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PHILIPS TECHNICAL
REVIEW
VOLUME 29
Flame-failure control with a UV -sensitive cold-cathode tube
I. Design of the tube and circuit
Il. Statistical aspects of the detection process and choice of the alarm level
Many heating systems - from the domestic gas water heater and the central heating
boiler to large industrialfurnaces and steam boilers - require a simple but reliable safety
device which monitors the flame to see that it is still alight. For this purpose there are
particular advantages in making use of the ultra-violet radiation from the flame: the
following two articles deal with this method of detection. The first describes a smal! gasdischarge tube which responds to UV radiation, There are statistical fluctuations in the
output voltage of the tube, and therefore the maximum acceptable risk of false alarm is
one of the factors determining the choice of the alarm level for the safety system. Since
an exact calculation of the required alarm level is impracticable, a statistical method of
approximation has been developed, and this is discussed in the second article.
J. Design of the tube and circuit
T. Poorter
If the flame of a gas-fired furnace or boiler is accidentally extinguished with the gas supply left on, there
is soon sufficient unburned gas accumulated to constitute an explosion hazard. Every furnace or boiler therefore requires a safety system which monitors the flames
continuously and shuts off the fuel supply and gives an
alarm signal if they go out.
In oil-fired equipment, continued supply of the fuel
. when the flame has gone out has consequences which
are perhaps less Serious but are still highly undesirable,
and here too it is standard practice to provide flame. failure control.
Various methods may be applied to detect the presence of a flame; they differ considerably in their speed
of response and the choice between them therefore
depends to a large extent on the response time required
in the safety system for a particular boiler. An exceptionally short response time can be achieved with a
detector that responds to the ultra-violet radiation of
the flame. A further advantage of this method is that
it provides a simple means of distinguishing between
the flame and the hot wall of the combustion chamber.
For use in. this method Philips have developed a small
Ir. T. Poorter is with the Philips Electronic Components and
Materials Division (Elcoma), Eindhoven,
cold-cathode gas-discharge tube which ignites when it
is irradiated with ultra-violet light (wavelength between
200 and 290 nm). Combined with a simple electronic
circuit, this tube gives a very reliable flame detector.
Before describing the tube we shall first consider in
more detail some aspects of flame-failure control in
boilers and furnaces [11. Other safety systems, such as
those which respond to the gas pressure and are sometimes used in addition to flame detection, will not be
considered here.
Some methods of flame-failure control
For large boilers which can deliver several hundred
kW, where the explosion hazard is relatively great and
the possible consequences
particularly
serious, the
safety system is required to have a very short response
time, no longer than a few seconds. For small boilers
a response time of a few tens of seconds is often permitted. The flame detector can then be a simple bimetallic strip or thermocouple,
and is usually placed
in the pilot flame. The advantage of these detectors is
that no electronic amplification for energizing a relay
. is required; the disadvantages are that they very quickly
[1]
A more general treatment can be found in: B. Maizier, C.R.
Congrès Ass. tech. Ind. Gaz 81, 769-825, 1964.
1968, No. 8/9
FLAME-FAILURE
CONTROL
WITH COLD-CATHODE
become sooted up, which -upsets the thermal contact
with the flame, and the bimetallic strips have only a
short life.
In furnaces the situation is similar. For domestic
cookers a bimetallic strip or thermocouple is considered
sufficient, but for industrial furnaces a safety system
with a much shorter response time is required.
A short reaction time is obtained by using either the
ionization in the flame or the radiation from the flame.
In the first case several electrodes are placed in the
flame; when a voltage is applied between these electrodes, a very small current (a few tens of microamperes) flows while the flame is alight. Electronic
amplification has to be provided if a relay is to be
energized while this ionization current flows. Disadvantages of the method are that the detected current
is so small that any leakage currents due to dirt and
moisture on the electrodes can cause considerable
difficulties, and that the electrodes burn away slowly
and therefore need regular replacement. The method is
completely unsuitable for oil-fired equipment.
With a device that detects the radiation from the
flame the problems of wear and leakage currents due
to contamination do not arise; a difficulty here, however, is that the detector, when used in a furnace, "sees"
the hot wall of the furnace. Fig. 1 shows the spectra
of the radiation, emitted by an oil flame, a gas flame
and the wall of a furnace at different temperatures. If
the detector is to be able to tell when the flame goes
out, it must be sensitive in a spectral region in which
the flame is a great deal "brighter" than the furnace wall.
The ability to distinguish between flame and furnace wall can
also be based on an entirely different criterion, the "flickering"
of the flame. This calls for the use of a fast detector (some infrared detectors are suitable - the spectral region does not matter
in this case) whose signal is applied to a selective a.c. amplifier,
tuned to about 15 Hz. This method, however, is rather complicated and costly.
At wall temperatures below about 1200 oe the oil
flame is brighter than the wall in the visible range
(above 400 nm), and in this case cadmium-sulphide
cells, which are sensitive to visible light, can therefore
be used. The brightness of the gas flame in the visible
range is however too low to permit safe operation with
a cadmium-sulphide cell. In the ultra-violet range, on
the other hand, between say 200 and 300 nm, both the
oil and the gas flame are much "brighter" than even
the hottest furnace wall. Ultra-violet detection thus
offers a universal means offlame-failure control. Moreover, as explained below, a UV detector can be given
such a high intrinsic "gain" that its output signal may
if required be used directly for actuating a relay, which
simplifies the system considerably. What, is more, a
TUBE,
255
I
UV detector can monitor the ignition spark as well as
the flame. Since large furnaces or boilers are always
automatically ignited by means of an electric spark,
this indicates the possibility of monitoring and safeguarding the entire ignition prograf!lme (a spark ignites
a pilot flame which ignites the main burner).
The radiation emitted by a flame becomes "redder", i.e, the
spectrum shifts to longer wavelengths, as the distance from
the base of the flame increases - the ultra-violet radiation is
found mostly in the base of the flame. The UV detector must
therefore preferably be situated in such a way that the radiation
from the base of the flame is incident upon it. The best place for
the detector is therefore in the air-supply opening; this has the
additional advantage that the detector is cooled by the jet of air.
1250oC..······
....
....
....
.. ..
'
/
10
....
'
11500C...·
.../,./
.
.'
.,/
.
400
.
500nm
_À
Fig. I. Spectral intensity distribution (in arbitrary units) of the
radiation emitted by a gas flame (solid line), an oil flame (dashed
line) and the furnace wall (black-body radiator) at different temperatures (chain-dotted lines).
A cold-cathode tube as UV detector
If a sufficiently high voltage is applied between the
cathode and anode of a gas-discharge tube (higher than
the "ignition voltage"), a self-sustaining discharge
occurs in the tube as soon as there are sufficient numbers
of free electrons between the electrodes. These electrons
may be released from the cathode by thermionic emission or by incident radiation (photoelectric effect). In
the latter case, which applies for the cold-cathode tube,
the type of cathode material used determines the wavelength range of the radiation to which the tube responds. The current of the self-sustaining discharge is
so very much greater than that of the originally generated electrons that the tube has an extremely high
"internal gain". These are the principles underlying the
UV detector described below.
The tube, 'type 155 DG (fig. 2), contains two identical molybdenum electrodes. The work function of this
metal (i.e. the minimum energy an electron must acquire
in order 'to leave the solid) is 4.26 eV, corresponding
PHILlPS
256
TECHNICAL
REVIEW
VOLUME
29
directly from the mains. The gas filling is a mixture of
hydrogen and helium, giving an ignition voltage of
200 V, i.e. about 60 % of the peak voltage of the a.c.
supply. The tube is operated in the glow-discharge
region, in which the maintaining voltage for this tube
is also about 200 V. An incident UV photon can thus
initiate a gas discharge when the instantaneous value of
the supply voltage is greater than 200 V; the discharge
goes out immediately the voltage drops below the maintaining voltage. In order to prevent spontaneous reignition due to residual ionization from a preceding
cycle, the de-ionization time of the gas mixture should
be very short; the gas mixture which we have used
meets this requirement.
Fig. 2. The cold-cathode
tube type 155 UG. If the voltage between the electrodes
is sufficiently
high, a self-sustaining
gas
discharge
is produced
when UV radiation
is incident on the
electrodes.
Since molybdenum
has been used as electrode
material,
the tube responds
only to UV.
to a photoelectric threshold of about 290 nrn ; only
photons with a wavelength below this threshold are
effective. Obviously, the bulb ofthe tube must be made
of a material that transmits UV at these wavelengths;
the glass used for the bulb is a type that transmits
radiation at wavelengths greater than 200 nm. The tube
thus responds to radiation between 200 and 290 n m.
Fig. 3 shows the spectral distribution of the photoelectric quantum efficiency (i.e. the ratio of the number
of electrons released to the total number of incident
photons), the transmission characteristic of the glass,
and the resultant spectral sensitivity for detection.
The tube was designed for operation at 220 V a.c. and
a frequency of 50 or 60 Hz, so that it can be supplied
e
Fig. 3. General spectral distribution
of the sensitivity
s of the
detector,
derived from the quantum efficiency e(À) of the photoelectric effect at the electrode
and the transmission
t(},) of the
glass bulb.
Fig. 4. Cut-away
view of the 155 UG, showing the electrodes.
The effective part of the electrodes
consists of closely-spaced
straight pieces of wire at a short distance apart. The electrodes
are identical and, since the supply is a.c. they serve alternately
as cathode and anode.
Fig. 5. Transverse cross-section
through the effective part of the
electrodes. The electrical
field strength
is greatest between
the
wires, and smallest at A. The probability
that a UV photon
will
initiate a discharge therefore depends on the place where it strikes
the electrode. The probability
is greater at a higher voltage.
Fig.4 illustrates
the electrode configuration with
which this value of the maintaining voltage is obtained.
As an a.c. supply is used, the two electrodes are identical, each acting alternately as cathode and anode. The
parallel parts of the wires constitute the active region
of the electrodes. These wires are roughly circular in
cross-section, so that the electric field strength is not
the sarne at every point ofthe surface. The field strength
is of course greatest between the wires (fig. 5). This
1968, No. 8/9
FLAME-FAILURE
CONTROL
WITH
COLD-CATHODE
TUBE,
I
257
our explanation of this rnechanism we shall briefly conmeans that electrons released at different places on the
sider some of the effects encountered in a cold-cathode
electrode surface have a different probability of initiagas-discharge tu be.
ting a self-sustaining discharge. Since, when the voltage
During a self-sustaining discharge in such a tube the
between the electrodes is increased, the area of the eleccathode surface is continuously
bombarded by ions
trode surface for which a released electron can initiate
which are accelerated by the electric field in the cathode
a self-sustaining discharge becomes greater, the sensitivfall. The electrons which maintain the discharge are
ity of the tube (the number of ignitions per unit time
released from the cathode by the bombardment, which
for a given incident radiation) will increase with rising
also releases particles ofthe electrode material from the
voltage. The 155 UG does not therefore have the
plateau so characteristic of the Geiger-Müller
tube, ; surface (sputtering). These sputtered particles spread
through the tu be by diffusion, perhaps forming cornwhich it closely resembles in operation. For this reason
pounds with molecules in the gas, e.g. oxygen molethe 155 UG is not so suitable for measuring the intencules, and finally settle in one form or another on the sursity of the radiation; this tube is primarily intended to
face of the electrodes or on the glass wall. The ion bombe a very sensitive device for detecting whether or not
bardment thus has a decontaminating effect on the part
radiation is present.
of the cathode which is covered by the discharge (and
The voltage between the electrodes is subject to an
also on the gas atmosphere), and a contaminating effect
upper limit. The maximum permissible value is deteron every part that is not covered. It is evident that the
mined by the "free-running" voltage, that is to say the
contarnination will be greatest on the part of the cathvoltage at which the tube no longer goes out when the
ode surface which lies just outside the limits of the disirradiation is interrupted but spontaneously re-ignites
charge.
in each successive cycle of the supply voltage. The cause
This effect occurs in the tube discussed here, as it
of this effect is a declining weak ionization which perdoes in all other tubes designed for this kind of applicasists, in spite of the short de-ionization time of the gas
tion. One of the forms which the contamination takes
mixture, after the discharge has gone out. In the
here is a spontaneous crystal growth of molybdenum
155 UG the free-running voltage is considerably higher
oxide at the boundary of the discharge (fig. 6). The
than the nominal supply voltage, so that in practice
there is little danger of this effect being encountered.
During the life of the tube, however, the value of the
free-running
voltage may decrease if the electrode
surface becomes contaminated,
e.g. by the growth
of molybdenum-oxide
crystals. Locally higher field
strengths occur at the tips of such crystals, increasing
the chance of re-ignition. The occurrence of such contaminations can be prevented, however, by applying a
suitably shaped current waveform during the discharge. We shall now deal with this point at somewhat
greater length.
Effect of current waveform on the reliability of the tube
Contamination
or "poisoning" of the cathode surface is harmful not only because it lowers the freerunning voltage: if the contaminants are materials of
relatively low work function, like molybdenum hydi ide
or alkali metals from the glass, the tube might begin to
respond to visible light, which is the very thing that has
to be avoided.
Fortunately, it so happens that the discharge itself
removes the contaminants.
Extensive life tests have
shown that the electrode surface remains completely
clean if at each discharge the glow is made to cover
the entire active area of the electrodes by sending a
short pulse of current which is sufficiently large through
the tube. Since an a.c. supply is used, both electrodes
are continuously decontaminated in this way. To assist
Fig. 6. Molybdenum-oxide
crystals, which can form on the electrodes of the 155 UG if the peak current through the tube is
too low. Magnification
30x.
oxygen needed for this reaction comes from the glass
wall. This release of oxygen from the wall is also one
of the reasons for the gradual decline in the sensitivity
of the tube, since the oxygen absorbs UV photons
produced in the discharge and thus hinders the transition from non-self-sustaining
to self-sustaining discharge, in which these photons play an important role.
Although the decline in sensitivity does not reduce
the margin of safety - if the sensitivity is inadeq uate
the tube gives the alarm while the flame is still burning
(it is "fail-safe") -, this deterioration
should obviously be avoided as far as possible for the sake of a
reasonable tube life.
258
.:1
PHILlPS
TECHNICAL
VOLUME
REVIEW
29
The way to stop cathode contamination by crystal quired waveform and produce an output signal that
growth has already been indicated: in each discharge indicates whether or not the flame is alight. We have
there should be a pulse of current which is large enough seen that two types of circuit are possible: one that
to make the discharge cover the entire active surface of gives a very small dissipation in the tube and one that
the cathode. During the remaining part of the half- gives a high dissipation.
In the first circuit a short high-current pulse must
cycle the current may not drop to such a value that the
discharge contracts to a small part of the cathode sur- flow in the tube at each discharge, and the current must
face: in this part of the cycle the current must be either then drop right down to zero. This is done by making
zero or so high that the whole cathode remains covered. the discharge self-quenching. The circuit is shown in
Both alternatives are possible, and the circuits which fig. 7. Vs is the mains voltage with an r.m.s. voltage
can be used will be discussed below. In the first case the of 220 V, the load resistance R2 has a high value and
mean current is very Iow and there is thus very little RI has a very Iow value. We start from the situation
dissipation; in the second case the dissipation is rela- in which the discharge is out; the full voltage then
appears across the tube. When Vs increases to a value
tively high.
It is interesting that this difference is reflected in all
kinds of ways in the sensitivity behaviour of the tube.
With low dissipation the glass wall remains relatively
155UG~
cold and gives off little oxygen. Nevertheless, oxygen
pressure is gradually built up. The glass wall is also
3L.. ,....,
----+
.gradually darkened by the UV radiation from the discharge. The overall result is a slight decline in sensitiv- V.
=FCt
ity, about to half the original value in 10000 hours
C2=='
VrtJ
RI,
of operation. With high dissipation the wall gets much
R2[
[JRt
hotter and the emission of oxygen is greater. However,
the oxygen pressure remains lower than it does for low
0--........
- ......
-----........
-0---'- ----- dissipation, since the higher current causes greater
Fig. 7. Circuit for the cold-cathode tube in which the discharge is
cathode sputtering and therefore better decontaminaself-quenching: at each discharge a short pulse of current passes
tion of the gas atmosphere. The higher mean current
through the tube, but the average value of this current - i.e. the
also gives rise to greater UV irradiation of the wall, but dissipation in the tube - is low. The supply voltage to the circuit
is 220 V from the a.c. mains; the output voltage V(t) is a measure
here again there is ample compensation; since the wall of the intensity of the UV radiation incident on the tube.
temperature is higher, the glass does not darken so
quickly. For one reason and another the decline in
sensitivity is even smaller for high dissipation than it greater than the ignition voltage VI, an incident UV
photon can initiate the discharge. Since RI is Iow, a
is for low dissipation.
What are the consequences for the practical applica- high current first flows through the tube via Cl and RI.
tion ofthe tube? Since the sensitivity of the tube grad- Cl becomes charged, the voltage across R2 rises and
ually decreases, while the free-running voltage does the voltage across the tube falls. The component values
not decrease when the tube is operated with the kind of are so chosen that the tube voltage then falls to below
current waveform we have described (in practice it may the steady-state maintaining voltage Vrn which correeven rise for various reasons), the tube gives a reliable sponds to the load resistance R2. Now when the current
flame-failure control. The behaviour of the tube out- through Cl and RI stops flowing because Cl is charged
lined above has been established from life tests of up up, the tube can no longer continue to operate and
to 25 000 hours and a total of one and a half million cuts out. The capacitor Cl now discharges through
hours of tube life. The end of the useful life of a tube RI and R2, which causes the voltage across the tube to
in a particular application is determined entirely by the rise again. Spontaneous re-ignition is not possible beRI)CI has been made
minimum sensitivity required for that application; this cause the time constant (R2
depends on factors such as the distance from the flame, so large that the voltage across the tube rises more
the size of the flame and the minimum level required slowly than the re-ignition voltage (which rises again
to actuate the electronic circuit in which the tube is rapidly because of the de-ionization). The discharge
thus remains out and can only be re-ignited again when
incorporated.
the voltage across the tube has risen again sufficiently
The circuit
and a new UV photon strikes the (acting) cathode.
The circuit in which the tube is incorporated must be The required value of the time constant has been found
designed to give the current through the tube the re- to be small enough for several discharges to take place
if
'---'
.e,
!IW
+
1968, No. 8/9
FLAME-FAILURE
CONTROL
in this way during a half-cycle of the supply voltage.
Each discharge produces a voltage pulse across R2.
The use of an a.c. supply voltage means that both
positive and negative pulses appear across R2 (in the
positive and negative half-cycles) with respect to the
reference potential in fig. 7. Only the positive pulses
are passed via Ra and the diode D to the capacitor C2;
this charges up and discharges again between two
pulses through the load resistance R4, giving rise to a
fluctuating voltage Vet) across R4; see fig. 8. This output voltage Vet) is a measure of the number of discharges that have taken place during a number of cycles
(or, to be more exact, during their "positive" halves)
before time t, and is thus a measure of the intensity of
the UV radiation. The average magnitude of Vet) at a
particular radiation intensity is defined as the sensitivity
of the tube in the circuit. The incident radiation is
adjusted such that Vet) is normally 10 to 15 V; ifthere
are no discharges, then Vet) is of course zero. The rate
at which C2 discharges between two pulses is determined, for a given R4, by the capacitance of C2; if the
capacitance has a high value (i.e. the circuit has a high
time constant), Vet) decreases slowly, so that the average value is relatively high. A smaller capacitance gives
a faster decrease in Vet), and therefore a greater speed
of response and a lower output voltage, which in turn
gives a lower sensitivity.
The fluctuations of Vet) have a statistical character.
In the first place, the incidence of the UV photons at
the electrodes is a statistical effect and in the second
place not every photon incident at the negative electrode
causes a discharge, the probability
of this depends
on the location. As already explained, this probability
increases with increasing supply voltage; mains voltage
fluctuations therefore affect the output voltage as well.
When the circuit is used in a flame-failure control system it is necessary to take these different fluctuations
into account; this point will be dealt with below.
In the circuit shown in fig. 7 the available current I
in the load resistor R4 is of the order of some tens of
microamperes, so that the current has to be amplified
to energize a relay in a flame-failure control system.
In the second circuit, where a high dissipation is
tolerated in the tube, there is no need to amplify the
output signal; a relay winding is incorporated directly
in the circuit. The circuit is given in fig. 9; the discharge here is not self-quenching.
Vs is the mains
voltage, RI has a high value and R2 a low value. The
relay Rel is shunted across the capacitor C. The current
surge begins here in the same way as in the circuitin
fig. 7, but the discharge goes out only when Vs falls
below the maintaining voltage. The average current
flowing through the tube in this circuit is considerably
higher than in fig. 7; the peak value can be as high as
WITH
COLD-CATHODE
I
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259
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Fig. 8. Illustrating the variation of the output voltage V of the
circuit in fig. 7 as a function of time (a). The waveform of the
supply voltage Vs(t) is shown in (b). A UV photon incident on
the tube can initiate a discharge in those parts of the cycle in
which Vs is greater than the ignition voltage Vi of the tube. On
account of the statistical character of this process there is a
fluctuation in V(t).
several hundred milliamps. The tube has been found
capable of withstanding this high dissipation without
suffering any damage.
The operation of this circuit differs from that of the
circuit described earlier in that there are fewer ignitions
per unit time, and because of this the tube does not
discriminate so sharply between flame and background
radiation. These details cannot be dealt with here. The
remainder of this article will be based on the circuit of
fig. 7, and the same applies for the following article.
The choice of alarm level
When the UV detection circuit in fig. 7 is used in a
flame-failure control system, the output voltage Vet) is
155UG
!
0
L
Rel
Fig. 9. Circuit in which the mean tube current is sufficiently high
to energize directly a relay Rel. The 155 UG tube can withstand this high dissipation without damage.
260
PHILTPS TECHNICAL
applied to a circuit which closes the gas valve when the
voltage Vet) drops below a critical value, the alarm
level. The gas valve is opened again when Vet) rises
above this level. There are some advantages in using
different levels for closing and opening the gas valve,
but here we shall confine ourselves to the simple case
of a single level.
Even if the flames are not alight, discharges can
still be caused by cosmic radiation, or by ultra-violet
radiation from sunlight or a fluorescent lamp shining
in through a furnace window. As a result, even when
the flames are out, the voltage Vet) can rise to a small
positive value. The alarm level must therefore lie well
above this value - the higher the better for safety. It
mayalso happen that, while the flame is alight, there
are no discharges at all during one or two positive halfcycles of the supply voltage, so that the voltage Vet)
drops below the alarm level and the burner is unnecessarily shut off. The chance of such a false alarm is of
course greater the higher the alarm level has been
chosen.
On the other hand, a higher alarm level implies a
faster response. The correct alarm level therefore represents a compromise between the speed of response and
the chance of a false alarm. The main parameters which
determine the circumstances under which the compromise is chosen are the time constant of the detector
REVIEW
VOLUME 29
circuit and the radiation level at the detector. By varying these parameters, for example in positioning the
detector in relation to the source, one has to ensure
that a compromise can be found which meets
the minimum requirements specified by the user
in both respects (speed of response and avoidance
of false alarm).
.
Since by its nature, the output signalof the UV detector is subject to fluctuations, the relation between alarm
level and the probability of a false alarm can only be
investigated by means of a statistical analysis. This is
the subject of the second article.
Summary. The flame-failure control system for a furnace or boiler
must shut offthe fuel feed the moment the flames are extinguished
for one reason or another. There are various methods of detecting
the presence of a flame. After an introduetion to this subject, a
small cold-cathode tube is discussed which is ignited by the
UV radiation from a flame provided the voltage across the tube
is greater than the ignition voltage. The tube operates on a 220 V
a.c. supply; there are two identical molybdenum electrodes,
alternately acting as cathode and anode. If steps are taken to
ensure that the glow covers the entire cathode during each discharge, there is no contamination of the electrodes, which could
reduce the reliability of the tube. The effects which determine the
life of the tube are dealt with at some length. Two circuits are
discussed which give the current through the tube the required
form and deliver an output current which is a measure of the
intensity of the incident UV radiation. There are statistical
fluctuations in the output signal, and a result of this is that a
certain chance of false alarm has to be accepted when establishing
the alarm level, i.e. the level at which the fuel supply is shut off.
Il. Statistical aspects of the detection process and choice of the alarm level
R. P. Adriaanse and P. van der Laan
The first of these two articles described a UV detector
for use in a flame-failure control system; there are
statistical fluctuations in the output voltage of the
detector. In this second article the output signal will be
mathematically analysed and described with the aid of
a statistical model. A calculation will then be given
which shows how the alarm level can be chosen in such
a way that a' false alarm will occur on an average no
more than twice in a year of continuous operation. The
problem is of a complicated nature since the statistical
model describes a "Markov" process with dependent
increments. One of the implications of this is that the
Ir. R. P. Adriaanse, is with the Technical University of Delft, and
Drs. P. van der Laan is with Philips Information Systems and
Automation (Research Dept.), Eindhoven; both were formerly
with Philips Research Laboratories, Eindhoven.
fluctuations in the output voltage can only be characterized by probability distributions.
The analysis has been carried out for the circuit in
fig. 7; a typical curve of the output voltage Vet) from
this circuit when the flame is alight is shown in fig. 8.
A false alarm occurs if Vet) drops below the alarm level
while the flame is alight: we are therefore interested in
the lowest values that Vet) can reach. The various components of the circuit of course each have a' spread
about a nominal value. These deviations have an effect
on V(t); in our calculations we must always use the
particular combination of values that yields the lowest
value of Vet) ("worst-case" combination). Since the
calculations will be illustrated with numerical examples,
Table I gives the nominal value of various components
and the worst-case value for. a particular version of the