Method and apparatus for detecting the end of life of a print cartridge for a thermal ink jet printer

A method and apparatus for detecting the end of life of a print cartridge for a thermal ink jet printer determines the status of the print cartridge and warns the user if the print cartridge is at or near the end of its useful life. In a first mode of operation, an initial temperature of a printhead contained in the print cartridge is checked after a threshold amount of ink is expelled from the printhead, such as for a high density print swath or during a service routine. This initial temperature is then compared with a maximum initial temperature. If the initial temperature exceeds the maximum initial temperature, a warning about the status of the print cartridge is sent to a user. If the initial temperature does not exceed the maximum initial temperature, the user is informed of the remaining life portion of the print cartridge. In a second mode of operation, a final temperature is checked after a period of time elapses since the threshold amount of ink is expelled from the printhead. This final temperature is then compared to a maximum final temperature. If the final temperature exceeds the maximum final temperature, a warning about the status of the print cartridge is sent to a user. If the final temperature is less than the maximum final temperature, the user is informed of the remaining life portion of the print cartridge. In a third mode of operation, the heat transfer efficiency of the print cartridge is calculated. If the heat transfer efficiency of the print cartridge is below a minimum heat transfer efficiency, a warning about the status of the print cartridge is sent to a user. If the heat transfer efficiency exceeds a minimum heat transfer efficiency, the user is informed of the remaining life portion of the print cartridge.

FIELD OF THE INVENTION
 This invention relates to the printer field. More particularly, this
 invention is a method and apparatus for detecting the end of life of a
 print cartridge for a thermal ink jet printer.
 BACKGROUND OF THE INVENTION
 Thermal ink jet printers have experienced great commercial success since
 they were invented back in the early 1980's. Modern day thermal ink jet
 printers give users high speed printing capabilities along with near
 photographic quality color reproduction, all for a very low price. These
 attributes have made a high quality thermal ink jet printer an essential
 part of a home or office computing system.
 In recent times, users have found that the thermal ink jet printer can be
 used not only to print text and numbers from word processing programs and
 spreadsheets, but can also be used to print images they have downloaded
 from the Internet, or even print their own photographs from pictures they
 have taken with their digital camera. In addition, users are now able to
 print off their own personalized catalogs, annual reports, newspapers and
 magazines-all using their ink jet printer in the comfort and convenience
 of their home or office.
 This increase in the amount of material printed by a printer has resulted
 in a trend in the printer industry towards replenishable printing systems.
 One example of a replenishable printing system is an "off axis" printing
 system, where the supply of ink in the print cartridge is replenished via
 another ink supply, typically located remotely to the print cartridge but
 connected via tubing or the like. Such replenishable printing systems
 allow the print cartridge to be used for a longer period of time than what
 has been conventionally done in the past, where the print cartridge was
 typically thrown away after the ink supply was exhausted.
 While such replenishable printing systems can result in a lower total
 printing cost to the user, such systems have raised new problems that,
 left unaddressed, may actually result in a great deal of inconvenience and
 additional expense to the user. One such problem is that the print
 cartridge of the ink jet printer can reach the end of its useful life and
 fail to print properly during a critical printing operation. While this
 failure may be proceeded by a diminished print quality, this may not be
 noticed by the user at all, or at least not until the print cartridge
 fails to print reliably and it is too late to go out and purchase a
 replacement print cartridge. Of course, these failures often seem to occur
 at the worst possible moment, usually the day a big deadline looms or a
 big presentation is due.
 While some attempts have been made to notify a user that the replenishable
 ink supply is running out of ink, these attempts do not solve the problem
 caused by a print cartridge failure independent of the amount of available
 ink, since a printer with a print cartridge at the end of its useful life
 will not print properly, or at all, even if there is an adequate supply of
 ink.
 SUMMARY OF THE INVENTION
 A method and apparatus for detecting the end of life of a print cartridge
 for a thermal ink jet printer determines the status of the print cartridge
 and warns the user if the print cartridge is at or near the end of its
 useful life. In a first mode of operation, an initial temperature of a
 printhead contained in the print cartridge is checked after a threshold
 amount of ink is expelled from the printhead, such as for a high density
 print swath or during a service routine. This initial temperature is then
 compared with a maximum initial temperature. If the initial temperature
 exceeds the maximum initial temperature, a warning about the status of the
 print cartridge is sent to a user. If the initial temperature does not
 exceed the maximum initial temperature, the user is informed of the
 remaining life portion of the print cartridge. In a second mode of
 operation, a final temperature is checked after a period of time elapses
 since the threshold amount of ink is expelled from the printhead. This
 final temperature is then compared to a maximum final temperature. If the
 final temperature exceeds the maximum final temperature, a warning about
 the status of the print cartridge is sent to a user. If the final
 temperature is less than the maximum final temperature, the user is
 informed of the remaining life portion of the print cartridge. In a third
 mode of operation, the heat transfer efficiency of the print cartridge is
 calculated. If the heat transfer efficiency of the print cartridge is
 below a minimum heat transfer efficiency, a warning about the status of
 the print cartridge is sent to a user. If the heat transfer efficiency
 exceeds a minimum heat transfer efficiency, the user is informed of the
 remaining life portion of the print cartridge.

DETAILED DESCRIPTION OF THE PREFERRED AND ALTERNATE EMBODIMENTS
 FIG. 1 shows a cross section of an print cartridge for a thermal ink jet
 printer used in the preferred embodiment of the invention. Print cartridge
 5 contains ink reservoir 6. In the preferred embodiment, ink reservoir 6
 is connected to hose 9 to be refilled automatically via "off axis" ink
 source 4. An alternate embodiment has been contemplated where hose 9 is
 not present and ink reservoir 6 is refilled manually via an aperture (not
 shown) in ink reservoir 6.
 During a printing operation, ink flows out of ink reservoir 6 towards
 printhead 12. Filter 7 screens out impurities and large air bubbles that
 may be present in the ink, thereby preventing these impurities and large
 air bubbles from reaching printhead 12. The filtered ink then passes
 through standpipe 8 to printhead 12. Printhead 12 contains hundreds of
 tiny resistors that selectively heat up the filtered ink and expel it
 through a corresponding number of tiny nozzles onto a media, such as paper
 or transparencies.
 As the filtered ink is heated by the resistors, any air that may still be
 present in the ink can separate out from the ink, and can become trapped
 in standpipe 8. While very little air separates out from the ink in any
 single printing operation, this trapped air can accumulate over time until
 a substantial amount of air is trapped in standpipe 8. When a substantial
 amount of air is trapped in standpipe 8, the trapped air prevents ink flow
 from reservoir 6 to printhead 12. This phenomenon, referred to herein as
 "die outgassing", in effect "starves" the printhead by not allowing ink to
 reach it. If ink cannot reach printhead 12, the printer cannot print. In
 addition, die outgassing can cause printhead 12 to overheat, since a
 liquid (i.e., ink) is much more efficient at dissipating heat from
 printhead 12 than a gas (i.e., an air bubble), as will be discussed in
 more detail later. If printhead 12 overheats too much, some or all of the
 hundreds of tiny resistors in printhead 12 can burn out and fail to
 function. In either event, print cartridge 5 has reached the end of its
 life and needs to be replaced.
 Printhead 12 also contains temperature sensor 16, the operation of which
 will be discussed in more detail later.
 FIG. 2 shows a block diagram of a ink jet printing system of the preferred
 embodiment of the invention. Ink jet printer 10 contains microprocessor 14
 connected to memory 15, interface electronics 13 and I/O channel 20.
 Microprocessor 14 is suitably programmed to carry out the operations of
 printer 10. Microprocessor 14 contains print cartridge end of life
 detector 100, the operation of which will be discussed in more detail
 later.
 Microprocessor 14 is operatively coupled to print cartridge 5 (FIG. 1) and
 status panel 25 via interface electronics 13. Status panel 25 is
 preferably one or more lights on the case of printer 10 that provides
 status information to the user, although an alternate embodiment has been
 contemplated where status panel 25 is a display or other form of
 enunciator of status to the user.
 Microprocessor 14 receives instructions and data from computer 40 via I/O
 channel 20. Computer 40 is connected to display 49 and input device 45. A
 printing operation is commenced when a user instructs computer 40 via
 input device 45 to print a desired document, image, or the like. Computer
 40 sends a print command to printer 10. This command is received by I/O
 channel 20 and sent on to microprocessor 14. Microprocessor 14 interprets
 the command and selectively fires the resistors contained in printhead 12
 of print cartridge 5, thereby expelling ink onto media 30 in a
 pattern/color corresponding to the desired document or image.
 In the preferred embodiment, end of life detector 100 contained in
 microprocessor 14 monitors the temperature of printhead 12 during the
 printing and servicing operation via temperature sensor 16 contained in
 printhead 12 (FIG. 1). In the preferred embodiment, temperature sensor 16
 contains a thermal sense resistor and associated memory. During the
 manufacturing process of print cartridge 5, the value of the thermal sense
 resistor is measured at a known, controlled ambient temperature. This
 measured value, along with the thermal coefficient of resistivity of the
 thermal sense resistor, is then used to calculate the value of this
 resistance at a typical operating temperature, such as 45.degree. C.,
 although the value at another preselected temperature could be the stored
 value and still fall within the spirit and scope of the invention. The
 operating resistance value is then stored in the associated memory of
 temperature sensor 16. For even greater accuracy, a "rolling average"
 thermal coefficient of resistivity value, representing the average thermal
 coefficient of resistivity values from the thermal sense resistors from
 the most recently manufactured batch of print cartridge units, is factored
 into the calculation discussed above. This serves a damping function to
 reduce the potentially negative effects of any one particular thermal
 sense resistor that has a value much higher or much lower than average. As
 will be discussed in more detail later, end of life detector 100 can
 accurately calculate the temperature of printhead 12 by measuring the
 value of the resistance of the thermal sense resistor in temperature
 sensor 16, and comparing this value with the resistance value stored in
 the associated memory of temperature sensor 16.
 FIGS. 3A-3D show a cross section of standpipe 8 of the print cartridge 5
 during different exemplary stages of the operating life of print cartridge
 5. FIG. 3A shows standpipe 8 at a point of time at the beginning of the
 life of print cartridge 5, referred to herein as t=t.sub.1. Standpipe 8 is
 shown filled with ink 51 between filter 7 and printhead 12. Convection
 current 61 is established that allows heat from printhead 12 to circulate
 through ink 51, thereby cooling printhead 12.
 FIG. 3B shows standpipe 8 at a point of time at the middle of the life of
 print cartridge 5, referred to herein as t=t.sub.2. Note that air bubble
 72 has formed on the surface of filter 7. Standpipe 8 is shown filled with
 ink 52 between bubble 72 and printhead 12. Convection current 62 is
 established that allows heat from printhead 12 to circulate through ink
 52, thereby cooling printhead 12. Since there is less ink in standpipe 8
 in FIG. 3B due to the existence of air bubble 72, convection current 62 is
 not as efficient at cooling printhead 12 as was convection current 61 of
 FIG. 3A.
 FIG. 3C shows standpipe 8 at a point of time near the end of the life of
 print cartridge 5, referred to herein as t=t.sub.3. Note that air bubble
 73 has gotten quite large and now takes up a significant portion of the
 volume of standpipe 8. Ink 53 makes up the remainder of the portion of the
 volume of standpipe 8. Convection current 63 is established that allows
 heat from printhead 12 to circulate through ink 53, thereby cooling
 printhead 12. Since there is still less ink in standpipe 8 in FIG. 3C due
 to the existence of air bubble 73, convection current 63 is not as
 efficient at cooling printhead 12 as was convection current 62 of FIG. 3B
 or convection current 61 of FIG. 3A.
 FIG. 3D shows standpipe 8 at a point of time at the end of the life of
 print cartridge 5, referred to herein as t=t.sub.4. Note that air bubble
 74 reaches all the way to printhead 12 and now takes up most of the volume
 of standpipe 8. At this point, die outgassing has occurred. Air bubble 74
 prevents the ink from flowing from reservoir 6 (FIG. 1) through filter 7
 to printhead 12. Print quality is very poor at this point of time, and
 remaining ink 54 will soon be expelled through printhead 12. No convection
 current is established in remaining ink 54, so printhead 12 is not cooled
 effectively. The temperature of printhead 12 at t=t.sub.4 is considerably
 hotter than it was at t=t.sub.1, t=t.sub.2, or t=t.sub.3. Some or all of
 the resistors in printhead 12 will now overheat and fail.
 FIG. 4 shows a graph of printhead temperature versus time for printhead 12
 during different exemplary stages of the operating life of print cartridge
 5, as calculated by end of life detector 100 via information it receives
 from temperature sensor 16, as discussed above. Graph 81 shows printhead
 12 when print cartridge 5 is at the beginning of its operating life:
 t=t.sub.1. Graph 81 corresponds to FIG. 3A. Graph 82 shows printhead 12
 when print cartridge 5 is at the middle of its operating life: t=t.sub.2.
 Graph 82 corresponds to FIG. 3B. Graph 83 shows printhead 12 when print
 cartridge 5 is near the end of its operating life: t=t.sub.3. Graph 83
 corresponds to FIG. 3C. Graph 84 shows printhead 12 when print cartridge 5
 is at the end of its operating life: t=t.sub.4. Graph 84 corresponds to
 FIG. 3D.
 At t=0, printer 10 has received a command to print, where a threshold
 amount of ink is expelled just prior to time t=0. The temperature of
 printhead 12 is highest immediately after the threshold amount of ink is
 expelled through the printhead, then decreases over time.
 Note that beginning of life curve 81 (corresponding to t=t.sub.1 and FIG.
 3A) reaches an initial temperature of T.sub.1, and quickly falls almost to
 T.sub.0 at time=t.sub.delay. This is considered normal and is indicative
 of a healthy print cartridge at or near the beginning of its life.
 Middle of life curve 82 (corresponding to t=t.sub.2 and FIG. 3B) reaches an
 initial temperature of T.sub.2 and falls more slowly to a temperature
 higher than T.sub.0 at time=t.sub.delay. Note that T.sub.2 is higher than
 T.sub.1, due to the less efficient cooling ability of convection current
 62 (FIG. 3B). This is considered normal and is indicative of a healthy
 print cartridge at the middle of its life. The user may be informed that
 his/her print cartridge has a portion (e.g., 50%) of its useful life
 remaining.
 Near end of life curve 83 (corresponding to t=t.sub.3 and FIG. 3C) reaches
 an initial temperature of T.sub.3 and falls still more slowly to a
 temperature higher than T.sub.delay.sub..sub.-- .sub.warn at
 time=t.sub.delay. Note that T.sub.3 is higher than both T.sub.2 and
 T.sub.1, due to the still less efficient cooling ability of convection
 current 63 (FIG. 3C). Note also that T.sub.3 is higher than
 T.sub.init.sub..sub.-- .sub.warn. Curve 83 is indicative of a print
 cartridge near the end of its life. The user should be warned, either now
 or soon, that s/he should replace the print cartridge with a new one.
 At end of life curve 84 (corresponding to t=t.sub.4 and FIG. 3D) reaches an
 initial temperature of T.sub.4 and falls ever so slowly to a temperature
 higher than T.sub.delay.sub..sub.-- .sub.fail at time=t.sub.delay. Note
 that T.sub.4 is higher than T.sub.3, T.sub.2 and T.sub.1, due to the lack
 of a convection current (FIG. 3D). Note also that T.sub.4 is higher than
 T.sub.init.sub..sub.-- .sub.fail. Curve 84 is considered indicative of a
 print cartridge at the end of its life, where die outgassing, causing ink
 starvation and/or resistor failure, has already occurred or will occur
 imminently. The user should be warned immediately that his/her print
 cartridge has failed (or will imminently fail) and should be replaced.
 FIG. 5 shows graph of heat transfer efficiency versus time for the life of
 a printhead. Note that in curve 89 the heat transfer efficiency of the
 printhead starts out high at t=t.sub.1 (corresponding to FIG. 3A and curve
 81 of FIG. 4), begins to fall at t=t.sub.2 (corresponding to FIG. 3B and
 curve 82 of FIG. 4), falls more rapidly at t=t.sub.3 (corresponding to
 FIG. 3C and curve 83 of FIG. 4), then bottoms out at t=t.sub.4
 (corresponding to FIG. 3D and curve 84 of FIG. 4). Those skilled in the
 art will appreciate that curve 89 may take on different characteristics in
 different printhead architectures and standpipe geometries.
 FIG. 6 shows a graph of a linearized function of temperature versus time
 for the life of a printhead. The graph of FIG. 6 is a linearized version
 of the graph of FIG. 4. The slopes of the lines in FIG. 6 are directly
 related to heat transfer efficiencies. Heat transfer efficiency line 91
 corresponds to a heat transfer efficiency at t=t.sub.1 (which in turn
 corresponds to FIG. 3A and curve 81 of FIG. 4). Heat transfer efficiency
 line 92 corresponds to a heat transfer efficiency at t=t.sub.2 (which in
 turn corresponds to FIG. 3B and curve 82 of FIG. 4). Heat transfer
 efficiency line 93 corresponds to a heat transfer efficiency at t=t.sub.3
 (which in turn corresponds to FIG. 3C and curve 83 of FIG. 4). Heat
 transfer efficiency line 94 corresponds to a heat transfer efficiency at
 t=t.sub.4 (which in turn corresponds to FIG. 3D and curve 84 of FIG. 4).
 Note that the slope of the curves in FIG. 6 gets smaller as the heat
 transfer efficiency of the printhead declines. The significance of this
 fact will be discussed shortly.
 FIGS. 7-8 show a flowchart of the operation of end of life detector 100 of
 the preferred embodiment of the invention. In the preferred embodiment,
 end of life detector 100 is software stored in memory 15 and executed in
 processor 14, although an alternate embodiment has been contemplated where
 end of life detector 100 is a comparable special purpose hardware circuit
 that performs the same functions shown in FIGS. 7-8. Referring now to FIG.
 7, block 101 checks to see if an end of life test for print cartridge 5
 should be run. In the preferred embodiment, this test is only run during
 another service event, such as a wet wipe, scrub, or prime operation.
 Printer 10 routinely performs such types of service on print cartridge 5
 to keep it operating at peak performance. During a service event, print
 cartridge 5 is typically parked in service station 21 (FIG. 2).
 An alternate embodiment has been contemplated where the end of life test is
 run more frequently during normal printing operations. This test could be
 run continuously as printer 10 is printing, or could be run less
 frequently, such as after a certain number of ink drops have been fired or
 after a certain period of time has elapsed. In any event, if block 101 is
 answered negatively, the flowchart terminates in block 199.
 If the end of life test is to be run, block 105 checks to see if a
 threshold amount of ink has been expelled from printhead 12. In the
 preferred embodiment, while print cartridge 5 is parked in service station
 21, a command to expel a threshold amount of ink (the equivalent of a high
 density print swath) into a "spittoon" or "diaper" in service station 21
 is executed. This command causes the resistors in printhead 12 to heat up
 and expel an amount of ink. In an alternate embodiment, the end of life
 test is run upon the occurrence of the printing of a high density print
 swath (equivalent to a threshold amount of ink being expelled) on media 30
 (FIG. 2) during a normal printing operation. In this embodiment, low
 density print swaths are ignored, since it is more difficult to accurately
 run the end of life test with low density print swaths, although other
 embodiments have been contemplated where the threshold amount of ink is
 any amount of ink.
 If block 105 detects that a threshold amount of ink has been expelled
 (either during a service event or during normal printing operation,
 depending on the embodiment), block 110 determines the temperature of
 printhead 12 at the completion of the expulsion of the threshold amount of
 ink (referred to herein as the "initial temperature", or t=0). This
 temperature is determined by measuring the resistance of the thermal sense
 resistor of temperature sensor 16 and comparing this resistance with the
 resistance value stored in the associated memory of temperature sensor 16.
 As has been discussed, the resistance value stored in the associated
 memory of temperature sensor 16 is the value of the thermal sense resistor
 at a typical operating temperature, such as 45.degree. C. By comparing
 these two resistance values and knowing the typical thermal coefficient of
 resistivity specified in the manufacturing process, the temperature of
 printhead 12 can be accurately determined.
 After block 110 determines the initial temperature of printhead 12, block
 115 waits a predetermined period of time. After this predetermined period
 of time has elapsed, block 120 determines the temperature of printhead 12,
 referred to herein as the "final temperature". The final temperature is
 determined in the same manner as the "initial temperature" was determined,
 as discussed above.
 Block 125 then measures the ambient temperature of the printer. In the
 preferred embodiment, this is determined by reading the value of ambient
 temperature sensor 22 contained inside printer 10 (FIG. 2). Typically,
 this ambient temperature will be at or slightly above the normal
 environmental temperature of the room or building printer 10 resides in.
 This printer ambient temperature is used in one of the modes of operation
 used to determine the status of the printer, as will be discussed.
 Block 200 calls the Determine Status of Print Cartridge subroutine of FIG.
 8. Referring now to FIG. 8, subroutine 200 preferably operates in a choice
 of three different modes of operation: Peak Temperature Mode, Delay Time
 Mode, and Heat Transfer Mode. While in the preferred embodiment the Heat
 Transfer Mode is selected, alternate embodiments have been contemplated
 where one of the other modes is selected instead. In addition, additional
 alternate embodiments have been contemplated where a combination of modes
 is selected. In these additional alternate embodiments, a "voting"
 procedure may be used, where a unanimous or majority vote of the different
 modes determines the status of the print cartridge.
 If Peak Temperature Mode is selected (either by a user, preselected at the
 factory, the only mode available, etc.), block 225 is answered
 affirmatively, and flow of control moves to block 230. Block 230 checks to
 see if the initial temperature is too high. In the preferred embodiment,
 this is done by comparing the initial temperature with a maximum initial
 temperature stored in memory 15 (FIG. 2). In the preferred embodiment, the
 maximum initial temperature is the highest temperature a printhead of a
 properly functioning print cartridge should reach after it prints a high
 density print swath. In our example shown in FIG. 4, this maximum
 temperature would be Temp.sub.init.sub..sub.-- .sub.warn shown as being
 between T.sub.2 and T.sub.3.
 If block 230 determines that the initial temperature is too high, block 235
 sets a warning flag, indicating that the print cartridge has less than a
 specified percentage of its life left. If Block 230 determined that the
 initial temperature exceeds T.sub.init.sub..sub.-- .sub.fail (FIG. 4), the
 print cartridge has reached the end of its life and a fail flag is set in
 block 235. Flow of control moves to block 299, where the subroutine
 returns to block 135 (FIG. 7), which warns the user that the print
 cartridge is either near the end of its useful life and should be replaced
 soon (if T.sub.init.sub..sub.-- .sub.warn &lt;T&lt;T.sub.init.sub..sub.--
 .sub.fail), or has reached the end of its useful life and must be replaced
 immediately (if T&gt;T.sub.init.sub..sub.-- .sub.fail). Preferably, printer
 10 sends a command to computer 40 via I/O channel 20 to display this
 message on display 49, but alternate embodiments have been contemplated
 where this message is printed out on media 30 and/or displayed on status
 panel 25. In any event, after the user is properly warned, flow of control
 returns back to block 101.
 An alternate embodiment has been contemplated where the warning message is
 not given immediately after the warning flag is set in block 235, but
 after a predetermined number of pages have been printed (or drops of ink
 expelled) after the warning flag is set. This embodiment may give more
 accurate results in some situations.
 Note that the warning message given does not tell the user that their print
 cartridge is low on or out of ink, but that their print cartridge is near
 or has reached the end of its useful life. In the preferred embodiment,
 there is a separate detection mechanism contained in or associated with
 ink source 4 that provides an additional warning to the user that he/she
 is almost out of ink. This mechanism typically measures the ink level of
 ink source 4 (FIG. 1). This can be done in much the same manner as the
 gasoline level in a gas tank of an automobile is measured, or by more
 complex measurement techniques, such as optical detection, monitoring the
 mechanism response (resistance, rebound, etc.) of the pump (not shown)
 between ink source 4 and ink reservoir, etc. As has been discussed
 previously, an end of life warning can be given even if ink source 4 is
 full of ink, due to die outgassing. Those skilled in the art will also
 appreciate that if a user ignores the warnings that ink source 4 is low on
 ink and allows ink source 4 to run dry of ink, the lack of ink in
 standpipe 8 will cause the temperature of printhead 12 to rise and trigger
 an end of life warning, as the air in standpipe 8 will permanently starve
 printhead 12 of ink--even if ink source 4 is later refilled.
 An alternate embodiment has been contemplated where the warning message
 discussed above is not sent to the user unless end of life detector 100
 also determines that a predetermined number of drops of ink have been
 fired from printhead 12, or a predetermined amount of total printing time
 has elapsed, thereby providing an independent, corroborating basis for
 concluding that print cartridge 5 is indeed reaching the end of its life.
 While this embodiment adds complexity to end of life detector 100 and may
 result in an increased number of false negatives (i.e., print cartridge
 deemed acceptable when it really isn't), it may tend to reduce the number
 of false positives (i.e., print cartridge deemed at end of life when it
 really isn't) and may be desirable in some applications.
 Referring again to FIG. 8, if block 230 determines that the initial
 temperature is within acceptable limits, block 236 sets an "inform flag"
 containing the portion of the useful life of the print cartridge estimated
 as being remaining. The subroutine then returns to block 135 of FIG. 7,
 where the user is informed of the percentage of life left in the print
 cartridge. In the preferred embodiment, this informational message is not
 given to the user unless the user has specifically requested to know such
 status about the ink supply unit, or if this status is unobtrusively
 displayed on display 49 or status panel 25. In any event, flow of control
 returns back to block 101.
 If the Peak Temperature Mode is not selected, block 225 (FIG. 8) is
 answered negatively, and block 238 checks to see if Delay Time Mode is
 selected. If Delay Time Mode is selected (either by a user, preselected at
 the factory, the only mode available, etc.), block 238 is answered
 affirmatively, and flow of control moves to block 240. Block 240 checks to
 see if the final temperature is too high. If the final temperature is too
 high, this would indicate that the printhead took longer to cool down to a
 normal operating temperature than it should have, probably as the result
 of die outgassing. In the preferred embodiment, the final temperature,
 measured as discussed above, is compared to a maximum final temperature.
 This maximum final temperature is the highest temperature the printhead
 should be after a predetermined period of time has elapsed since the
 threshold amount of ink was expelled from printhead 12. In our example
 shown in FIG. 4, this maximum temperature is T.sub.delay.sub..sub.--
 .sub.warn, shown as being between the temperatures of curve 82 and curve
 83 at time=t.sub.delay.
 If block 240 determines that the final temperature is too high (i.e.,
 T.sub.delayt.sub..sub.-- .sub.warm &lt;T&lt;T.sub.delay.sub..sub.-- .sub.fail),
 block 235 sets a warning flag, indicating that the print cartridge has
 less than a specified percentage of its life left. If Block 240 determined
 that the initial temperature exceeds T.sub.delay.sub..sub.-- .sub.fail
 (FIG. 4), the print cartridge has reached the end of its life and a fail
 flag is set in block 235. Flow of control moves to block 299, where the
 subroutine returns to block 135 (FIG. 7), which warns the user that the
 print cartridge is either near the end of its useful life and should be
 replaced soon (if T.sub.delay.sub..sub.-- .sub.warn
 &lt;T&lt;T.sub.delay.sub..sub.--fail ), or has reached the end of its useful
 life and must be replaced immediately (if T&gt;T.sub.delay.sub..sub.--
 .sub.fail), in the manner discussed in more detail above. After the user
 is properly warned, flow of control returns back to block 101.
 A second embodiment of the Delay Time Mode has been contemplated where the
 period of time it takes the printhead to cool to a given temperature, such
 as T.sub.0, is measured in block 240. If this final time is too high, this
 would indicate that the printhead took longer to cool down to a normal
 operating temperature than it should have, probably as the result of die
 outgassing. As with the first embodiment of the Delay Time Mode described
 above, the final time to reach a predetermined temperature can be used to
 warn the user that the print cartridge has less than a specified
 percentage of its life left or that the print cartridge has reached the
 end of its life.
 If block 240 determines that the final temperature (or final time) is
 within acceptable limits, block 236 sets an "inform flag" containing the
 portion of the useful life of the print cartridge estimated as being
 remaining. The subroutine then returns to block 135 of FIG. 7, where the
 user is informed of the percentage of life left in the print cartridge. As
 discussed above, this informational message is not given to the user
 unless the user has specifically requested to know such status about the
 ink supply unit, or if this status is unobtrusively displayed on display
 49 or status panel 25. In any event, flow of control returns back to block
 101.
 If the Delay Time Mode is not selected, block 245 (FIG. 8) selects Heat
 Transfer Efficiency Mode, and flow of control moves to block 250. Block
 250 checks to see if the heat transfer efficiency is too low. In the
 preferred embodiment, this is determined by looking at a linearized graph
 of temperature versus time such as that shown in FIG. 6. If the slope of
 the heat transfer efficiency line is less than a warning slope, such as a
 slope between the slopes of heat transfer efficiency lines 92 and 93 of
 FIG. 6, the heat transfer efficiency of the printhead is too low. If block
 250 determines that the heat transfer efficiency of the printhead is too
 low, block 235 sets a warning flag, indicating that the print cartridge
 has less than a specified percentage of its life left. If Block 250
 determined that the slope of the heat transfer efficiency line is less
 than a failure slope, such as a slope between heat transfer efficiency
 lines 93 and 94 of FIG. 6, the print cartridge has reached the end of its
 life and a fail flag is set in block 235. Flow of control moves to block
 299, where the subroutine returns to block 135 (FIG. 7), which warns the
 user that the print cartridge is either near the end of its useful life
 and should be replaced soon (if Warning Slope&gt;Slope&gt;Failure Slope), or has
 reached the end of its useful life and must be replaced immediately (if
 Slope&gt;Failure Slope), in the manner discussed in more detail above. After
 the user is properly warned, flow of control returns back to block 101.
 If block 250 determines that the heat transfer efficiency is within
 acceptable limits, block 236 sets an "inform flag" containing the portion
 of the useful life of the print cartridge estimated as being remaining.
 The subroutine then returns to block 135 of FIG. 7, where the user is
 informed of the percentage of life left in the print cartridge. As
 discussed above, this informational message is not given to the user
 unless the user has specifically requested to know such status about the
 ink supply unit, or if this status is unobtrusively displayed on display
 49 or status panel 25. In any event, flow of control returns back to block
 101.
 Referring back to FIGS. 3-6 in conjunction with the above discussion of
 FIG. 7-8, the flowchart of FIGS. 7-8 would determine that the printhead at
 or near the beginning of its useful life (FIG. 3A, curve 81 of FIG. 4,
 t=t.sub.1 of FIG. 5, and heat transfer efficiency line 91 of FIG. 6) was
 operating acceptably, and the user would be informed as to the estimated
 percentage of useful life remaining. The printhead at the middle of its
 useful life (FIG. 3B, curve 82 of FIG. 4, t=t.sub.2 of FIG. 5, and heat
 transfer efficiency line 92 of FIG. 6) was also operating acceptably, and
 the user would be informed as to the estimated (albeit lower) percentage
 of useful life remaining. The printhead near the end of its useful life
 (FIG. 3C, curve 83 of FIG. 4, t=t.sub.3 of FIG. 5, and heat transfer
 efficiency line 93 of FIG. 6) would result in a warning to the user that
 the printhead was near the end of its useful life and should be replaced
 soon. The printhead at the end of its useful life (FIG. 3D, curve 84 of
 FIG. 4, t=t.sub.4 of FIG. 5, and heat transfer efficiency line 94 of FIG.
 6) would result in a warning to the user that the printhead was at the end
 of its useful life and should be replaced immediately.