An intelligent temperature controller durability testing system

Abstract

The present invention relates to the field of equipment testing technology, and specifically to an intelligent thermostat durability testing system, comprising: a state modeling unit, the state modeling unit being used to define a state set and an extended variable set of a target thermostat, defining a state transition condition of the target thermostat based on the extended variable set and the state set, and constructing a state transition diagram based on the extended variable set, the state set, and the state transition condition. By defining the state set, the extended variable set, and the state transition condition of the target thermostat, the present invention can accurately simulate and describe the behavior and state changes of the thermostat under different operating conditions. By constructing a state transition diagram, the present invention can ensure that test cases cover all operating states of the thermostat and comprehensively test the system, thereby better evaluating the reliability of the device.

Description

Technical Field

[0001] The present invention relates to the technical field of equipment testing, and in particular to an intelligent temperature controller durability testing system. Background Art

[0002] A thermostat is a device that automatically adjusts temperature and is often used to maintain the temperature within a preset range.

[0003] Traditional systems lack systematic modeling of thermostat states and often rely solely on empirical evidence or fixed test cases. Without comprehensive state transition diagrams, test coverage is limited and certain operating states or edge cases may be overlooked, resulting in incomplete testing and the risk of missed tests. Traditional systems also rely on predetermined test scripts or static test paths, lacking the flexibility to explore complex state spaces. Test paths are typically predefined and unsuitable for dynamic changes in diverse operating environments. Furthermore, because traditional systems are typically based on limited manual test paths, their test coverage and efficiency are low, making comprehensive test coverage difficult to ensure, especially in complex operating environments or for large-scale equipment. Traditional systems also require manual intervention to generate test cases, execute tests, and perform data analysis. Manual script writing and test case design consume significant manpower during the testing process. Furthermore, traditional testing systems typically lack optimization for real-time monitoring and anomaly detection during testing. While thermostat performance can be monitored using sensors, the monitoring range and response speed are often insufficient to detect even minor anomalies. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the above-mentioned prior art and provide an intelligent temperature controller durability testing system.

[0005] The technical solution adopted to solve the above technical problems is: an intelligent temperature controller durability testing system, including:

[0006] a state modeling unit, the state modeling unit being configured to define a state set and an extended variable set of a target thermostat, define a state transition condition of the target thermostat based on the extended variable set and the state set, and construct a state transition diagram based on the extended variable set, the state set, and the state transition condition;

[0007] a state matching unit configured to generate a random extended variable set sequence, and match the random extended variable set sequence with the state transition graph according to a depth-first search algorithm to obtain a state transition path corresponding to each random extended variable set in the random extended variable set sequence;

[0008] a use case generation unit, configured to generate a test case based on the random extended variable set and the state transition path, convert the test case into a script instruction, and control the target thermostat according to the script instruction sequence;

[0009] A test determination unit, wherein the abnormality determination unit is used to monitor the temperature of the temperature-controlled environment controlled by the target thermostat to obtain the real-time temperature of the temperature-controlled environment, and determine the test tag of the target thermostat according to the test case and the real-time temperature, wherein the test tag includes an abnormal tag and a normal tag.

[0010] Preferably, the system further comprises:

[0011] an abnormality determination unit, configured to count the test tags of the target thermostat within a preset test period, and determine that the target thermostat has an abnormality if the number of the test tags that are abnormal tags is greater than a preset threshold;

[0012] The durability prediction unit is configured to calculate a response time series of the target thermostat within a preset test period if the number of abnormal test tags is not greater than a preset threshold, and perform durability prediction on the target thermostat based on the response time series.

[0013] Preferably, the state set includes standby state, heating state, cooling state, over-temperature warning state, low-temperature warning state and fault state; the extended variable set includes current temperature, target temperature, maximum safe temperature, minimum safe temperature, elapsed time, temperature change rate and maximum safe available time; the test case includes the state transition path of the target thermostat and the random extended variable set before each state transition of the target thermostat.

[0014] Preferably, defining the state transition condition of the target thermostat according to the extended variable set and the state set includes:

[0015] If the current temperature reaches the target temperature and the temperature change rate becomes zero, the target thermostat enters a standby state;

[0016] If the current temperature is lower than the target temperature, the target thermostat enters a heating state;

[0017] If the current temperature is higher than the target temperature, the target thermostat enters a cooling state;

[0018] If the current temperature is higher than the maximum safe temperature, the target thermostat enters an over-temperature warning state;

[0019] If the current temperature is lower than the minimum safe temperature, the target thermostat enters a low temperature warning state;

[0020] If the elapsed time is higher than the maximum safe available time, the target thermostat enters a fault state.

[0021] Preferably, constructing a state transition diagram according to the extended variable set, the state set and the state transition condition includes:

[0022] Using each state in the state set as a state node of the state transition diagram;

[0023] For each state node in the state transition diagram, judging whether there is a transition path that meets the state transition condition based on a combination of an extended variable set and a state transition condition; if there is a transition path that meets the state transition condition, adding a transition edge in the state transition diagram, wherein the transition edge represents a transition from the current state to the next state;

[0024] On each transfer edge in the state transfer diagram, the corresponding extended variable value and state transfer condition are marked.

[0025] Preferably, converting the test case into script instructions includes:

[0026] Determining a signal type required for the test case based on a random extended variable set in the test case, wherein the signal type includes a step signal and a ramp signal, and when the difference between the current temperature and the target temperature is greater than a preset first difference threshold, using a step signal; otherwise, using a ramp signal;

[0027] Encode the signal types required by the test case as script instructions.

[0028] Preferably, determining the test tag of the target thermostat according to the test case and the real-time temperature includes:

[0029] Comparing the target temperature required in the test case with the real-time temperature within a preset control period;

[0030] If the difference between the target temperature required in the test case and the real-time temperature is greater than a preset second difference threshold, the test tag of the target thermostat is determined to be an abnormal tag; otherwise, the test tag of the target thermostat is determined to be a normal tag.

[0031] Preferably, counting the response time series of the target thermostat within a preset test period includes:

[0032] Counting the reaction time of the target thermostat from the current temperature to the target temperature in the test case within a preset control period;

[0033] All test cases are processed repeatedly within a preset test cycle to obtain the response time series of the target thermostat.

[0034] Preferably, performing durability prediction on the target thermostat according to the reaction time series includes:

[0035] defining a reaction time degradation characteristic quantity of the target thermostat according to a reaction time sequence;

[0036] defining a relative increment of the reaction time degradation characteristic quantity;

[0037] Calculating the drift parameter and diffusion coefficient of the relative increment of the reaction time degradation characteristic quantity based on maximum likelihood estimation;

[0038] A probability density function of the remaining durability of the target thermostat is constructed, the drift parameter and diffusion coefficient of the relative increment of the reaction time degradation characteristic quantity are substituted into the remaining durability probability density function, and the time corresponding to the maximum value of the remaining durability probability density function is used as the remaining service durability of the target thermostat.

[0039] Preferably, the expression of the reaction time degradation characteristic value is as follows:

[0040] X(t)=a+μt+σ B B(t);

[0041] Where X(t) represents the reaction time degradation characteristic, a represents the initial value of the reaction time, μ represents the drift coefficient, σ B represents the diffusion coefficient, B(t) represents the standard Wiener process, and t represents the reaction time series;

[0042] The relative increment expression is as follows:

[0043] ΔX(t i )=a+μt i +σ B ΔB(t i );

[0044] Among them, ΔX(t i ) represents the relative increment of the reaction time degradation characteristic, t i represents the i-th reaction time in the reaction time series, ΔB(t i ) represents the relative increment of the standard Wiener process;

[0045] The expression of the residual durability probability density function is as follows:

[0046]

[0047] Among them, f(t|μ,σ B ,h) represents the probability density function of residual durability, and h represents the failure threshold.

[0048] The beneficial effects of the present invention are as follows: (1) The present invention can accurately simulate and describe the behavior and state changes of the thermostat under different working conditions by defining the state set, extended variable set and state transition conditions of the target thermostat. This modeling method provides a detailed theoretical basis for the generation of subsequent test cases and the performance evaluation of the system. By constructing a state transition diagram, it can ensure that the test cases cover all working states of the thermostat and conduct a comprehensive test on the system, thereby better evaluating the reliability of the equipment; (2) The present invention generates a random extended variable set sequence that matches the state transition diagram by utilizing a depth-first search algorithm, which makes the test path generation more flexible and can cope with various complex working environments and state transitions, avoiding test omissions that may occur in traditional testing methods, thereby effectively exploring in complex state spaces and generating more diverse and comprehensive test cases, thereby improving the test coverage of the system. Moreover, by analyzing the reaction time series, the durability of the thermostat can be dynamically predicted during the test. The reaction time is an important indicator of equipment performance, and By grasping the changing trend of the device's response time in real time, the long-term performance of the device can be effectively predicted, possible degradation or failure can be identified in advance, and corresponding maintenance or optimization can be carried out; (3) The present invention generates test cases by combining a random extended variable set and a state transition path, and converts them into script instructions to automatically execute the test. This automated test can reduce manual intervention, improve test efficiency, and ensure the consistency and repeatability of the test process; and by monitoring the temperature of the temperature-controlled environment in real time, the performance of the thermostat can be obtained in real time during its operation, and by comparing it with the predetermined test case to determine whether an abnormality occurs. Real-time abnormality monitoring helps to discover problems in a timely manner and adjust or repair the device to avoid failure of the device in actual use. Moreover, by counting the number of abnormal tags in the test cycle, it is possible to quickly evaluate whether the device has abnormal problems after the test cycle ends. If the number of abnormalities exceeds the preset threshold, the system will determine that the target thermostat has a fault. This judgment mechanism can efficiently discover potential faults and handle them in a timely manner to avoid serious failures of the device during formal use. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a schematic diagram of the system architecture of the overall system in an embodiment of the present invention.

[0050] Reference numerals: 1. state modeling unit; 2. state matching unit; 3. use case generation unit; 4. test determination unit; 5. abnormality determination unit; 6. durability prediction unit. DETAILED DESCRIPTION

[0051] Example 1, as Figure 1 As shown, the present invention proposes an intelligent temperature controller durability testing system, comprising:

[0052] State modeling unit 1, which is used to define a state set and an extended variable set of a target thermostat, define a state transition condition of the target thermostat based on the extended variable set and the state set, and construct a state transition diagram based on the extended variable set, the state set, and the state transition condition;

[0053] State matching unit 2, which is used to generate a random extended variable set sequence, and match the random extended variable set sequence with the state transition graph according to a depth-first search algorithm to obtain a state transition path corresponding to each random extended variable set in the random extended variable set sequence;

[0054] The use case generation unit 3 is used to generate a test case based on the random extended variable set and the state transition path, convert the test case into a script instruction, and control the target thermostat according to the script instruction sequence;

[0055] The test judgment unit 4, the abnormality judgment unit 4 is used to monitor the temperature of the temperature-controlled environment controlled by the target thermostat to obtain the real-time temperature of the temperature-controlled environment, and judge the test label of the target thermostat according to the test case and the real-time temperature, wherein the test label includes an abnormal label and a normal label.

[0056] In the present invention, a thermostat is a device that automatically adjusts temperature, often used to maintain the temperature within a preset range. A state transition diagram is a graphical representation that shows the transition relationships between different states and their triggering conditions, and is often used to describe the behavior of complex systems. A random extended variable set sequence is a sequence of extended variables generated according to a certain rule or random method. This sequence contains a series of extended variable sets, representing a series of operating conditions that the thermostat may encounter. A depth-first search algorithm (DFS) is an algorithm for traversing or searching a graph. Here, DFS is used to find a path in a state transition diagram, that is, to find the corresponding state transition path based on a given random extended variable set sequence. A test case is a specific operation step and expected result used to verify the function of a target thermostat. It usually includes input conditions, execution steps, and expected output. The case generation unit designs the test case based on the generated random extended variable set and the corresponding state transition path. Script instructions are a set of commands that can be automatically executed, usually executed by a test tool. These instructions control the target thermostat, simulate its operation, and observe its response. A test case script converts a test case into automatically executable code or commands. These code instructions control the operation of the thermostat and record its response.

[0057] In an optional embodiment, the system further includes:

[0058] The abnormality determination unit 5 is used to count the test tags of the target thermostat within a preset test period, and if the number of abnormal test tags is greater than a preset threshold, it is determined that the target thermostat has an abnormality;

[0059] The durability prediction unit 6 is used to count the response time series of the target thermostat within a preset test period if the number of test tags that are abnormal tags is not greater than a preset threshold, and perform durability prediction on the target thermostat based on the response time series.

[0060] Example 2. An intelligent thermostat durability testing system proposed by the present invention, compared with Example 1, this embodiment also includes: a state set including standby state, heating state, cooling state, over-temperature warning state, low-temperature warning state and fault state; an extended variable set including current temperature, target temperature, maximum safe temperature, minimum safe temperature, elapsed time, temperature change rate and maximum safe available time; a test case including a state transition path of the target thermostat and a random extended variable set before each state transition of the target thermostat.

[0061] In an optional embodiment, the state transition condition of the target thermostat is defined according to the extended variable set and the state set, including:

[0062] If the current temperature reaches the target temperature and the temperature change rate becomes zero, the target thermostat enters the standby state;

[0063] If the current temperature is lower than the target temperature, the target thermostat enters the heating state;

[0064] If the current temperature is higher than the target temperature, the target thermostat enters the cooling state;

[0065] If the current temperature is higher than the maximum safe temperature, the target thermostat enters the over-temperature warning state;

[0066] If the current temperature is lower than the minimum safe temperature, the target thermostat enters the low temperature warning state;

[0067] If the elapsed time is higher than the maximum safe available time, the target thermostat enters a fault state.

[0068] In an optional embodiment, a state transition diagram is constructed based on the extended variable set, the state set, and the state transition condition, including:

[0069] Each state in the state set is used as a state node of the state transition diagram;

[0070] For each state node in the state transition diagram, based on the combination of the extended variable set and the state transition condition, determine whether there is a transition path that meets the state transition condition. If there is a transition path that meets the state transition condition, add a transition edge in the state transition diagram. The transfer edge represents the transition from the current state to the next state.

[0071] On each transfer edge in the state transition diagram, indicate the corresponding extended variable value and state transition condition.

[0072] It should be noted that the combination of state transition conditions refers to the combination of multiple extended variables or system conditions to form a composite transition condition, which is usually intended to cope with more complex system behaviors and transition rules in different scenarios.

[0073] In an optional embodiment, converting the test case into script instructions includes:

[0074] Determining the signal type required by the test case based on the random extended variable set in the test case, wherein the signal type includes a step signal and a ramp signal. When the difference between the current temperature and the target temperature is greater than a preset first difference threshold, the step signal is used; otherwise, the ramp signal is used;

[0075] Encode the signal types required by the test case as script instructions.

[0076] It should be noted that a step signal usually refers to a sharp change in the signal, that is, an instantaneous jump from one value to another. It is usually used to simulate rapid state switching; a ramp signal refers to a smooth change in the signal value, usually increasing or decreasing gradually, linearly or nonlinearly. This signal is used to simulate smooth, gradual changes.

[0077] In an optional embodiment, determining a test tag of a target thermostat based on a test case and a real-time temperature includes:

[0078] Compare the target temperature required in the test case with the real-time temperature within the preset control period;

[0079] If the difference between the target temperature required in the test case and the real-time temperature is greater than a preset second difference threshold, the test tag of the target thermostat is determined to be an abnormal tag; otherwise, the test tag of the target thermostat is determined to be a normal tag.

[0080] In an optional embodiment, collecting statistics on the response time series of the target thermostat within a preset test period includes:

[0081] Count the reaction time of the target thermostat from the current temperature to the target temperature in the test case within the preset control period;

[0082] All test cases are processed repeatedly within a preset test cycle to obtain the response time series of the target thermostat.

[0083] It should be noted that the control cycle refers to a period of time during which the system (such as a thermostat) performs a complete operation or adjustment. In a temperature control system, the control cycle can be the time interval between each temperature measurement and adjustment; the test cycle refers to the time range set during the test process to observe and record the performance of the system. During this period, the reaction behavior of the test system (such as a thermostat) is tested.

[0084] In an optional embodiment, performing durability prediction on a target thermostat based on a reaction time series includes:

[0085] Defining the reaction time degradation characteristic of the target thermostat according to the reaction time series;

[0086] Define the relative increment of the characteristic quantity of reaction time degradation;

[0087] The drift parameter and diffusion coefficient of the relative increment of the reaction time degradation characteristic are calculated based on maximum likelihood estimation;

[0088] The residual durability probability density function of the target thermostat is constructed, the drift parameter and diffusion coefficient of the relative increment of the reaction time degradation characteristic are substituted into the residual durability probability density function, and the time corresponding to the maximum value of the residual durability probability density function is taken as the remaining service durability of the target thermostat.

[0089] It should be noted that the reaction time degradation characteristic quantity is a quantity that describes the change in the reaction time of the thermostat with usage time or workload. As time goes by, the performance of the equipment may degrade, resulting in a gradual increase in the reaction time. Therefore, the reaction time degradation characteristic quantity is used to quantify this degradation process; the relative increment of the reaction time degradation characteristic quantity refers to the proportional change between the current reaction time and the initial reaction time, which is used to quantify the degree of increase in the reaction time; maximum likelihood estimation is a statistical method that estimates the value of the model parameters by maximizing the likelihood function of the data under a certain hypothetical model. In this scenario, maximum likelihood estimation is used to estimate the drift of the relative increment of the reaction time degradation characteristic quantity Parameters and diffusion coefficients; drift parameters are parameters that describe the long-term trend of changes in random processes or degradation processes. In the reaction time degradation model, the drift parameters reflect the average rate of change of the thermostat reaction time over time; the diffusion coefficient is a parameter that describes the uncertainty or degree of fluctuation of the random process; the remaining durability probability density function describes the probability distribution of the remaining service life of a device that can continue to work normally after the current moment. It indicates the probability that the device may continue to work until a certain moment at a certain moment; the remaining service life refers to the time that the device can continue to work normally after the current moment. It is usually related to the degradation process, performance degradation rate and uncertainty of the device.

[0090] In an optional embodiment, the expression of the reaction time degradation characteristic value is as follows:

[0091] X(t)=a+μt+σ B B(t);

[0092] Where X(t) represents the degradation characteristic of the reaction time, a represents the initial value of the reaction time, μ represents the drift coefficient, σ B represents the diffusion coefficient, B(t) represents the standard Wiener process, and t represents the reaction time series;

[0093] The relative increment expression is as follows:

[0094] ΔX(t i )=a+μt i +σ B ΔB(t i );

[0095] Among them, ΔX(t i ) represents the relative increment of the reaction time degradation characteristic, ti represents the i-th reaction time in the reaction time series, ΔB(t i ) represents the relative increment of the standard Wiener process;

[0096] The expression of the probability density function of residual durability is as follows:

[0097]

[0098] Among them, f(t|μ,σ B ,h) represents the probability density function of residual durability, and h represents the failure threshold.

[0099] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.

Claims

1. An intelligent temperature controller durability testing system, characterized in that: include: A state modeling unit (1), the state modeling unit (1) is used to define a state set and an extended variable set of a target thermostat, define a state transition condition of the target thermostat according to the extended variable set and the state set, and construct a state transition diagram according to the extended variable set, the state set and the state transition condition; A state matching unit (2) is used to generate a random extended variable set sequence, and match the random extended variable set sequence with the state transition graph according to a depth-first search algorithm to obtain a state transition path corresponding to each random extended variable set in the random extended variable set sequence; A use case generation unit (3), the use case generation unit (3) is used to generate a test case according to the random extended variable set and the state transition path, convert the test case into a script instruction, and control the target thermostat according to the script instruction sequence; A test determination unit (4), the test determination unit (4) is used to monitor the temperature of the temperature-controlled environment controlled by the target thermostat to obtain the real-time temperature of the temperature-controlled environment, and determine the test label of the target thermostat according to the test case and the real-time temperature, wherein the test label includes an abnormal label and a normal label; An abnormality determination unit (5), the abnormality determination unit (5) is used to count the test tags of the target thermostat within a preset test period, and if the number of the test tags that are abnormal tags is greater than a preset threshold, it is determined that the target thermostat has an abnormality; A durability prediction unit (6), wherein if the number of abnormal test tags is not greater than a preset threshold, the durability prediction unit (6) is configured to count the reaction time series of the target thermostat within a preset test period, and perform durability prediction on the target thermostat based on the reaction time series; The state set includes a standby state, a heating state, a cooling state, an over-temperature warning state, a low-temperature warning state, and a fault state; the extended variable set includes a current temperature, a target temperature, a maximum safe temperature, a minimum safe temperature, an elapsed time, a temperature change rate, and a maximum safe available time; the test case includes a state transition path of the target thermostat and a random extended variable set before each state transition of the target thermostat; Performing durability prediction on the target thermostat according to the reaction time series includes: defining a reaction time degradation characteristic quantity of the target thermostat according to a reaction time sequence; defining a relative increment of the reaction time degradation characteristic quantity; Calculating the drift parameter and diffusion coefficient of the relative increment of the reaction time degradation characteristic quantity based on maximum likelihood estimation; A probability density function of the remaining durability of the target thermostat is constructed, the drift parameter and diffusion coefficient of the relative increment of the reaction time degradation characteristic quantity are substituted into the remaining durability probability density function, and the time corresponding to the maximum value of the remaining durability probability density function is used as the remaining service durability of the target thermostat.

2. The intelligent temperature controller durability testing system according to claim 1, characterized in that: Defining a state transition condition of the target thermostat according to the extended variable set and the state set includes: If the current temperature reaches the target temperature and the temperature change rate becomes zero, the target thermostat enters a standby state; If the current temperature is lower than the target temperature, the target thermostat enters a heating state; If the current temperature is higher than the target temperature, the target thermostat enters a cooling state; If the current temperature is higher than the maximum safe temperature, the target thermostat enters an over-temperature warning state; If the current temperature is lower than the minimum safe temperature, the target thermostat enters a low temperature warning state; If the elapsed time is higher than the maximum safe available time, the target thermostat enters a fault state.

3. The intelligent temperature controller durability testing system according to claim 2, characterized in that: Constructing a state transition diagram according to the extended variable set, the state set, and the state transition condition, including: Using each state in the state set as a state node of the state transition diagram; For each state node in the state transition diagram, judging whether there is a transition path that meets the state transition condition based on a combination of an extended variable set and a state transition condition; if there is a transition path that meets the state transition condition, adding a transition edge in the state transition diagram, wherein the transition edge represents a transition from the current state to the next state; On each transfer edge in the state transfer diagram, the corresponding extended variable value and state transfer condition are marked.

4. The intelligent temperature controller durability testing system according to claim 3, characterized in that: Convert the test case into script instructions, including: Determining a signal type required for the test case based on a random extended variable set in the test case, wherein the signal type includes a step signal and a ramp signal, and when the difference between the current temperature and the target temperature is greater than a preset first difference threshold, using a step signal; otherwise, using a ramp signal; Encode the signal types required by the test case as script instructions.

5. The intelligent temperature controller durability testing system according to claim 4, characterized in that: Determining a test tag of the target thermostat according to the test case and the real-time temperature includes: Comparing the target temperature required in the test case with the real-time temperature within a preset control period; If the difference between the target temperature required in the test case and the real-time temperature is greater than a preset second difference threshold, the test tag of the target thermostat is determined to be an abnormal tag; otherwise, the test tag of the target thermostat is determined to be a normal tag.

6. The intelligent temperature controller durability testing system according to claim 5, characterized in that: Counting the response time series of the target thermostat within a preset test period includes: Counting the reaction time of the target thermostat from the current temperature to the target temperature in the test case within a preset control period; All test cases are processed repeatedly within a preset test cycle to obtain the response time series of the target thermostat.

7. The intelligent temperature controller durability testing system according to claim 6, characterized in that: The expression of the reaction time degradation characteristic is as follows: X(t)=a+μt+σ B B(t); Where X(t) represents the degradation characteristic of the reaction time, a represents the initial value of the reaction time, μ represents the drift coefficient, σ B represents the diffusion coefficient, B(t) represents the standard Wiener process, and t represents the reaction time series; The expression of the relative increment is as follows: ΔX(t i )=a+μt i +s B ΔB(t i ); Among them, ΔX(t i ) represents the relative increment of the reaction time degradation characteristic, t i represents the i-th reaction time in the reaction time series, ΔB(t i ) represents the relative increment of the standard Wiener process; The expression of the residual durability probability density function is as follows: Among them, f(t|μ,σ B ,h) represents the probability density function of residual durability, and h represents the failure threshold.

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