Title of Invention

METHOD AND DEVICE FOR DETERMINING THE REMAINING SERVICEABLE LIFE OF A PRODUCT

Abstract

The present invention relates to methods and an apparatus for recording operating lives, in particular until technical failure, of a product and for determining the remaining operating life of the product. In order to make it possible to estimate as accurately as possible, and without the use of a model, the life of any given products which have an operating data memory or have access to such an operating data memory, without storing time-domained signal profiles, the invention proposes that the remaining operating life of the product be determined, that operating lives of the products be recorded, and that operating life threshold values be determined on the basis of (so- called classified) operating variables which are subdivided into classes. In the process, weighting factors (a_ij) are determined first of all. The weighting factors (a_ij) are then used to determine weighted, accumulated operating lives and operating life threshold values. The reliability of s = 1...S products is thus monitored during production use. 8 (Figure 1)

Full Text

February 17, 2000 Robert Bosch GmbH, 70469 Stuttgart Methods and apparatus for determining the remaining operating life of a product Prior art The present invention relates to a method and an apparatus for determining the remaining operating life of a product; in this case, the invention also relates to methods and an apparatus for recording operating lives until technical failure of the product, and methods and an apparatus for determining operating life •threshold values of products as a function of specific operating variables, which vary with time, for monitoring the reliability of products and, finally, the invention also relates to an apparatus which is arranged in a product whose reliability is intended to be monitored, for comparing the actual operating life of the product with operating life threshold values as claimed in the precharacterizing clauses of the independent claims. A method for life determination is known from DE 195 16 481 Al. A controller is described for a motor vehicle, which has an operating data memory in which operating variables for the motor vehicle are stored, and can provide details relating to the failure probability and to the future reliability of the controller. The operating data memory is used to store significant data relating to the life history of a controller, in order to make it possible to make a statement of the reliability of the controller, when required. Object and advantages of the invention The object of the present invention is to allow estimation as accurately as possible, and without the use of any models, of the life of any given products which have an operating data memory or have access to such an operating data memory. A further objective is optimum recording of data and storage in an operating data memory, in order to allow the memory to be used optimally, and in particular in order to save memory space. In order to achieve this object, against the background of a method for recording operating lives until technical failure of a product, the invention proposes that values of specific operating variables be recorded, that the value range of the individual operating ■variables be subdivided into classes, and that the operating lives be recorded as a function of the class in which the recorded value of the operating variable falls. In addition, in order to achieve the object, the invention proposes a method and an apparatus for determining the remaining operating life of a product before technical failure, with values of a value range of at least one operating variable of the product being recorded, with the value range of the operating variable being subdivided into classes, and an operating life of the product being determined for each class and being stored in an operating data memory which is associated with that product, with the operating lives being assigned weighting factors which can be predetermined, and with at least one weighted, accumulated operating life for the product thus being determined, with the weighted, accumulated operating life being compared with at least one operating life threshold value which can be predetermined, and with the remaining operating life of the product being determined from this. The product whose operating life until technical failure is recorded is, for example, in the form of a controller or a subsystem (for example the brakes, engine, transmission, steering etc.) of a motor vehicle. The products have an operating data memory or are associated with such an operating data memory, in which the recorded operating variables and/or the operating lives are stored, and can be called up again when required. The operating data memory preferably has a nonvolatile memory (for example an EEPROM or a flash-EEPROM), as well as means for recording operating variables and/or the operating lives. In a motor vehicle, the operating data memory may be embodied, for example, in one or more controllers. The operating data memories are used to record discrete system states (for example the number of start attempts, the number of emergency starts, the number of thermal disconnections etc.), as well as the operating variables which vary with time. By way of example, sensor data such as temperature, current, voltage, pressure etc. is recorded as operating variables. The value range of the operating variables which is permissible in operating conditions is in each case subdivided linearly or non-linearly into a number of classes. Extreme values, which lead to immediate destruction of the product, are outside the permissible value range. The class allocation is based on the subdivision of the entire value range into relevant load groups. The individual classes have a different influence on the aging/wear of the product. The operating life of the product for each operating variable in each class is recorded in the operating data memory. According to the present invention, the determination of the individual technical operating life of a product and the calculation of the extent of wear at any given point in time are carried out on the basis of (so-called classified) operating variables which are subdivided into classes. The classified operating variables allow particularly reliable and accurate determination of the operating life of a product, with the memory requirement for the operating data memory being minimized, since there is no need to record time profiles of the operating variables. This allows particularly reliable preventative maintenance/repair to be carried out shortly before reaching the end of the technical operating life. One preferred development of the present invention proposes that the values of the operating variables be recorded at regular time intervals and that a class counter for a specific class be incremented if the value of a recorded operating variable falls in this class. Each operating variable for a specific product can thus be assigned an operating life histogram once the operating lives have been recorded, from which the operating life of the product is evident for that operating variable within a specific class. The size of the operating data memory, in bytes, which is required for storing the operating data is given by the product of the number of operating variables, the average number of classes for each operating variable, and the average number of bytes per class counter. The method according to the invention for recording operating lives on the basis- of classified operating variables has particular advantages, especially for determining operating life threshold values for products for monitoring the reliability of products. According to one advantageous development of the present invention, a method is therefore proposed for determining operating life threshold values of the type mentioned initially, which is characterized in that the operating lives of the products are determined for the classes of the operating variables until technical failure of the product by using the method as claimed in claim 1 or 2; the classes of the operating variables are assigned weighting factors; the weighting factors are determined from the solution of an optimization product min{ f(x) }, where x = {a„ij, t_ijk} taking account of the correlation between the individual operating variables; critical accumulated operating lives for the individual operating variables of the products are determined from the equation The individual classes have a different influence on the aging/wear of the products. The classes of the operating variables are therefore assigned weighting factors, which expresses the relative influence of a specific class of a specific operating variable on the aging and/or wear of the. product. The invention provides for the weighting factors to be determined from a subset K of the products, and for these then to be applied to the subset Z of the products. The critical weighted accumulated operating lives of the operating variables for series use can thus be determined for the products from the subset S, in such a way that the end of the technical life can be deduced from the fact that these operating lives have been reached. The weighting factors are determined from the solution of an optimization problem min{ f (x) }, where x = {a_ij, t__ijk} taking account of the correlation between the individual operating variables, with a_ij being the weighting factor which is assigned to the class j for the operating variable i, and t_ijk being the operating life of the product k for the class j of the operating variable i. The correlation between the operating variables can be taken into account, for example, by determining the weighting factors of an equation system ■in which the weighted accumulated operating lives for each operating variable are linked to one another by means of operators. The operators may represent, for example, an AND logic operation (product formation), an OR logic operation (sum formation) or a fuzzy logic operation (for example an intermediate state between AND and OR). Once the weighting factors have been determined by solving an optimization problem using suitable mathematical optimization algorithms, the critical accumulated operating lives for the individual operating variables are to be defined, such that the end of the technical life can be deduced from the fact that these operating lives are reached. To do this, using K products, a total of Z products are operated until technical failure, with the weighting factors calculated from the K products being applied to the classified operating variables of the Z products. is determined for all operating variables and for all Z products, with P_iz_krit being the critical accumulated operating life of the product z for the operating variable i, and t_ijz being the operating life of the product z for the class j for the operating variable i. This results in Z vectors for the weighted accumulated operating lives: The operating life threshold values which, when reached, make it possible to deduce that the technical life of the product will soon end are determined for the •individual products from the column minima of the matrix Y_z based on the equation: min{ P_iz_krit }, where i = 1...N or from the average of the column elements in the matrix Y__z using the equation AM -I- — -I_ This functions with the required reliability if the individual column elements are sufficiently close to one another, that is to say if the standard deviation of the column elements is not excessive. Spurious values should be excluded from the choice of the column minima. Once the critical accumulated operating lives have been determined for the individual operating variables, it is possible for the product tq signal the necessity for repair, for replacement or for maintenance, shortly before the critical threshold value is reached, for all the series products which are equipped with operating data memories. Alternatively, the operating variables stored in the product are evaluated in the course of regular product maintenance. Thus, in summary, k = 1...K products are first of all operated to technical failure, in order to make it possible to determine the weighting factors a_ij. The weighting factors a__ij are then integrated in the operating data memory of z = 1...Z products, which are once again operated until technical failure, in order to determine the critical accumulated operating lives P_iz_krit and, via a minimum selection or the average of the critical accumulated operating lives P_iz_krit, the operating life threshold values. The reliability of s = 1...S products is then monitored during series use, with the actual operating life of a product s being compared with a threshold value. One preferred embodiment of the present invention proposes that the weighting factors be determined from the solution of the optimization problem N K M_i min{ SUM SUM ABS{ SUM{ a_ij x t_ijk } -1 }} i=l k=l j=l with the secondary inequality condition a_ij > 0, where a_ij is the weighting factor which is assigned to the class j for the operating variable i, and t„ijk is the operating life of the product k for the class j for the operating variable i. According to this embodiment, no correlation between the individual operating variables is taken into account when calculating the weighting factors. It is thus based on the assumption that each operating variable can lead to technical destruction of the product, independently of the values of the other operating variables. If the determination of the weighting factors is not based on any correlation between the individual operating variables, the greatest ratio of a weighted accumulated operating life for one operating variable to the critical threshold value of the operating variable can be interpreted as the extent of wear. The remaining life in % is then calculated on the basis remaining life [%] = 1 - extent of wear [%]. An alternative embodiment of the present invention proposes that the weighting factors be determined from the solution of the optimization problem with the secondary inequality condition a_ij > 0. This embodiment takes account of the correlation between the individual operating variables. It is thus based on the assumption that a number of operating variables jointly lead to technical destruction of the product. According to this embodiment, the operating variables are linked to one another by means of pure AND logic operations (product formation). The weighting factors are determined such that the weighted class sums which are logically linked by the AND operator for each product have a minimum "separation" from one another. According to a third alternative embodiment, it is assumed that a number of operating variables are logically linked at the level of individual classes. This is based on the assumption that a number of operating variables within specific classes lead to technical destruction of the product. In order to achieve the object of the present invention against the background of an apparatus for recording the operating lives until technical failure of a product, the invention furthermore proposes that the apparatus have first means for recording the values of specific operating variables at regular time intervals, that the value range of the individual operating variables be subdivided into classes, and "the apparatus have second means for recording the operating lives as a function of the class in which the recorded value of the operating variable falls. One advantageous development of the invention proposes that the second means increment a class counter for a specific class if the value of the recorded operating variable falls in this class. The apparatus according to the invention for recording operating lives on the basis of classified operating •variables has particular advantages especially when determining operating life threshold values for products for monitoring the reliability of products. For this reason, according to one advantageous development of the present invention, an apparatus is proposed for determining operating life threshold values of the type mentioned initially, which is characterized in that the apparatus has means for carrying out the method as claimed in one of claims 5 to 8. In order to achieve the object of the present invention against the background of an apparatus of the type mentioned initially and arranged in a product that is to be monitored, the invention proposes that the operating life threshold values be determined according to the method as claimed in one of claims 5 to 8. The operating data memory for the apparatus may be designed to be particularly small since, when determining the operating life threshold values according to the invention, there is no need for memory-intensive recording of time profiles of the operating variables. Furthermore and in particular, operating data recording in classes has the advantage that the memory can be used optimally, that is to say in particular only a small amount of memory space is required, since there is no need to carry out complex recording of operating variables over the entire time axis, or with respect to the time axis. The invention, in particular the operating data recording, can expediently be implemented as an additional function in a controller, or in an apparatus which is specifically provided for this purpose. Further advantages and advantageous refinements can be found in the description and the features of the claims. Drawings One preferred exemplary embodiment of the present invention is explained in more detail in the following text with reference to the drawings, in which: Figure 1 shows a flow chart of a method according to the invention for recording operating lives until technical failure of a product, according to one preferred embodiment; and Figure 2 shows a flow chart of a method according to the invention for determining operating life threshold values of products, according to one preferred embodiment. Description of the exemplary embodiment Figure 1 shows a flow chart of the method according to the invention for recording operating lives t_ijk of a product k = 1...K until technical failure of the product k, according to one preferred embodiment. The product k, whose operating life t„ijk is recorded is, for example, in the form of a controller or a subsystem (for example the brakes, engine, transmission, steering etc.) of a motor vehicle. The product k has an operating data memory, in which recorded operating variables i = 1. . .N and/or the operating lives t_ijk are stored and can be called up again when required. The operating data memory preferably has a nonvolatile memory (for example an EEPROM or a flash-EEPROM) and means for recording the operating variables and/or operating lives. In a motor vehicle, the operating data memory may be provided, for example, in one or more controllers. The operating data memories are used to record discrete system states (for example the number of start attempts, the number of emergency starts, the number of thermal disconnections etc.), as well as the operating •variables i which vary with time. By way of example, sensor data such as temperature, current, voltage, pressure etc. is recorded as the operating variables i. The method starts in a function block 10. The value range which is permissible in operating conditions for the individual operating variables i to be recorded is subdivided linearly or nonlinearly into classes j = l...M_i in a function block 11. Extreme values, which lead to immediate destruction of the product k, are outside the permissible value range. The class association is based on the subdivision of the entire value range into relevant load groups. The individual classes j have a different influence on the aging/wear of the product k. Values of the operating variables i are recorded at regular time intervals in a subsequent function block 12. The operating lives t_ijk are recorded as a function of the class j in which the recorded value of the operating variable i falls. For this purpose, a class counter for a specific class j is incremented in a function block 13 if the value of the recorded operating variable i falls in this class j. Each operating variable i for a specific product k may thus be assigned an operating life histogram once the operating lives t_ijk have been recorded, from which the operating life t_ijk of the product k is evident for the operating variable i within a specific class j. The product of the state of the class counter and the time interval between the recorded values of the operating variables i resorts in the operating lives t_ijk. A check is carried out in a subsequent question block 14 to determine whether the recording of the operating lives t_ijk has been completed. If no, a jump is made back to the function block 12 again. If the recording of the operating lives t__ijk has been completed, a jump •is made to the end of the method, in the function block 15. Figure 2 shows a flow chart of a method according to the invention for determining operating life threshold values for the products z, according to one preferred embodiment. The method according to the invention starts in a function block 20. The operating lives t_ijk of the products k for the class j of the operating variables i are then first of all determined until technical failure of the product k, by using the method as shown in Figure 1. Weighting factors a_ij are then assigned to the classes of operating variables i in a function block 21. Since the individual classes j have a different influence on the aging/wear of the products k, the classes j of the operating variables i are assigned weighting factors a_ij which express the relative influence of a specific class j of a specific operating variable i on the aging and/or wear of the product k. In a subsequent function block 22, the weighting factors a_ij are determined from the solution of an optimization problem min{ f(x) }, where x = {a_ij, t__ijk} taking account of the correlation between the individual operating variables i. The weighting factors a_ij may be determined, for example, from the solution of the optimization problem with the secondary inequality condition a_ij > 0. In this case, no correlation is taken into account between the individual operating variables, and the process is based on the assumption that each operating variable i •can lead to technical destruction of the product k independently of the values of the other operating variables i. Alternatively, the weighting factors a__ij may also be determined from the solution of the optimization problem with the secondary inequality, condition a__ij > 0. This takes account of the correlation between the individual operating variables i, and is based on the assumption that a number of operating variables i lead jointly to technical destruction of the product k. In the exemplary embodiment, the operating variables i are logically linked to one another by means of pure AND logic operations (product formation). According to a third alternative, it is feasible for a number of operating variables i to be logically linked at the level of individual classes j . This is based on the assumption that a number of operating variables i within specific classes j lead to technical destruction of the product k. The invention provides for the weighting factors a_ij to be determined from a subset K of the products k, and for this then to be applied to the subset Z of the products z. Critical accumulated operating lives P__ iz_krit for the operating variables i can thus be determined for series use, from which, when these are •reached, it is possible to deduce the end of the technical operating life. Critical accumulated operating lives P__iz_krit are then determined in a function block 23 for the products z for the individual operating variables i, using the equation Finally, in the function block 24, the operating life threshold values are determined for the individual products z from which, when reached, it is possible to deduce that the technical life of the product will end soon, from the column minima of the matrix Y_z based on the equation This functions with the required reliability if the individual column elements are sufficiently close to one another, that is to say if the standard deviation of the column elements is small. Spurious results, if there are any, should thus be ignored when choosing the column minima. The method for determining operating life threshold values for the products z is completed in the function block 25. In addition to an absolute or relative minimum selection and simple averaging, it is also possible to use other methods and procedures, such as sliding, empirical or harmonic averaging or meridian •formation, etc., for determining the operating life threshold values. Once the critical accumulated operating lives P„iz_krit have been determined for the individual operating variables i, it is possible for the product s to signal the necessity for repair, for replacement or for maintenance, shortly before the critical threshold value is reached, for all series products s which are equipped with operating data memories. This may also be done, in particular, in the form of a self-diagnosis on the series product. Alternatively, the operating variables stored in the product s are evaluated in the course of regular product maintenance. This product maintenance may also be carried out, for example, for a product element of a vehicle, or on the vehicle itself during operation, in the form of an on-board diagnosis. In this context, Figure 3 shows a schematic illustration of one possible apparatus according to the invention. P denotes the product itself. This is connected to an operating data memory BSe, external to the product, by means of a communication system KS, in particular a cable system or bus system. Alternatively, an internal operating data memory BSi may be provided in the product itself. Both memories may also be present at the same time and, for example, a virtual memory may be formed from BSe and BSi. The means are combined in M, for example in the form of a microcomputer or microcontroller, which are used to carry out the method according to the invention, as described above. These means may also, for example, be provided or installed in a controller in a motor vehicle. The product P whose operating life is recorded is, for example, a controller or a subsystem (for example the brakes, engine, transmission, steering etc.) of a motor vehicle. The products P have an operating data memory BSi or are associated with such an operating data •memory (BSe), in which the recorded operating variables and/or the operating lives can be stored, and be called up again when required. The operating data memory preferably has a nonvolatile memory (for example an EEPROM or a flash memory) , as well as means EM for recording the operating variables and/or the operating lives. In a motor vehicle, the operating data memory may be implemented, for example, in one or more controllers. The recording means EM obtain their information for example via the communication system KS or other interfaces of the product, for example, to other sensors or actuators. The evaluation, operating life recording, operating life determination by threshold value comparison etc. are carried out in particular by the means M, which also initiate and carry out the signaling or the initiation of further measures. The recording means EM and the means M may also exist in combination, that is to say in a combined form, and may likewise be specifically associated with the operating data memories, or integrated in them. The operating data memories are used to record discrete system states (for example the number of start attempts, the number of emergency starts, the number of thermal disconnections etc.), as well as the operating variables which vary with time. By way of example, sensor data such as temperature, current, voltage, pressure etc. is recorded as the operating variables. The sensors required for this purpose are, for example, linked via the communication system KS or are coupled to the product via further interfaces. Depending on the product, the sensors may also be partially or entirely integrated in the product. The same applies to actuators which in particular supply information according to the invention. The necessity for repair, for replacement or for maintenance can thus be signaled by the product s, shortly before the critical threshold value is reached, for all series products s which are equipped with operating data memories. This may also be done, in particular, in the form of a self-diagnosis of the series product s, for example by means of operating data memories with integrated means M and/or recording means EM. February 17, 2000 Robert Bosch GmbH, 7 0469 Stuttgart 5 We Claims 1. A method for determining the remaining operating life of a product before technical failure, characterized in that values of a value range of at least one operating variable of the product are recorded, with the value range of the operating variable being subdivided into classes, and an operating life of the product being determined for each class and being stored in an operating data memory which is associated with that product, with the operating lives being assigned weighting factors which can be predetermined and hence at least one weighted, accumulated operating life being determined for the product, with the weighted, accumulated operating life being compared with at least one operating life threshold value which can be predetermined, and the remaining operating life of the product being determined from this. 2. The method as claimed in claim 1, characterized in that the process of determining the remaining operating life in the product is itself carried out in the form of a self-diagnosis of the product and, before or when at least one operating life reaches the at least one operating life threshold value, this fact is signaled and suitable measures are initiated. 3. A method for recording of operating lives (t__ijk) of a product (k) , characterized in that values are recorded from value ranges of specific operating variables (i), the value range of the individual operating variables (i) is subdivided into classes (j = 1. ..M_i), and the operating lives are recorded as a function of the class in which the recorded value of the operating variable falls. 4. The method as claimed in claim 1 or 3, charac- terized in that the values of the operating variables (i) are recorded at regular time intervals, and a class counter for a specific class (j) is incremented if the value of a recorded operating variable (i) falls in this class (j ) . 5. A method for determining an operating life thres hold value for a product for monitoring the reliability of the product by comparing an operating life with a threshold value, characterized in that values of value ranges of operating variables of the product which can be predetermined are recorded, with the respective value range of the respective operating variable being •subdivided into classes, and the values and/or the operating lives being stored on the basis of the classes in an operating data memory which is associated with that product, and in that a first subset of a product is operated until technical failure, by which means the operating lives of the classes of the operating variables of the product which can be predetermined are determined, with this being used to determine a weighting factor for each class and operating variable, which weighting factor reflects the influence on technical failure of the product of the respective class and operating variable, and a second subset of the product is operated until technical failure, with the weighting factors which have been determined from the first subset being applied to the second subset, and a critical operating life for all the classes being determined for each operating variable for the second subset of the product, and the operating life threshold value for all the classes of all the operating variables being determined from the critical operating lives. 6. A method for determining operating life threshold values of products (z = 1...Z) as a function of specific operating variables (i = 1...N) which vary with time, for monitoring of the reliability of products (s = 1...S), with the actual operating life of a product (s) being compared with a threshold value in the course of the monitoring process, characterized in that - the operating lives (t„ijk) of the products (k) are determined for the classes (j) of the operating variables (i) until technical failure of the product (k) by using the method as claimed in claim 3 or 4; - the classes (j) of the operating variables (i) are assigned weighting factors (a_ij); - the weighting factors (a_ij) are determined from the solution of an optimization problem min{ f(x) }, where x = {a_ij, t_ijk} ■taking account of the correlation between the individual operating variables; - critical accumulated operating lives (P_iz_krit) for the individual operating variables (i) of the products (z) are determined from the equation 7. The method as claimed in claim 1 or 5 or 6, characterized in that the weighting factors (a_ij) are determined from the solution of the optimization problem 9. An apparatus for determining the remaining operating life of a product before technical failure, characterized in that first means are included, which record values of a value range of at least one operating variable of the product, with the value range of the operating variable being subdivided into classes, and second means are included, which determine an actual operating life of the product for each class and store this in an operating data memory which is associated with that product, with third means furthermore being included, which assign weighting factors which can be predetermined to the operating lives and thus determine at least one weighted, accumulated operating life for the product, and with fourth means being included, which compare the weighted, accumulated operating life with at least one operating life threshold value which can be predetermined, and use this to determine the remaining operating life of the product. 10. An apparatus for recording the operating lives (t_ijk) of a product (k) , characterized in that the apparatus has first means for recording the values of specific operating variables (i) at regular time intervals, the value range of the individual operating variables (i) is subdivided into classes (j = 1...M_i), and the apparatus has second means for recording the operating lives as a function of the class in which the recorded value of the operating variable falls. 11. The apparatus as claimed in claim 9 or 10, characterized in that the second means increment a class counter for a specific class (j) if the value of a recorded operating variable (i) falls in this class (j). 12. An apparatus for determining operating life threshold values of products (z = 1...Z) as a function of specific operating variables (i = 1...N) which vary with time, for monitoring of the reliability of products (s = 1...S), with the operating life of a product (s) being compared with a threshold value in the course of the monitoring process, characterized in that the apparatus has means for carrying out the method as claimed in one of claims 5 to 8. 13. An apparatus which is arranged in a product (s = 1...S) whose reliability is intended to be monitored, having means for comparing the operating life of the product (s) with threshold values, characterized in that operating life threshold values according to the method as claimed in one of claims 5 to 8 are used as threshold values. 14, A method for determining the remaining operating life of a product before technical failure, substantially as hereinabove described and illustrated with reference to the accompanying drawings. 15. An apparatus for determining the remaining operating life of a product before technical failure, substantially as hereinabove described and illustrated with reference to the accompanying drawings.

Documents:

in-pct-2002-che-1467-abstract.pdf

in-pct-2002-che-1467-claims duplicate.pdf

in-pct-2002-che-1467-claims original.pdf

in-pct-2002-che-1467-correspondance others.pdf

in-pct-2002-che-1467-correspondance po.pdf

in-pct-2002-che-1467-description complete duplicate.pdf

in-pct-2002-che-1467-description complete original.pdf

in-pct-2002-che-1467-drawings.pdf

in-pct-2002-che-1467-form 1.pdf

in-pct-2002-che-1467-form 26.pdf

in-pct-2002-che-1467-form 3.pdf

in-pct-2002-che-1467-form 5.pdf

in-pct-2002-che-1467-other documents.pdf

in-pct-2002-che-1467-pct.pdf