Some standard content:
National Standard of the People's Republic of China
Programmes for reliability growth
This standard is equivalent to the international standard IEC1014 (1989) "Programmes for reliability growth". 1 Subject content and scope of application
GB/T 1517494
This standard specifies the requirements and guidelines for the preparation of reliability growth programs. In order to increase reliability, it is necessary to expose and eliminate weak links in hardware and software. This standard is appropriate when the specification requires a reliability program for equipment (electronic, electromechanical, mechanical hardware and software), or when the design is known to be immature and cannot meet the requirements of verification tests without improvement. After explaining the basic concepts, the required management, planning, testing (laboratory and field testing), failure analysis and improvement techniques are described. In order to estimate the reliability level achieved after growth, a brief overview of mathematical models is also given.
This standard is applicable to situations where reliability improvement is carried out through testing, and its general principles are also applicable to other activities. Improvement work can be carried out on the basis of the following results: theoretical research (e.g. failure mode and effect analysis); - field test;
——user experience;
——projects that are not primarily dedicated to reliability improvement. 2 Referenced standards
GB3187 Reliability and maintainability terms
General requirements
GB5080.1 Equipment reliability test
GB5080.2 Equipment reliability test
Test cycle design guidelines
GB5080.4 Equipment reliability test Point estimation and interval estimation methods for reliability determination tests (exponential distribution) GB6992 Reliability and maintainability management
GB7288.2 Equipment reliability test Recommended test conditions Fixed use in a climate-protected location Equipment precision simulation 3 Terms
The basic reliability terms used in this standard comply with GB3187. The terms that require special definition or explanation in this standard are described as follows. Unless otherwise specified, these terms apply to products consisting of only hardware as well as products containing software or mainly software. It is very important to distinguish between the terms "failure intensity" (for repairable products) and "failure rate" (for non-repairable or disposable products) in GB3187. 3.1 Reliability improvement A process of improving reliability characteristics by eliminating the causes of systematic failures and/or reducing the probability of other failures.
Note: ① The method described in this standard is to make corrective changes to achieve the purpose of reducing systematic weaknesses. ② For any product, the growth that can be achieved is limited due to feasibility, economy, etc. Approved by the State Administration of Technical Supervision on August 20, 1994 and implemented on April 1, 1995
3.2 Reliability growth GB/T 15174-94
Indicates a process in which the reliability characteristics of a product gradually improve over time. 3.3 Weak link failure weaknessfailure Failure caused by the weak link of the product itself when the applied stress is within the specified capacity of the product. Note: ① Weak links can be inherent or induced. ② Weak links are any known or unknown defects in the product, which can cause one or more weak links to fail. ③ It is assumed that each type of weak link is independent of each other in a statistical sense. 3.4 Systematic weakness systematicweakness Weak links whose impact can only be eliminated or reduced by changing the design, manufacturing process, operating method, document or other relevant factors, or by eliminating inferior component batches. Note: ①) There are no improvement measures, only repairs and replacements (repeated operation in the case of software) are likely to cause the recurrence of similar failures. ② Software weaknesses are all systematic. 3.5 Residual weakness residualweakness Non-systematic weakness.
Note: ①) In this case, the risk of recurrence of similar failures within the expected test time can be ignored. ②The weak link of software cannot be residual. 3.6 Relevant failure
Failures that should be included when interpreting test or operation results or calculating reliability characteristic values. Note: ①The criteria for relevant failures should be listed. ②The criteria for relevant failures are shown in 7.2:
3.7 Non-relevant failures Failures that should not be included when interpreting test or operation results or calculating reliability characteristic values. Note: ①The criteria for non-relevant failures should be listed. ②The criteria for non-relevant failures are shown in 7.1.
3.8 Systematic failure
Systematic failure
Failures that are directly related to a certain cause, and these failures can only be eliminated by changing the design, manufacturing process, operating methods, documents or other related factors.
Note: ①Corrective maintenance without changes usually cannot eliminate the cause of failure. ②Systematic failures can be induced by simulating the cause of failure. ③In this standard, systematic failures are considered to be failures caused by systematic weak links. 3.9 residual failure residual failure Failure caused by residual weak links. 3.10 Category A failure failure category A
Systematic failures for which management decides not to make corrective changes due to cost, time, technical limitations or other reasons. 3.11 Category B failure failure category B Systematic failures for which management decides to make corrective changes. 3.12 instantaneous reliability measure instantaneous reliability measure of a product at a given moment (past or present) in a reliability growth process. Note: (D) Common reliability measures are (instantaneous) failure intensity or mean time between failures (MTBF> and instantaneous failure rate or mean time before failure (MTTF).
② These measures are estimated using the reliability growth model. 3.13 Extrapolated reliability measure Extrapolated reliability measure The reliability measure estimated at a given time in the future for a product that can make timely corrective changes during the entire process of reliability growth.
GB/T 1517494
Note: The definition of the modifier "extrapolated" in DGB3187 applies here, but is limited to time extrapolation. ② Assume that the previous test conditions and corrective change procedures remain unchanged. ③ Assuming that there will be a similar trend in the future, the reliability characteristic quantity can be estimated using the reliability growth model using past data. () Common reliability measures are (instantaneous) failure intensity or mean time between failures (MTBF) and (instantaneous) failure rate or mean time before failure (MTTF).
3.14 Projected reliability measure The product reliability measure predicted after introducing multiple corrective measures at the same time. Note: ① Changes are often made between two consecutive stages of the growth program. ② Commonly used reliability measures are (instantaneous) failure intensity or mean time between failures (MTBF) and (instantaneous) failure rate or mean time before failure (MTTF).
③ These measurement values are estimated using the reliability growth model. 4 Basic concepts
In the reliability growth program, laboratory or field tests are usually used to stimulate and expose the weak links of the product in order to improve the reliability of the system, equipment, components or similar products. If a failure occurs, it is necessary to diagnose, repair or replace it, and then continue the test. At the same time, for the failure that has occurred, it should be analyzed and the root cause of the failure should be found. When the exact cause is found, it is necessary to make appropriate changes to its design, other related procedures or the results of the reliability growth development process, so as to promote the gradual increase of product reliability. This procedure is applicable to both pure hardware and supporting software. For the reliability growth program of non-repairable or disposable products or components, continuously improved samples should be provided, and each improved design sample should be more reliable than the previous sample. The reliability growth of software is not restricted by the actual environment (such as temperature and humidity) and is not affected by reliability screening, but may be affected by other environments (such as use and maintenance). The estimation of hardware and software reliability characteristics can only be obtained by observing, monitoring and recording failures. The estimation of reliability characteristics will be affected by the ability of performance tests to expose weak links. In order to include various special and unknown conditions and various combinations of conditions that may be encountered in actual use, reliability growth tests should use comprehensive environmental conditions that may occur in actual use as much as possible. 4.1 Weak Links and Failures
Before a failure occurs, the weak link is usually unknown. In some operations that affect the product, due to unconscious human errors, the weak link may exist before an observable failure occurs. In other words, the weak link of the product is inherent in the material or caused by incomplete control of the manufacturing process. The reliability growth of the product is usually only related to reducing the impact of systematic weak links. The process of systematic weak links and residual weak links from initiation to elimination is shown in Figure 1. 301
4.2 Systematic weak links
Growth process
GB/T 15174--94
Tightness weak links
Systematic failure
Manager or replacement (phase-to-phase type failure
may recur)
Take improvement measures
Reduce failure intensity
Reliability growth
Repair only
Residual weak links
Residual failure
Repair or replacement (same type failure
technique may recur
No reliability growth
Figure 1, comparison of growth and repair process
Systematic weak links are generally related to design or similar procedures. Various types of weak links are often affected by the following factors : The accuracy of the specified use environment or conditions; a.
b. The novelty, complexity or criticality of the design, manufacturing process or use; c. Constraints, such as tight development or production time, insufficient funds, or too strict size, weight or performance requirements; d. Personnel training level and technical proficiency. Systemic weaknesses can exist in both hardware and software and have a wide range of impacts. The same cause may cause similar weaknesses in the product. The improvement measures used to eliminate systemic weaknesses may themselves introduce new systemic weaknesses. 4.3 Residual weaknesses
Residual weaknesses are usually only related to the manufacture of products or components. The factors described in Section 4.2 above contribute to the generation of residual weaknesses. There are also effects, but these effects can be reduced through personnel training, continuous proficiency processes and quality control. Residual weak links only exist in hardware. Unlike systematic weak links, residual weak links can be limited to a single product. Most residual weak links in products can be eliminated through reliability screening. The remaining weak links will remain and may randomly cause failures during the life of the product. Any large-scale repair, replacement or improvement implies the risk of introducing new residual weak links.
4.4 Failure mode of reliability growth process
During the reliability growth process, since the failure intensity of the product decreases with each successful improvement, the constant failure rate cannot be used. Assumptions are used to estimate the failure intensity or MTBF of the growth process. This standard describes the principles of mathematical reliability models used to estimate existing growth and make plans. In reliability improvement plans, relevant techniques can be used to estimate the time required for testing in order to achieve the specified reliability goals. The accuracy of various reliability evaluation methods depends on how effectively the test environment, monitoring procedures, failure reports and recorded test times are controlled, so laboratory data are more reliable than data obtained from field tests or "informal" test plans. If there is doubt about the degree of control, that is, if the control is not effective, do not use mathematical models. However, even if the control is not effective and the mathematical model has to be used, it is important to recognize that the improvement process described in this standard 310
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will always increase reliability. Therefore, even if the growth results cannot be quantitatively estimated, the reliability growth outline should still be implemented. In Figure 2, curve (1) is an idealized step curve, which represents the cumulative number of first failures caused by various systematic weaknesses relative to the test time. This curve is exponential, reflecting the curve trend formed by a certain number of inherent systematic weaknesses. Curve (2) is the characteristic curve of residual weaknesses relative to the observation time. After the early failure period, it is linear. Curve (3) is the sum of curves (1) and (2). It represents the total number of product-related failures. Curve (3) eventually tends to be linear. If the improvement measures are ineffective or delayed, the same type of systematic failure may recur. The curve in Figure 2 is based on the following assumptions: a. Early failures have been excluded, otherwise curve (2) will be nonlinear at the beginning; b. New weaknesses generated during the growth period due to repairs or changes are not included. For example, such new weaknesses may be introduced during repairs or changes;
c. Failures caused by normal or permissible wear are not included; d. During the entire growth process, the environment, working methods, and depth of the test remain unchanged. Any test cycle should be short-term and consistent;
e. Accurately monitor the test time.
Cumulative correlation test time
Figure 2 Relationship between correlation failure and test time Curve (1) - the first soft failure of various systemic weak links: Curve (2) - residual failure; Curve (3) - the sum of curve (1) and curve (2) 5 Management Overview
In order to implement the reliability outline, a management procedure should be established, and an important information communication network should be established between the test activities and the corresponding corrective change activities.
5.1 Management Procedure
The block diagram of the management procedure is shown in Figure 3.
Make a plan
Train personnel
Establish an information
network
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Performance monitoring
Effective detection, diagnosis
and repair
Failure distribution
Failure investigation and correction
Mathematical model
Figure 3 Overall diagram of reliability growth outline
Documents and records
Track and follow up on economic growth
Supervisory monitoring
Interim reports and final report
There should be a preparation stage (see Chapter 6) to arrange the plan. All staff need to be familiar with the equipment under test and a formal or informal information network needs to be established between the test organization and the design organization (see Section 5.2). The requirements for testing are detailed in Chapter 6, failure classification in Chapter 7, and corrective actions in Chapter 8, and Figure 5 summarizes these three parts. Mathematical models can only be applied after a statistically significant number of failures have occurred (see Chapter 9). Since the improvement process is more important than growth estimates, if the modeling conditions are not met, do not model to avoid the risk of drawing incorrect conclusions. The basis for the report should be composed of detailed daily records, feedback on the design, and user reports. See Chapter 10 for more details on this part.
5.2 Information Network
Documents alone are often not effective in facilitating the adoption of necessary measures, so corrective changes aimed at eliminating systemic weaknesses usually require the supervision and implementation of reliability engineers in person. Reliability engineers should maintain close contact with personnel related to failure information and those responsible for eliminating systemic weaknesses. The main sources of failure data are:
Reliability improvement test;
Reliability screening;
Reliability verification;
Environmental identification test;
Acceptance test;
Field test;
Operational use.
Reliability improvement test can be considered the most meaningful source of information. Since its purpose is improvement, it requires strict control of the environment and data collection. However, in terms of failure classification, other information can also provide useful background material. Computer databases with retrieval and classification functions can classify the same failure types from various sources. The scope that needs to be tracked includes:
Design and development;
Component suppliers and subcontractors;
Drawing room;
Technical specifications;
Production plan;
Manufacturing;
Reliability screening;
Acceptance test:
Technical manual;
Operation and maintenance instructions;
Training;
Transportation and loading and unloading;
Users.www.bzxz.net
GB/T 15174-—
Figure 4 illustrates the basic contact relationship of the information contact network. Design and production 1. Engineer
Other
sources
of failure data (e.g. production
tests
Engineer
Component testing
Reliability improvement
Reliability verification
5.3 Manpower and cost
Reliability 1. Engineer
General recommendations for reliability
Estimation and other analysis
Effect analysis and tracking
Other functional areas
e.g. maintenance and support, etc.
Failure analysis and comparison
Component
Functional testing
Physical and chemical analysis
Damage simulation
Component testing
|Figure 4 Communication network and functional diagram
Due to the wide variety and scale of products and projects, only general principles can be given here. For small projects, reliability engineers only need to use part of their time to complete the tasks described in Article 5.2 above. In other cases, other relevant personnel are required to assist him in his work.
The arrangement of manpower should take into account the strength of reliability engineers and the design capabilities required to find weak links. If there is no reliability growth outline, some weak links are difficult to find. In terms of failure analysis and improved design, it should be possible to absorb meaningful results from design and other aspects.
Generally speaking, the subjects Products and test equipment are recyclable. If these products can be delivered or repaired for other purposes, they have no effect on the total test cost. Unused spare parts can also be recycled. 5.4 Cost-effectiveness
Investing in reliability growth programs can greatly save the maintenance costs of products throughout their life cycle. These savings depend on many factors, including the total number of products (or the number of failed units of a single product), extending the life cycle, reducing the average repair cost, and reducing the investment in on-site maintenance facilities.
6 Reliability Growth Outline Plan
It should be recognized that after efforts and within a certain effective time, It is impossible to eliminate all weak links. Some systematic and residual weak links still exist and will affect the actual failure strength of the project. The total test time for reliability improvement is related to the required improvement level, usually within a few thousand hours. In order to deliver the required completed products and equipment in a timely manner, the test plan should be formulated in the early stage of the reliability growth program. When formulating the test plan, the following should be determined: a. The number of each type of tested products and their design standards; b. Test equipment (standards and specifications);
Spare products (assemblies and components); c.
d. Test conditions and environmental test equipment;
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e. The expected duration of the program, including working time and calendar time; f. Manpower invested in debugging, testing, communication, repair, analysis, investigation and modification. 6.1 Number of tested products
Increase the number of products tested at the same time to make them more representative of the whole. Usually, it has lower costs and higher reliability for simple and less complex products. Therefore, in an appropriate time, more test samples need to be put into the test to produce a sufficient number of failures. This solution is acceptable because each product has a low cost and a small actual size. 6.2 Test stress
Usually, since only failure can reveal weak links, the work of the reliability improvement program includes both stimulating failures and eliminating the exposed systematic weak links. However, in general, planned stimulating failures in the laboratory is better than stimulating failures on the spot. The environmental stress selected for stimulating failures should be guided by the contents of GB5080.1, GB5080.2, and GB7288.2. In order to stimulate failures as quickly as possible, the most severe environment and enhanced use conditions allowed by the design specifications (operating state, not storage state) should be used. Similarly, the product is repeated in a series of real functional tests so that the design gives the maximum allowable stress of the product. The environmental stress and working mode are not required to strictly correspond to the actual use conditions of the product, but should adopt the use conditions that can accelerate the stimulation of potential weak links. It should be noted that failure mechanisms that are not typical in normal use should not be introduced to avoid making the mathematical model unable to reflect the actual situation. Additional failure data may be provided if separate qualification tests are performed under extreme environmental conditions. The type and severity of the stimulus used will vary with the different structural levels of the product.
6.3 Outline duration
To ensure that all failures are detected, a comprehensive and frequent performance test schedule is listed in accordance with the test specifications. Where the product includes software, this test schedule should include all expected operating modes and their possible combinations. With the help of reliability growth models, the duration required to achieve a given reliability goal can be predicted based on past experience (public or private). Mathematical models provide a means to predict the number of correlated failures, which is based on model parameters assumed based on previous experience and then corrected by the number of additional failures (e.g., non-correlated failures and repetitions of systematic failures caused by weaknesses that still exist). Estimate the mean calendar time for repair and modification, as well as the mean calendar time required for accidental failures of the equipment.
The total calendar time for the entire program is constructed as follows: the total work time required, converted into calendar time based on the maximum number of work hours per week (or month); a.
Total downtime to repair all expected failures; b.
Total downtime required to make changes to all expected systematic weaknesses; c.
d. Calendar time allowed for contingency events. 6.4 Planned growth and growth monitoring
The target values for the reliability measures of the equipment under test are usually specified by the user. During the execution of the program, in order to assess the progress of the reliability growth level, a planned growth curve should be prepared. This curve may indicate the expected reliability level at certain times in the program in calendar time or test time. If the program is executed in different time stages, the points of the growth curve should coincide with the end of each corresponding stage. Plotting the overall planned growth pattern or plotting the "ideal growth curve" can usually be constructed using an acceptable mathematical model (see Chapter 9), the parameters of which reflect the actual growth rate in combination with past experience. If there are different phases, the individual objectives for each phase must be determined, see Figure 8. At the specified times in the program, the actual reliability growth should be estimated from the model and compared with the planned growth (growth monitoring).
6.5 Special considerations for non-repairable or disposable products and components In general, the principles of the reliability growth program for repairable products are usually also applicable to the reliability growth program for non-repairable or disposable products or components. However, the reliability growth program for these products is somewhat different from that for equipment. In this case, the commonly used reliability metrics are failure rate and MTTF. Each sample of a model of product used for testing should be tested as many items as possible. When samples are not provided to replace failed samples, there will generally be no significant reduction in the number of samples. In order to further expose undiscovered inherent weaknesses, a systematic failure analysis should be performed at the same time as the test. Usually, improvement measures are taken for the product after the occurrence of systematic failures. All tested samples should be immediately changed to the improved type and the test should be restarted to verify the effectiveness of the changes and further expose new unknown weaknesses. If the wear of the product is severe, improvement work can extend the life of the product. Because the number and number of changes to many systematic weak links may not be statistically significant, it is not necessarily practical or reliable to evaluate them using the reliability growth mathematical model. However, if the number of samples is large enough, other methods, such as Weibull analysis, are also applicable (see GB5080.4). 7 Failure classification
The failure classification described in this chapter is different from the basic factors such as design or structure described in Chapter 4, and is independent of improvement measures, growth models and evaluation. The first step in classification is to identify and eliminate non-related failures, and the second step is to further classify related failures into systematic and residual ones.
The classification process requires engineering judgment based on the much information obtained from the investigation. Failure classification attempts to trace the sequence of failure concepts described in Section 4.1, that is, to further trace the cause of failure from failure to weak link. 7.1 Classification of non-related failures
Non-related failures in general have been described in Section 9.3 of GB5080.1. According to the special requirements of the outline (defined in the corresponding specifications or plans), all failure modes listed below can be classified in the category that does not require corrective changes. In reliability growth assessment (see clause 9), they can also be considered as unrelated failures. Any of the following expanded unreliability factors, such as interfaces, equipment interfaces or test equipment, can be related to corrective changes even if they are unrelated to the main product in the outline. 7.1.1 Dependent failures - see clause 9.3.1 of GB 5080.1 If dependent failures are considered to be systematic, then these failures are related. 7.1.2 Misuse failures - see clause 9.3.2 of GB 5080.1 If misuse failures are considered to be systematic, then these failures are related. 7.1.3 Failures in the process of correction, or failures that have been eliminated by design changes - see clause 9.3.3 of GB 5080.1 When mathematical models are used for reliability growth assessment, it should be stated separately whether these failures have been eliminated. 7.1.4 Intermittent failures
After the first occurrence of any type of failure, these failures can be considered unrelated. Potential weaknesses are related if they are systematic. 7.1.5 Failures requiring operator adjustment or maintenance (failures that occur only during normal operator use) Failures that can be corrected by adjustment and maintenance are considered uncorrelated. If they are considered to be systematic, then these failures are correlated. 7.1.6 Failures of components that do not meet the test specification requirements but meet the requirements of the specific use function are considered uncorrelated if they can be detected during investigation without affecting the performance of the equipment during the entire operation. 7.1.7 Failures after the acceptable life
Product wear failures after the specified minimum life period are considered uncorrelated. 7.1.8 Failures during the reliability screening process Failures that occur during the reliability screening process are uncorrelated for the purpose of reliability growth assessment. However, failures that expose new systematic weaknesses during reliability screening always require investigation and corrective changes when possible. 7.2 Classification of dependent failures
Classification of dependent failures as systematic or residual has two purposes: a. To determine whether corrective changes are necessary; 315
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b. Because some reliability growth models require different failure types to be input separately. The following basic principles are useful for failure classification: a. Systematic failures
Failures that are likely to recur after actual conditions or design analysis can be confirmed by true recurrence of failure results after long-term testing. For example, components subjected to moderate overstress for a sufficiently long period of time can show recurring failures caused by design errors.
b. Residual failures
Residual failures will not recur, assuming that their recurrence is impossible. For example, failures caused by components that are occasionally missed or accidental process errors.
Failure classifications must be reviewed frequently based on the latest failure events, which can provide new evidence for reclassification, especially for Class B systematic failures (see 7.3). 7.3 Types of Related Failures
Systematic failures shall be classified as either Class A or Class B as follows: a Class A
Failures for which no corrective changes are necessary as specified in 3.10; b Class B
Failures for which corrective changes are necessary as specified in 3.11 to prevent recurrence of the failure. 8 Reliability Improvement Process
Figure 5 shows the sequence of failure diagnosis, repair or replacement, classification, and further investigation and corrective changes when appropriate. The above process is applicable when the information comes from an informal outline or an activity that is different from the original objective. To reduce test interruption time, the test is suspended as soon as a failure occurs that is sufficient for diagnosis, repair or replacement. While the test is being conducted, systematic failures should be investigated and improved as much as possible. If the weak link still exists, there is a risk of the same type of failure recurring.
Corrective changes should be made for Class B systematic failures. When a change is proposed, the change should be made as early as possible (e.g. after another failure or interruption for other reasons). However, better results may be achieved if the program is divided into different stages and some (especially when the workload is large) changes are postponed until the end of each stage. Figure 8 shows such an example. Spare parts can be used to restore the performance of the failed sample, and modules or other replaceable units can be replaced. Allowing changes to independent spare parts units can greatly shorten the test downtime. It is therefore beneficial to have a set of such spare parts, which must be changed in advance, otherwise these spare parts can only be used temporarily. The effect of the change can only be known after the test time is several times the first failure caused by this specific weak link. This not only shows whether the impact of the specific weak link has been successfully reduced or eliminated, but also whether another systematic weak link has been introduced. In order to expose new residual weak links introduced by errors in the production process and the use of new parts, a running period (which is similar to the period of reliability screening) is also required to expose new residual weak links introduced by errors in the production process and the use of new parts. 2316
9 Mathematical model
1 See, 1 article
Non-US joint effect
Record data
(See 1.3)
Residual failure
Record data
Class A failure
No change measures
Record data
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(See Chapter 4)
Second classification
Related failure
(7.2)
Second classification
1 Possible
Reclassify
Systematic effect
Adjustment and classification
Class B failure
Design change
Record data
【(see .2)
Figure 5 Reliability improvement flow chart
Continue testing
Observe failure
Suspend testing
Repair or replace
Terminate testing
Stop testing
Implement changes
This chapter describes mathematical models for reliability characteristics based on failure intensity or MTBF. For other reliability characteristics, such as failure rate MTTF or success rate, other mathematical models can be used. Reliability growth models enable quantitative estimation of the reliability characteristics that have been or will be achieved at the end of the growth plan or at an intermediate point in the process. These reliability characteristics can be used in the following forms: a. Instantaneous failure intensity or MTBF at a given point in the outline; Extrapolated failure intensity or MTBF at several future points in the outline; b.
The planned failure intensity MTBF after delaying changes or stopping improvements. Instantaneous or extrapolated failure intensities are most useful during the course of the program, and the planned metrics are most valuable as final estimates at the end of each phase or program.
In addition, the following ratios can be estimated:
The ratio of the metrics listed above to the metrics at the beginning of the program; a.
The ratio of the number of exposed systematic weaknesses to the inherent total estimated by the model; the ratio of the number of modified systematic weaknesses to the inherent total. 317
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The length of the early failure period can be estimated directly from the failure data by observing the characteristics of the number of failures and time or by other means. Failures and times during this period should not be included in the reliability growth calculation. 9.1 Nature and Objectives of the Model
Reliability growth models use mathematical functions that accurately reproduce the characteristics of a set of data when its variables or parameters have optimal values for the data. As shown in Figure 2, the cumulative associated failures and the cumulative test time corresponding to each failure form an original data set that best expresses such functions and characteristics. The functions of the model can be divided into continuous and discrete types. Discrete models more realistically describe the failures at each stage. When evaluating, discrete models usually require more test stages than continuous models. When choosing a model, a trade-off should be made between simplicity, evaluability, and authenticity. Most models have no more than two parameters because more parameters will complicate the evaluation work. In order to obtain the maximum likelihood estimate or least squares estimate of the parameters, it is often necessary to solve the equations and substitute the parameter estimates (the solutions to the equations) into the model, so that the reliability characteristics described in this chapter can be obtained. Two important requirements of the growth model:
a. Sufficient data;
b. The test environment remains unchanged.
It cannot be assumed that the use of mathematical models is absolutely reliable. Be cautious when applying models. Models are used only as statistical tools to help make engineering decisions.
9.2 Concept of reliability characteristic quantities used in models 9.2.1 Instantaneous failure intensity
As shown in curve (3) of Figure 2, the characteristics of total associated failures relative to test time can generally be represented by the solid curve in Figure 6.
The instantaneous failure intensity at any point is the slope of the tangent of the curve at that point. Figure 6 shows the tangent at the starting point and the middle point (t1, n). The slope of this tangent represents the instantaneous failure intensity of this product (or a batch of products). After fitting with a mathematical model, the slope can be estimated.
Cumulative associated test time
Figure 6 Characteristics of instantaneous failure intensity and extrapolated failure intensity The slope of the tangent line between the origin and (t, n) is the instantaneous failure intensity; the slope of the tangent line at (t2·n2) is the extrapolated failure intensity However, if changes are made later in the entire test time, there may not be enough time to use the model to reflect the results of the growth. Therefore, the true instantaneous failure intensity is lower than the estimated value. If most or all changes are postponed until the end of the test (or a specific test phase), a special problem arises, that is, this method cannot be used to evaluate reliability, and only the method described below can be used to estimate the planned failure intensity.
9.2.2 Extrapolated failure intensity
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