GO-FLOW-based complex system reliability rapid analysis method

Abstract

The invention provides a GO-FLOW-based rapid reliability evaluation method, which is particularly suitable for reliability analysis of a complex system with multiple states, time sequences, staged tasks and states changing along with time. The method comprises the following steps of: 1, identifying information of each component of a system according to a topological structure of the system, and inputting related initial information into an Excel spreadsheet; 2, numbering the nodes according to a signal transmission path, and converting the numbered nodes into two-dimensional coordinate data, so as to facilitate the subsequent identification of the series-parallel connection relationship of the system by using software; 3, traversing all operators, and calculating the reliability of each operator and the reliability of the whole system based on the reliability data and a GO-FLOW operator calculation formula; according to the method, the system structure change can be quickly adapted, a user only needs to update the structure change data in the spreadsheet without modifying a bottom-layer program code, manual intervention and maintenance cost can be remarkably reduced, and reliability analysis of a complex system can be completed in a quick and accurate mode.

Description

Technical Field

[0001] The invention belongs to the technical field of GO-FLOW method reliability analysis, and in particular relates to a GO-FLOW-based complex system reliability rapid analysis method. Background Art

[0002] In the context of rapid technological development, the complexity of various systems continues to increase. This increase in complexity enhances system performance on the one hand, but also leads to higher potential faults and failure risks on the other. Especially in the fields of aviation, aerospace and military, which have extremely high reliability requirements, any minor failure in the system may cause serious economic losses and safety hazards. Therefore, ensuring and improving system reliability has become the focus of many industries, and how to efficiently and accurately analyze and evaluate the reliability of complex systems has become an urgent challenge in scientific research and engineering practice.

[0003] Fault tree analysis (FTA) is a widely used reliability analysis method in engineering. However, when faced with complex situations where dynamic systems or system states change over time, the static characteristics of FTA may make its analysis results incomplete or inaccurate. The GO-FLOW method can meet the needs of more effective safety and reliability assessment of complex systems by introducing dynamic analysis and more detailed fault mode identification. It is especially suitable for complex systems with staged tasks and states that change over time, and can identify common cause failures and deal with uncertainty problems in the system. However, the quantitative calculation formula of operators in GO-FLOW is relatively complex and involves a lot of manual calculations. Especially for ordinary users, they must have corresponding professional knowledge to construct the GO-FLOW diagram of the system. In addition, once the system structure changes, the GO-FLOW diagram also needs to be adjusted accordingly, which undoubtedly increases the labor intensity of the analysis. The above problems have limited the popularization and application of the GO-FLOW method to a certain extent.

[0004] In summary, it is very meaningful to provide a simplified analysis method to address the limitations of the current GO-FLOW method, such as complex calculation formulas and high requirements for user professional knowledge. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a rapid analysis method for the reliability of complex systems based on GO-FLOW, which is suitable for reliability analysis of complex systems with multiple states, time sequences, staged tasks and states that change over time.

[0006] The technical solution of the present invention is: a complex system reliability rapid analysis method based on GO-FLOW, comprising:

[0007] S1: Identify the information of each component of the system according to the system topology structure and enter it into an Excel spreadsheet 1, where the information of the component includes the name, failure mode, reliability data, and timing of each component;

[0008] S2: Based on the information of the component parts, use the GO-FLOW operator to characterize each component, obtain the reliability data of each operator, and enter the reliability data of each operator into Excel spreadsheet 2;

[0009] S3: Obtaining a signal transmission path according to the positions of the components of the system and the order formed after the operators characterize the components;

[0010] Determine the primary input, secondary input and output of the operator according to the signal transmission path;

[0011] The nodes of the system are numbered according to the signal transmission path, and the position information of the components in the system is converted into two-dimensional coordinate data and entered into Excel spreadsheet 3; wherein the node is defined as: a node is set on the left and right sides of each component, and if the right node of the current component is in the same position as the left node of the next component, the two components share this node;

[0012] S4: using the data in the Excel spreadsheet 3 to determine the series-parallel relationship of each component;

[0013] S5: Traverse all operators, determine the primary input, secondary input and output of the operator based on the signal transmission path and the reliability data of the operator in Excel spreadsheet 2 and the calculation formula of GO-FLOW, and calculate the reliability of each operator and the reliability of the system.

[0014] Furthermore, in S4: using the data in Excel spreadsheet 3 and Python software to automatically determine the series and parallel relationships between the components.

[0015] Furthermore, in S3, the nodes of the system are numbered according to the signal transmission path according to the following rules:

[0016] For a series structure system, natural numbers are used to number the nodes from left to right from small to large;

[0017] If there are both series and parallel structures, they shall be marked according to the following standard method:

[0018] According to the direction of signal flow, in the case of parallel branches, they are numbered from left to right and from top to bottom. If the coordinate positions of two components are the same, they are considered to be in parallel. If the right node of one component is connected to the left node of another component in sequence, the two components are considered to be connected in series.

[0019] Furthermore, S5 includes:

[0020] Create an empty list named "Result" to store the reliability of each operator and the reliability of the entire system obtained during the calculation process;

[0021] Call the corresponding reliability calculation function for different types of operators to obtain the reliability of the operator;

[0022] The reliability of the system is calculated based on the reliability of the operators.

[0023] The present invention provides a complex system reliability rapid analysis method based on GO-FLOW, which combines Python and Excel spreadsheet technology to accelerate and simplify the GO-FLOW reliability analysis process. The present invention uses a spreadsheet to guide users to input basic data and structural information of the system, automatically processes data through a built-in Python script, and generates intermediate analysis results. In addition, the present invention also allows users to adjust system structure and parameters through simple operations, and instantly see the reliability analysis results after the changes, which significantly reduces the professional knowledge and analysis workload required for reliability analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0025] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0026] Figure 1 A flow chart of a method for rapid system reliability assessment based on GO-FLOW provided in an embodiment of the present invention;

[0027] Figure 2 A schematic diagram of a system including three components connected in series provided in an embodiment of the present invention;

[0028] Figure 3 A schematic diagram of a simple light bulb system provided in an embodiment of the present invention;

[0029] Figure 4 A schematic diagram of a system including seven components connected in series and parallel is provided for an embodiment of the present invention. DETAILED DESCRIPTION

[0030] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present invention. Instead, they are merely examples of systems consistent with some aspects of the present invention as detailed in the appended claims.

[0031] In order to solve the many inconveniences of the existing GO-FLOW reliability analysis, the present invention provides a complex system reliability rapid analysis method based on GO-FLOW;

[0032] S1: Identify the information of each component of the system based on the system topology, and input the relevant initial information into Excel spreadsheet 1.

[0033] The user enters the name, failure mode, reliability data, and timing of each component in Excel;

[0034] S2: The professional selects appropriate GO-FLOW operators to simulate and characterize each component in the system, obtains reliability data of each operator, and enters the data into Excel spreadsheet 2;

[0035] Determine the primary input, secondary input, and output of the operator according to the direction of signal flow;

[0036] S3: Number the nodes according to the signal transmission path and convert them into two-dimensional coordinate data to facilitate the subsequent use of software to identify the series and parallel relationship of the system;

[0037] The nodes of the system are numbered according to the signal transmission path to identify the position of each component in the system, that is, the position information of the component in the system is converted into two-dimensional coordinate data and entered into electronic form three.

[0038] Using spreadsheets, users can easily enter and modify data without relying on complex software modeling tools, thus saving time and energy invested in software operation and modeling.

[0039] By integrating Python's powerful data processing capabilities and the flexibility of spreadsheets, it is possible to quickly process large-scale data and perform reliability calculations, allowing users to obtain reliability analysis results for complex systems in a shorter period of time and provide timely support for decision-making.

[0040] S4: Using the established spreadsheet data, the prepared Python software is used to automatically determine the series and parallel relationships between the components.

[0041] S5: traverse all operators, and calculate the reliability of each operator and the reliability of the entire system based on the reliability data and the calculation formula of the GO-FLOW operator;

[0042] S51: creating an empty list named "Result" specifically for storing the reliability of each operator obtained during the calculation process and the reliability of the entire system;

[0043] S52: calling corresponding reliability calculation functions for different types of operators, taking commonly used normally-off components, two-state components and components that fail over time as examples to illustrate the program implementation process of quantitative calculation, and the remaining operators are processed similarly.

[0044] If the operator begins with "26" (entered in the spreadsheet), it means that the operator is a normally-off component and the following calculation is performed:

[0045] Obtain the reliability data of the operator, and find the operator whose output is equal to its primary input (i.e., the operator provided to the primary input of this operator), and the operator whose output is equal to its secondary input (i.e., the operator provided to the secondary input of this operator);

[0046] Get the reliability data of the operator provided to the secondary input of this operator, and get the reliability of the operator provided to the primary input of this operator in the "Result" list;

[0047] The calculation formula of the normally-off component and the acquired data are used to calculate the reliability of the current operator, and the name of the current operator and its calculation result are stored in the "Result" list;

[0048] If the operator starts with "21", it means that the operator is a two-state element and performs the following calculations:

[0049] Get the reliability data of the operator and find the operator whose output is equal to its primary input (i.e. the operator that provides the primary input to this operator);

[0050] Create an empty list named "Value" specifically for storing the reliability data of the operator provided to the main input of this operator, and make the following judgments:

[0051] If the reliability data of the operator provided to the main input of this operator exists in the spreadsheet, then its value is multiplied by the success probability of the component represented by the operator to obtain the reliability of the current operator, and the name of the current operator and its calculation result are stored in the "Result" list;

[0052] If the reliability data of the operator provided to the main input of this operator does not exist in the electronic form, the reliability of the operator provided to the main input of this operator is obtained in the "Result" list, and then the reliability of the current operator is obtained by multiplying the value with the success probability of the component represented by the operator, and the name of the current operator and its calculation result are stored in the "Result" list;

[0053] If the operator begins with "35", it means that the operator is a component that fails over time and the following calculation is performed:

[0054] Obtain the reliability data of the operator, and find the operator whose output is equal to its primary input (i.e., the operator provided to the primary input of this operator), and the operator whose output is equal to its secondary input (i.e., the operator provided to the secondary input of this operator);

[0055] Get the reliability data of the operator provided to the secondary input of this operator, and get the reliability of the operator provided to the primary input of this operator in the "Result" list;

[0056] Calculate the reliability of the current operator using the calculation formula for components that fail over time and the acquired data, and store the name of the current operator and its calculation result in the "Result" list;

[0057] S53: Calculating the reliability of the system according to the reliability of the operator;

[0058] Obtain the completed component reliability data in the "Result" list, and then calculate the reliability of the system.

[0059] As an effective analysis tool, the GO-FLOW method can directly generate a GO-FLOW diagram from a system diagram, thereby facilitating the inspection, adjustment and update of system reliability. The present invention is based on the rapid reliability analysis of the GO-FLOW method, and by effectively integrating the user-friendliness of spreadsheets with the data processing capabilities of Python, it greatly simplifies the operation process and reduces the user's dependence on the professional knowledge of the GO-FLOW method. The present invention can quickly adapt to changes in system structure. Users only need to update the structural change data in the spreadsheet without modifying the underlying program code, which can significantly reduce manual intervention and maintenance costs, so that the reliability analysis of complex systems can be completed in a fast and accurate manner.

[0060] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0061] Example 1

[0062] This embodiment takes a simple light bulb system as an example ( Figure 3), based on the Python programming platform, the GO-FLOW-based system reliability rapid evaluation method of the present invention is used to analyze the reliability of each component and system of the system according to the requirements. The requirements of this embodiment are: after the battery is connected, switch A is closed, and switch B is closed after 10 hours. The average life of the bulb is assumed to be 1000 hours. Calculate the probability that at least one bulb maintains light during its operation.

[0063] Implementation steps: Figure 1 As shown, the details are as follows:

[0064] Step 1: Determine the information of each component in the system, use the GO-FLOW operator to replace each component in the system, and enter the initial information of these components and operators into an Excel spreadsheet;

[0065] Enter the name, failure mode, reliability data, and timing of each component in Excel;

[0066] Figure 3 The relevant information of the components in the lamp system shown is shown in Table 1.

[0067] Table 1 Related information of components in the lamp system

[0068]

[0069] Characterize each component with the GO-FLOW operator, obtain reliability data for the operator, and record this information in a spreadsheet;

[0070] by Figure 3 Take this as an example to explain the specific implementation method:

[0071] Step 2: Use the GO-FLOW operator to characterize each component based on its functional characteristics:

[0072] The battery is represented by a type 21 operator, and its output signal is transmitted through a type 25 operator. It is connected to two switches, which need to receive signals to close, so it is represented by a type 26 operator, and the signal that controls the switch closing is also output through a type 25 operator. The two light bulbs are represented by a type 21 operator. Considering that the light bulbs have a certain lifespan, a type 35 operator is introduced to simulate the change of the light bulb failure probability over time, and the working time interval of the light bulb is also output through a type 25 operator. In the system, any light bulb is considered to be successful when it is lit, so the light-emitting state of the two light bulbs is connected by a type 22 or gate operator to achieve a logical "or" connection.

[0073] Enter the reliability data of each operator in Excel in turn according to the direction of signal flow;

[0074] In this embodiment, six time points are defined as follows:

[0075] Time point 1 is the initial time point, that is, the system has no action; time point 2 is the moment when the battery is connected; time point 3 is the moment when switch A is closed; time point 4 is 10 hours after time point 3; time point 5 is the moment when switch B is closed immediately after time point 4; time point 6 is 10 hours after time point 5.

[0076] Figure 3 The operator information after conversion is shown in Table 2.

[0077] Table 2 Operator information corresponding to components in the system

[0078]

[0079] Among them, I1 to I6 are time point 1 to time point 6.

[0080] Determine the primary input, secondary input, and output of the operator according to the direction of signal flow;

[0081] Step 3: Convert the connection node numbers of each component in the system into two-dimensional coordinate data to identify the location of the component;

[0082] In this embodiment, the user only needs to convert the position information of the components in the system into two-dimensional coordinate data. After Python reads it, it can automatically determine the system topology. The method for identifying the position of the components in the system is as follows:

[0083] According to the signal transmission path, the connection nodes of each component are numbered using natural numbers from small to large;

[0084] Convert the position information of the components in the system into two-dimensional coordinate data and enter it into an Excel spreadsheet;

[0085] by Figure 2 The serial system is used to illustrate the numbering principles and the identification and judgment of the system structure.

[0086] Figure 2 There are 3 components in total. Each component in the system is represented by two-dimensional data, the first data represents the left node of the component, and the second data represents the right node of the component. For a series structure system, the nodes can be numbered from left to right using natural numbers from small to large, as shown in Table 3.

[0087] Table 3 Node marking of series system

[0088] part coordinate Battery (1,2) switch (2,3) Light bulb (3,4)

[0089] During the execution of the Python program, the system can automatically identify and confirm that the battery and the switch are connected in series, given that the right node of the battery matches the left node of the switch. Similarly, the switch and the light bulb are also connected in series, thus forming a circuit structure consisting of three components connected in series: battery, switch, and light bulb.

[0090] In the system, if there are both series and parallel structures, they can be identified according to the following standard methods.

[0091] In view of the different positions of components in the system, the left and right nodes of the components are numbered from left to right according to the direction of signal flow. In the case of parallel branches, the numbering is preferably from left to right and from top to bottom. If the coordinate positions of two components are the same, the two components are considered to be in parallel; if the right node of one component is connected to the left node of another component in sequence, the two components are considered to be connected in series.

[0092] by Figure 3 The series-then-parallel system further illustrates the identification and judgment of the system structure. Figure 3 The node annotations are shown in Table 4.

[0093] Table 4 Node marking of series-parallel system

[0094] Part Name coordinate Battery (1,2) Switch A (2,3) Light bulb A (3,5) Switch B (2,4) Light bulb B (4,5)

[0095] The right node of switch A is the same as the left node of bulb A. Based on this, the program can determine that switch A and bulb A are in series and are equivalent to a series module E1. Similarly, the series relationship between switch B and bulb B can also be identified and is equivalent to another series module E2. The left and right nodes of E1 and E2 are consistent. The program can determine that the two modules are in parallel and further simplify them into a single module E3. The right node of the battery is the same as the left node of E3. Based on this, the program automatically identifies the series relationship between the battery and E3, thereby realizing the identification and judgment of the series-parallel structure of the entire system.

[0096] by Figure 4 The complex series-parallel system further illustrates the identification and judgment process of the system structure. Figure 4 The node annotations are shown in Table 5.

[0097] Table 5 Node marking of complex series-parallel system

[0098] part coordinate Battery (1,2) Switch A (2,3) Light bulb A (3,5) Light bulb B (3,5) Switch B (2,4) Light bulb C (4,5) Light bulb D (4,5)

[0099] The coordinates of bulb A and bulb B are the same, that is, their left and right nodes are exactly the same. Based on this, it can be judged that bulb A and bulb B are in a parallel relationship and can be regarded as an equivalent module E1. Similarly, the right node of switch A is the same as the left node of E1. It can be judged that switch A and E1 are connected in series to form a new equivalent module E2, whose left node is 2 and right node is 5. Similarly, it can be judged that bulb C, bulb D and switch B can also be equivalent to a module E3, whose left node is 2 and right node is 5. Since the left and right nodes of E2 and E3 are the same, they form a parallel equivalent module E4. Finally, the battery is connected in series with E4, thereby realizing the identification and judgment of the series-parallel structure of the entire system.

[0100] After the program determines the system structure, GO-FLOW can be used to perform reliability analysis of components and systems. Figure 3 The following describes the subsequent operations using the system as an example.

[0101] Step 4: Traverse all operators and calculate the reliability of each operator and the reliability of the system based on the reliability data of the operators and the calculation formula of GO-FLOW;

[0102] Step 4.1: Create an empty list named "Result" to store the reliability of each operator and the reliability of the entire system obtained during the calculation process;

[0103] Step 4.2: Use corresponding reliability calculation methods for different types of operators;

[0104] Step 4.2.1: If the operator starts with "26", it means that the operator is a normally-off element. Perform the following calculation:

[0105] Obtain the reliability data of the operator, and find the operator whose output is equal to its primary input (i.e., the operator provided to the primary input of this operator), and the operator whose output is equal to its secondary input (i.e., the operator provided to the secondary input of this operator);

[0106] Get the reliability data of the operator provided to the secondary input of this operator, and get the reliability of the operator provided to the primary input of this operator in the "Results" list;

[0107] Use the calculation formula of the normally-off component and the acquired data to calculate the reliability of the current operator O(t1)=pp, O(t)=O(t')+[1.0-O(t')]·P(t)·pg, and store the current operator name and its calculation result into the "Result" list;

[0108] Where pp is the probability that the normally-off element has been turned on before the initial time point; pg is the probability that the normally-off element is successfully turned on when there is an input signal; O(t) is the probability that the normally-off element is turned on at time point t, t′ is the time point before t, and t1 is the initial time point;

[0109] Step 4.2.2: If the operator starts with "21", it means that the operator is a two-state element, and the following calculation is performed:

[0110] Get the reliability data of the operator and find the operator whose output is equal to its primary input (i.e. the operator that provides the primary input to this operator);

[0111] Create an empty list named "Value" specifically for storing the reliability data of the operator provided to the main input of this operator, and then make the following judgments:

[0112] If there is reliability data of the operator provided to the main input of this operator in the electronic form, then use its value to calculate the reliability of the current operator R(t)=S(t)·pg, and store the current operator name and its calculation result in the "result" list;

[0113] If the reliability data of the operator provided to the main input of this operator does not exist in the electronic form, the reliability of the operator provided to the main input of this operator is obtained in the "Result" list. Then, the reliability of the current operator is calculated using its value R(t)=S(t)·pg, and the name of the current operator and its calculation result are stored in the "Result" list;

[0114] Step 4.2.3: If the operator begins with "35", it means that the operator is a working component that fails over time. Perform the following calculations:

[0115] Obtain the reliability data of the operator, and find the operator whose output is equal to its primary input (i.e., the operator provided to the primary input of this operator), and the operator whose output is equal to its secondary input (i.e., the operator provided to the secondary input of this operator);

[0116] Get the reliability data of the operator provided to the secondary input of this operator, and get the reliability of the operator provided to the primary input of this operator in the "Results" list;

[0117] Calculate the reliability of the current operator using the calculation formula for working components that fail over time and the acquired data And store the current operator name and its calculation result into the "result" list;

[0118] Where λ is the failure probability per unit time of the working component that fails over time represented by the operator, that is, the failure rate. Assume that the failure rate λ does not change with time and is a constant;

[0119] Step 4.3: Calculate the reliability of the system based on the reliability of the operator:

[0120] In this embodiment, the OR gate is the last operator, and its strength represents the probability that at least one bulb is lit. Get the required reliability data and get the required value in the "Result" list, and use the calculation formula of the OR gate to calculate the reliability of the system

[0121] In this embodiment, the initial information of the components in the system is first input into an Excel spreadsheet, including the name, failure mode, reliability data and timing of each component. Then, according to the functional characteristics of the system, the components in the system are converted into corresponding operators and also input into the Excel spreadsheet.

[0122] Next, the position information of the components is converted into two-dimensional coordinate data and entered into a spreadsheet. The Excel data is read using the pandas library function in Python and stored in files. These files contain information about the data requirements of the components and operators. First, the two-dimensional coordinate data of each component is extracted from these files to obtain the series and parallel relationship of each component in the system. Then the data of each operator and the reliability data of the component represented by the operator are extracted.

[0123] Finally, based on the above data, the system reliability is calculated in the Python programming platform according to the method described in steps 3 and 4.

[0124] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These changes and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A rapid reliability analysis method for complex systems based on GO-FLOW, characterized by: include: S1: Identify the information of each component of the system according to the system topology structure and enter it into an Excel spreadsheet 1, where the information of the component includes the name, failure mode, reliability data, and timing of each component; S2: Based on the information of the component parts, use the GO-FLOW operator to characterize each component, obtain the reliability data of each operator, and enter the reliability data of each operator into Excel spreadsheet 2; S3: Obtaining a signal transmission path according to the positions of the components of the system and the order formed after the operators characterize the components; Determine the primary input, secondary input and output of the operator according to the signal transmission path; The nodes of the system are numbered according to the signal transmission path, and the position information of the components in the system is converted into two-dimensional coordinate data and entered into Excel spreadsheet 3; wherein the node is defined as: a node is set on the left and right sides of each component, and if the right node of the current component is in the same position as the left node of the next component, the two components share this node; S4: using the data in the Excel spreadsheet 3 to determine the series-parallel relationship of each component; S5: Traverse all operators, determine the primary input, secondary input and output of the operator based on the signal transmission path and the reliability data of the operator in Excel spreadsheet 2 and the calculation formula of GO-FLOW, and calculate the reliability of each operator and the reliability of the system.

2. The complex system reliability rapid analysis method based on GO-FLOW according to claim 1 is characterized in that: In S4: Use the data in Excel spreadsheet 3 and Python software to automatically determine the series and parallel relationships between the components.

3. The complex system reliability rapid analysis method based on GO-FLOW according to claim 1 is characterized in that: In S3, the system nodes are numbered according to the signal transmission path according to the following rules: For a series structure system, natural numbers are used to number the nodes from left to right from small to large; If there are both series and parallel structures, they shall be marked according to the following standard method: According to the direction of signal flow, in the case of parallel branches, they are numbered from left to right and from top to bottom. If the coordinate positions of two components are the same, they are considered to be in parallel. If the right node of one component is connected to the left node of another component in sequence, the two components are considered to be connected in series.

4. The complex system reliability rapid analysis method based on GO-FLOW according to claim 1, characterized in that S5 include: Create an empty list named "Result" to store the reliability of each operator and the reliability of the entire system obtained during the calculation process; Call the corresponding reliability calculation function for different types of operators to obtain the reliability of the operator; The reliability of the system is calculated based on the reliability of the operators.

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