Sampling of displayed information in process control

This is part of a paper by Crossman, Cooke and Beishon discussing whether sampling by industrial process operators can be modelled in the same way as was done at the time for sampling in tasks with quickly changing dynamics such as flying.  This is the section describing a case study of sampling by operators of a paper mill.  The rest of the paper discusses sampling in a simpler slow response laboratory task.

Excerpt from

Visual Attention and the Sampling of Displayed Information in Process Control

E.R.F.W.Crossman, J.E.Cooke, and R.J.Beishon

In E. Edwards and F. P. Lees. (eds.)  The Human Operator in Process Control.  Taylor & Francis 1974, pp.25-50.

5.  Sampling Behaviour in the Control of Basis Weight in a Papermill

We were first stimulated to undertake the foregoing uncertainty analysis of the sampling problem by observations made during industrial field studies of process operator behaviour and skill, from which one rather clear case will be cited by way of illustration.  It concerns the machineman's task of controlling the basis weight of paper being made in a modern [1960s] high-quality mill: a full account of the process and of the machineman's job has been given elsewhere (Beishon, 1963).

The weight of a given area of paper, or 'basis weight', is specified in each customer's order, and it must be held to within ± 1 lb of a nominal value lying between 15 and 30 lb per demy during a production run which may last several hours or even days. Its current value can be obtained either by removing and weighing a sample, a procedure which can only be carried out during a reel change, or (less precisely) by means of a beta-ray gauge situated at the 'dry end' of the machine; and it is controlled by means of a 'stuff valve' which controls the flow of pulp into the 'wet end' of the machine.  Its value also changes with the overall speed of the machine.  One of the machineman’s subtasks, then, is to adjust basis weight to the desired value for each successive order and monitor it during production to ensure that it remains within the specified limits until the order is completed.

The paper-making machine is a complicated system, containing many interacting variables and sources of chance variation, but broadly speaking it gives a proportional response of basis weight to small alterations both of stuff valve and of speed setting.  Stuff valve changes are subject to a total lag of the order of 5 minutes, made up as follows: first there is an exponential lag with time constant about 3 minutes because an increased (or decreased) pulp flow must change the concentration of pulp in a large volume of circulating water before it can begin to produce heavier or lighter paper, and second there is a transmission lag because paper emerging from the 'wet end' takes some 0.9 minutes to pass through the drying train to the 'dry end' where its basis weight can be ascertained. If a physical sample of paper is taken, the cutting and weighing operations require a further 2 minutes approximately, and then 5 to 7 minutes elapse between a stuff valve change and its final result in a measured change of output basis weight (see Figure 4a). The speed control has a more rapid effect, following approximately a ramp function of time (see Figure 4b).

5.1. Sampling during Long Production Runs

The time course of basis weight fluctuation was recorded by virtually con­tinuous observation of the beta-ray gauge through 6 hours of a typical day's run following the change to a new order, and is shown in Figure 5a together with the times at which the machineman inspected the beta-ray gauge or weighed a sample, adjusted the speed or stuff valve, and at which reel changes were made. [I can still remember being the person who either stood next to the beta-ray gauge writing down its reading at regular intervals.  Or walked around after the paperman and made a note of the time and what he did, whenever he did something observable.] The sampling interval, that is the interval between occasions on which the operator noted the current basis weight, had a mean value through the day of 8·5 minutes (s.d. = 7, n = 25) with a highly skewed, almost exponen­tial distribution (see Figure 5b). There were two periods of very frequent inspection at 34 and 284 minutes from start during which sampling intervals could not be recorded, both occurring shortly after control changes. However, after excluding periods within 10 minutes of any adjustment (Figure 5c) the mean sampling interval was found to be 14·1 minutes (s.d. = 11·0, n = 12); and when reel changes which in effect produced forced samples were also excluded the mean interval was 24·8 minutes (s.d. = 8·0, n = 5). The background sampling rate thus seems to have been about 2 per hour, which would corre­spond on Senders' analysis (see Section 3) to a bandwidth of 1 cycle per hour. The actual bandwidth was obviously greater than this, since basis weight drifted up and down significantly over periods of only a few minutes, but the amplitude of these relatively high-frequency disturbances was small in relation to the permitted tolerance range.  It seems that the operator was aware of this fact and used it in determining his sampling rate which suggests that when applying Senders' formula the proper bandwidth figure to use is the highest frequency component of random fluctuation having a peak amplitude greater than the assigned tolerance. Using this 'effective bandwidth' to calculate the proper sampling rate makes the latter depend on required accuracy, as the uncertainty analysis suggests that it should.  There were also irregular long-term drifts in the beta-gauge record, correlated with small control changes made at about hourly intervals. Indeed the complete day's record of basis weight shows an extremely slow oscillatory approach to a central stationary state, and it is possible that the sampling rate would subsequently have dropped to a much lower level, say once per two or three hours. Further observations extending over very long production runs will be needed to test this prediction.

5.2. Sampling after Major Control Changes

The pattern of control adjustment and sampling was also recorded during several occasions of readjusting basis weight to the next required value after finishing an order (see Figure 6a). The beta-ray gauge was off scale during this period, but the paper produced until the correct new basis weight had been achieved went to waste, so that pieces could be torn off and weighed at any time on a signal from the machineman to the dryerman. The mean interval between such sampling actions was found to be 4·7 minutes (s.d. = 2·5, n = 25) with a distribution more nearly symmetrical than that found during long runs (see Figure 6b). This interval is nearly equal to the lag in the stuff valve system measured to 80% of final response, as shown in Figure 4a, and it seems that, as might reasonably be expected, the next sampling interval after a control change is equal to the lag in system response to the particular disturbance applied. Most basis weight changes were achieved by making a sequence of 2-5 diminish­ing control adjustments resulting in a monotonic approach to the desired value, one sample being taken per adjustment.

The accuracy with which the operator's sampling behaviour matched the system lag was particularly striking since the men had many other things to do and there was no conveniently placed clock that they could refer to, nor did they use their watches. When questioned, operators gave widely differing estimates (from 1 to 8 minutes) of the time within which they would expect a given control change to be effective and it seems that their actual behaviour did not depend on explicit estimates of clock time but on an internal 'feeling' for system behaviour.

These findings have been repeated in several other factory studies, to be reported elsewhere, and it seems clear that in industrial process operation bandwidth alone does not suffice to predict operators' sampling behaviour. Quite extensive knowledge of the factors contributing to uncertainty is needed to form even approximately realistic estimates.

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