two successive pulses at terminal 10 represents the mass variations along the length of rod which will become one individual cigarette and the integral of the voltage at terminal 1 during that period indicates the total mass of tobacco in that one cigarette.

The integrator units 2, 22 are mutally similar and will be described in more detail with reference to Figure 4; at the moment is is sufficient to say that the unit 2 receives at its three inputs the voltage from terminal 1, the analogue voltage from converter 6, which serves as a reference voltage representing directly a particular value of mass per unit length of the cigarette rod and hence indirectly a particular total mass per cigarette and the reset pulses from terminal 11. From the first two of these inputs the unit 2 delivers an output voltage to the comparator 3, which output voltage at any instant represents the integral of the difference between the voltages at said first two inputs in the period since the last reset pulse was received at the third input of the unit 2 from terminal 11.

The reset pulses at terminal 11 occur immediately after the end-of-cigarette pulses - in fact, terminal 11 could be omitted and the relevant inputs of the units 2, 22 could be connected to terminal 10 through a delay circuit.

In the comparator 3, the voltage received from unit 2 is compared with the voltage at the second input of the comparator - in this instance zero, as said second input is earthed - and the comparator 3 delivers a voltage to gate 25 whenever the voltage from unit 2 is negative relative to that at its second input hence, in this case, whenever the voltage from unit 2 is negative relative to earth. This condition is achieved whenever the mean value of the voltage at terminal 1 in the period since the last reset pulse at terminal 11 is less than the reference voltage supplied by the converter 6, i.e. when the mean mass per unit length of cigarette rod in that period is less than the value represented by said reference voltage. When an end-ofcigarette pulse appears at terminal 10 and is applied to gate 25, if the comparator 3 is at the same time delivering an output then a pulse (of duration equal to that of the end-of-cigarette pulse) will be delivered to the first input of counter 5 and the number registered in the latter will increase by one.

This pulse to the counter 5 represents the passage of one cigarette (actually, one cigarette-length of rod) of total mass less than a limit defined by the reference voltage.

The integrator unit 22 and comparator 23 operate in exactly the same manner as just described in relation to the units 2, 3 but as the unit 22 receives the voltage from terminal 1 not directly, but after inversion, although it receives the same reference voltage as unit 2 the overall effect will be that the counter 5 receives a pulse (causing the number registered therein to increase by one) whenever a cigarette-length of rod passing the measuring device has a mass greater than the limit defined by the reference voltage (if the latter were inverted).

Thus the counter 5 receives a pulse at its first input, and increases the number reg istered in it by one, whenever a cigarette length of rod (i.e. a section of rod which is to become an individual cigarette) passing the Beta-ray device has a total mass which is either below or above a lower or an upper limit respectively, both limits being control led by the reference voltage delivered by converter 6.

However the end-of-cigarette pulses from terminal 10 also go to the divider unit 4 and this unit delivers one output pulse to the second input of counter 5 for every six end-of-cigarette pulses received; each of these pulses causes the number registered in counter 5 to decrease by one. Accordingly, over a period, if one-sixth of the total number of cigarettes (or, rather, cigarettelengths in the rod) are so heavy or so light as to cause a pulse to be delivered to the first input of counter 5, then the number registered in said counter - and, therefore, the reference voltage - will be unchanged at the end of the period. The amount represented by the reference voltage will be 1.38 times the prevailing standard deviation as, in a normal distribution, the mass of one-sixth of the cigarettes is known to be more than 1.38 times the standard deviation above or below the mean.

A change of standard deviation causes the reference voltage to change correspondingly until the same balanced condition is reached i.e. that the first input of counter 5 in any period receives a number of pulses equal to one-sixth of the number of cigarettes. If for example the standard deviation increases, then more than one-sixth of the cigarettes will be too heavy or too light so that the first input of counter 5 receives pulses more frequently than the second input; the number registered by counter 5 therefore increases, and the reference voltage supplied by converter 6 also increases. This reference voltage increases, by widening the limits outside which a cigarette's mass must be before its passage results in a pulse to the first input of the counter, reduces the frequency at which pulses arrive at said first input of the counter and the reference voltage become stable at a new value when the numbers of pulses received by the two counter inputs in a period are again equal.

There is then a new value of the reference voltage corresponding to, and hence representing the new value of standard deviation.

If the means mass of individual cigarettes changes, then the effect of the apparatus can be appreciated by referring to Figures 2A to 2C, showing three distribution curves. Figure 2A is a graphical representation of a normal distribution of cigarette masses, the measured actual mean value corresponding to a desired value indicated by the vertical line D-D. Dashed lines L, H respectively indicate low and high limits, each separated from the desired mean by a selected amount S1. The shaded areas are proportional to the numbers of cigarettes having masses outside the respective limits, and thus proportional to the number of pulses delivered to the first input of counter 5.

In Figure 2B is illustrated the condition in which the actual mean mass of the cigarettes is higher than the desired mean by an amount E. In this condition it can be seen that the total shaded area is larger than in Figure 2A as the number of cigarettes of mass above limit H has increased much more than the number of mass below limit L has decreased. However, Figure 2C shows the effect of new limits H+, L+ which are effective when, as described aboove, the reference voltage changes in response to the situation illustrated by curve B. The new limits H+, L+ are each separated from the desired mean D by an amount S2 (greater than S1), and the total shaded area is equal to that in curve A.

In the three curves of Figures 2A-2C it will be understood that the standard deviations are the same in all three cases; however, the apparatus of Figure 1 in response to the change E of mean mass does change its reference voltage, giving the new limits H+, L+ of Figure 2C.

In the absence of any change of mean mass the reference voltage as explained above indicates standard deviation, but in the situation of Figure 2C, the indication is erroneous to the extent indicated by the difference between S2 and S1. However calculation reveals that this error need not be large. The error varies according to the choice of balance point for the apparatus the example described, in which divider unit 4 delivers one pulse to the counter for every six cigarettes past the measuring device gives an error in the standard deviation, as indicated by the reference voltage, which does not exceed 1% for mean weight errors (amount E of curves B and C) up to two standard deviations. Figure 3 shows graphically the reading error (i.e. error in indicated standard deviations) plotted against mean mass error (shown in multiples of standard deviations e.g. 1.5 S.D.) for several values of N (where N is the number of cigarettes per count pulses).

Figure 4 shows schematically the preferred arrangement of each of the integrators 2, 22, which is almost identical with that disclosed in our specification No. 1,406,219.

Input terminals T1, T2 are connected by respective resistors 27, 28 of equal value to a common point 29, an inverting amplifier 30 having its input connected to the point 29 and its output connected to output terminal TO. A capacitor 31 is connected between the input and output of the amplifier 30, and a normally-open reset switch 32 is connected so that, when closed, it discharges the capacitor 31. The third input T3 of the integrator is connected to the reset switch 32 - for illustrative purposes the latter is represented as an electro-mechanical relay but in practice, to obtain a suitably quick response, an electronic device is employed as the reset switch, preferably a field-effect transistor.

In operation, input terminal T1 receives the continuously - varying voltage from the Beta-ray measuring device and terminal T2 receives the reference voltage. It will be assumed that the signal received at terminal T1 goes positive as tobacco mass per unit length falls below a desired mean value. At any instant, at point 29 there is an input signal proportional to the algebraic sum of the voltages at terminals T1 and T2 and the amplifier 30 and capacitor 31 coact in known manner under control of said input signal so that at any instant the charge on capacitor 31 represents the integral of said input signal at point 29 over a period prior to that instant. As the signal at terminal T1 represents the mass of tobacco in the portion of cigarette rod in the beam of the measuring device at the relevant instant and the reference voltage at terminal T2 represents in magnitude a particular value of that mass (being proportional to the value S1 of Figure 2A) but is of opposite polarity to the voltage at terminal T1, the integral represented by the voltage across capacitor 31 represents the total error in the tobacco mass, relative to the value represented by the reference voltage over the period of integration.

The capacitor 31 is discharged by operation of the reset switch 32 in response to a reset pulse at terminal T3 (immediately after an end-of-cigarette pulse at terminal 10, Figure 1) hence at the time of the next reset pulse the voltage across capacitor 31 represents the total mass error in a portion of rod which will after cutting of the rod become an individual cigarette; said voltage across capacitor 31 also represents the mean mass error, as cigarette lengths are uniform and end-of-cigarette pulses occur regularly.

It will be seen therefore that apparatus embodying the present invention can produce an indication of standard deviation which is for practical purposes unaffected by variation in the mean value of the property being measured, although the invention permits the apparatus to be somewhat simpler than our prior apparatus.

The apparatus of Figure 1, when used with a continuous-rod cigarette-making machine, may serve merely to provide an indication of the standard deviation of the individual masses of cigarettes produced, e.g. the output from converter 6 may be applied to a meter or some other form of display device. However, it is to be noted that at any instant the standard deviation is not only represented (in analogue form) by the converter output but a digital indication of the same value is also present in the counter 5. If it is desired to employ electronic data-processing equipment to monitor and/or control the operation of one or more cigarette-making machines then such equipment is most likely to be some form of digital computer and it may be supplied with an indiciation of standard deviation whenever required by sensing the number stored in the counter.

Claims (3)

WHAT WE CLAIM IS:

1. Apparatus according to Claim 1 of Patent No. 1,406,218 for producing an electrical indication of standard deviation of a property of articles while a succession of such articles are being fed past a measuring device adapted to provide an electric signal indicating the value of said property for each article, in which the comparing means is arranged to emit a resultant pulse whenever said electric signal represents a value of said property which is outside a range defined by upper and lower limits represented by at least one reference voltage fed to said comparing means.

2. Apparatus as claimed in claim 1, in which said comparing means comprises a pair of summing integrators each delivering its output to a comparator, both comparators having their outputs linked via a common gate to an input of the counter, both integrators being connected to receive the same reference voltage and one integrator being connected to receive the signal from the measuring device direct and the other integrator being connected to the measuring device via an inverter.

3. Apparatus for producing an electrical indication of standard deviation, substantially as described with reference to the accompanying drawings.