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Dfr Presentation

  1. 1. RAL VEM DFR – Design for Reliability DFR – Fundamentals for Engineers Reliability Audit Lab
  2. 2. RAL VEM Topics that will be covered: 1. Need for DFR 2. DFR Process 3. Terminology 4. Weibull Plotting 5. System Reliability 6. DFR Testing 7. Accelerated Testing Reliability Audit Lab
  3. 3. RAL VEM 1. Need for DFR Reliability Audit Lab
  4. 4. RAL VEM What Customers Care about: 1. Product Life…. i.e., useful life before wear-out. 2. Minimum Downtime…. i.e., Maximum MTBF. 3. Endurance…. i.e., # operations, robust to environmental changes. 4.Stable Performance…. i.e., no degradation in CTQs. 5. ON time Startup…. i.e., ease of system startup Reliability Audit Lab
  5. 5. RAL VEM Reliability Audit Lab
  6. 6. RAL VEM Reliable Product Vision Failure Mode Failure Rate Resources/Costs Identification (Pre-Launch) Release Release Resources/costs # Failure Modes DFR Failure Rate 50% No DFR No DFR No DFR DFR Goal DFR 5% Time Time Time Identify & “eliminate” Start with lower “running Reduce overall costs by inherent failure modes rate”, then aggressively employing DFR from the beginning. before launch. (Minimize “grow” reliability. (Reduce Excursions!) Warranty Costs) Take control of our product quality and aggressively drive to our goals Reliability Audit Lab
  7. 7. RAL VEM 2. DFR - Process Reliability Audit Lab
  8. 8. RAL VEM NPI Process • Field data analysis • CTQ Identification DP1 DP3 • Customer Metrics DP0 Specify Design DP2 Implement Rel. Goal Setting Production / Field • Assess Customer needs • Establish audit program • Develop Reliability metrics • FRACAS system using ‘Clarify’ • Establish Reliability goals • Correlate field data & test results System Model Verification • Execute Reliability Test strategy Design • Construct functional block diagrams • Continue Growth Testing • Define Reliability model • Accelerated Tests • Apply robust design tools • ID critical comps. & failure potential • Demonstration Testing • DFSS tools • Allocate reliability targets • Agency / Compliance Testing • Generate life predictions • Begin Growth Testing Reliability Audit Lab
  9. 9. RAL VEM Legacy Product DFR Process . . . Review Historical Data • Review historical reliability & field failure data 1 • Review field RMA’s • Review customer environments & applications Analyze Field & In-house Endurance Test Data • Develop product Fault Tree Analysis 2 • Identify and pareto observed failure modes Develop Reliability Profile & Goals • Develop P-Diagrams & System Block Diagram • Generate Reliability Weibull plots for operational endurance 3 • Allocate reliability goals to key subsystems • Identify reliability gaps between existing product & goals for each subsystem Develop & Execute Reliability Growth Plan • Determine root cause for all identified failures 4 • Redesign process or parts to address failure mode pareto • Validate reliability improvement through accelerated life testing & field betas Institute Reliability Validation Program • Implement process firewalls & sensors to hold design robustness 5 • Develop and implement long-term reliability validation audit Reliability Audit Lab
  10. 10. RAL VEM Design For Reliability Program Summary Keys to DFR: • Customer reliability expectations & needs must be fully understood • Reliability must be viewed from a “systems engineering” perspective • Product must be designed for the intended use environment • Reliability must be statistically verified (or risk must be accepted) • Field data collection is imperative (environment, usage, failures) • Manufacturing & supplier reliability “X’s” must be actively managed DFR needs to be part of the entire product development cycle Reliability Audit Lab
  11. 11. RAL VEM 3. DFR - Terminology Reliability Audit Lab
  12. 12. RAL VEM What do we mean by 1. Reliability 2. Failure 3. Failure Rate 4. Hazard Rate 5. MTTF / MTBF Reliability Audit Lab
  13. 13. RAL VEM 1. Reliability R(t): The probability that an item will perform its intended function without failure under stated conditions for a specified period of time 2. Failure: The termination of the ability of the product to perform its intended function 3. Failure Rate [F(t)]: The ratio of no. of failures within a sample to the cumulative operating time. 4. Hazard Rate [h(t)]: The instantaneous probability of failure of an item given that it has survived until that time, sometimes called as instantaneous failure rate. Reliability Audit Lab
  14. 14. RAL VEM Failure Rate Calculation Example EXAMPLE: A sample of 1000 meters is tested for a week, and two of them fail. (assume they fail at the end of the week). What is the Failure Rate? 2 2 failures Failure Rate = = failures /hour 1000 * 24 * 7 hours 168 , 000 = 1.19E-5 failures/hr Reliability Audit Lab
  15. 15. RAL VEM Probability Distribution Function (PDF): The Probability Distribution Function (PDF) is the distribution f(t) of times to failure. The value of f(t) is the probability of the product failing precisely at time t. f (t) Probability Distribution Function time t Reliability Audit Lab
  16. 16. RAL VEM Common Distributions Probability Density Variate, Probability Distribution Function, f(t) Range, t −λt f  t =λe 0≤t∞ Exponential t −  β β t β−1 0≤t∞ f  t = ⋅  ⋅e β Weibull ηη 2 − t− μ  1 2 2σ f  t = ⋅e Normal −∞t ∞ σ  2π  ln  t −μ 2 1 Log 2 2σ 0≤t∞ f  t = ⋅e Normal σt  2π Reliability Audit Lab
  17. 17. RAL VEM Cumulative Distribution Function (CDF) : The Cumulative Distribution Function (CDF) represents the probability that the product fails at some time prior to t. It is the integral of the PDF evaluated from 0 to t. t CDF =F  t =∫ f  t dt 0 f (t) Probability Distribution Function time t1 Cumulative Distribution Function Reliability Audit Lab
  18. 18. RAL VEM Reliability Function R(t) The reliability of a product is the probability that it does not fail before time t. It is therefore the complement of the CDF: t Typical characteristics: R t =1−F  t =1−∫ f  t dt • when t=0, R(t)=1 0 or • when t→∞, R(t) →0 ∞ R t =∫ f  t  dt t f (t) Probability Density Function R(t) = 1-F(t) time t Reliability Audit Lab
  19. 19. RAL VEM Hazard Function h(t) The hazard function is defined as the limit of the failure rate as Δt approaches zero. In other words, the hazard function or the instantaneous failure rate is obtained as h(t) = lim [R(t) – R(t+Δt)] / [Δt * R(t)] Δt -> 0 The hazard function or hazard rate h(t) is the conditional probability of failure in the interval t to (t + Δt), given that there was no failure at t. It is expressed as h(t) = f(t) / R(t). Reliability Audit Lab
  20. 20. RAL VEM Hazard Functions As shown the hazard rate is a function of time. What type of function does hazard rate exhibit with time? The general answer is the bathtub-shaped function. The sample will experience a high failure rate at the beginning of the operation time due to weak or substandard components, manufacturing imperfections, design errors and installation defects. This period of decreasing failure rate is referred to as the “infant mortality region” This is an undesirable region for both the manufacturer and consumer viewpoints as it causes an unnecessary repair cost for the manufacturer and an interruption of product usage for the consumer. The early failures can be minimized by improving the burn-in period of systems or components before shipments are made, by improving the manufacturing process and by improving the quality control of the products. Reliability Audit Lab
  21. 21. RAL VEM At the end of the early failure-rate region, the failure rate will eventually reach a constant value. During this constant failure-rate region the failures do not follow a predictable pattern but occur at random due to the changes in the applied load. The randomness of material flaws or manufacturing flaws will also lead to failures during the constant failure rate region. The third and final region of the failure-rate curve is the wear-out region. The beginning of the wear out region is noticed when the failure rate starts to increase significantly more than the constant failure rate value and the failures are no longer attributed to randomness but are due to the age and wear of the components. To minimize the effect of the wear-out region, one must use periodic preventive maintenance or consider replacement of the product. Reliability Audit Lab
  22. 22. Product's Hazard Rate Vs. Time : RAL VEM “The Bathtub Curve” Random Failure Infant Mortality Wear out (Useful Life) h(t) decreasing h(t) increasing Hazard Rate, h(t) h(t) constant Wear out Manufacturing Failures Defects Random Failures Time Reliability Audit Lab
  23. 23. RAL VEM Mean Time To Failures [MTTF] - One of the measures of the system's reliability is the mean time to failure (MTTF). It should not be confused with the mean time between failure (MTBF). We refer to the expected time between two successive failures as the MTTF when the system is non-repairable. When the system is repairable we refer to it as the MTBF Now let us consider n identical non-repairable systems and observe the time to failure for them. Assume that the observed times to failure are t1, t2, .........,tn. The estimated mean time to failure, MTTF is MTTF = (1/n)Σ ti Reliability Audit Lab
  24. 24. Useful Life Metrics: Mean Time RAL VEM Between Failures (MTBF) Mean Time Between Failures [MTBF] - For a repairable item, the ratio of the cumulative operating time to the number of failures for that item. (also Mean Cycles Between Failures, MCBF, etc.) EXAMPLE: A motor is repaired and returned to service six times during its life and provides 45,000 hours of service. Calculate MTBF. Total operating time 45 ,000 MTBF = = = 7,500 hours ¿ of failures 6 MTBF or MTTF is a widely-used metric during the Useful Life period, when the hazard rate is constant Reliability Audit Lab
  25. 25. RAL VEM The Exponential Distribution If the hazard rate is constant over time, then the product follows the exponential distribution. This is often used for electronic components. ht = λ=constant 1 MTBF mean time between failures = λ −λt f t =λe  −λt F t =1−e  Rt =e−λt 1 −λ   At MTBF: R t =e−λt =e =e−1 =36. 8 λ Appropriate tool if failure rate is known to be constant Reliability Audit Lab
  26. 26. RAL VEM The Exponential Distribution 0.0003 λ=.0003 0.0002 PDF: λ=.0002 f(t) 0.0001 λ=.0001 0 4 4 4 4 4 0 1 10 2 10 3 10 4 10 5 10 Time to Failure 1 λ=.0001 0.667 CDF: F(t) λ=.0002 0.333 λ=.0003 0 4 4 4 4 4 0 1 10 2 10 3 10 4 10 5 10 Time Reliability Audit Lab
  27. 27. RAL VEM Useful Life Metrics: Reliability Reliability can be described by the single parameter exponential distribution when the Hazard Rate, λ, is constant (i.e. the “Useful Life” portion of the bathtub curve),  =e t − MTBF − FR t Where: t = Mission length R=e (uptime or cycles in question) EXAMPLE: If MTBF for a motor is 7,500 hours, the probability of operating for 30 days without failure is ...   = 0 .908 = 90 . 8 30 ∗ 24 hours − 7500 hours R=e A mathematical model for reliability during Useful Life Reliability Audit Lab
  28. 28. RAL VEM 3. DFR – Weibull Plotting Reliability Audit Lab
  29. 29. RAL VEM Weibull Probability Distribution • Originally proposed by the Swedish engineer Waloddi Weibull in the early 1950’s • Statistically represented fatigue failures • Weibull probability density function (PDF, distribution of values):  β β -1 − t t  β η f t  = e β η Equation valid for minimum life = 0 t = Mission length (time, cycles, etc.) β = Weibull Shape Parameter, “Slope” Waloddi Weibull 1887-1979 η = Weibull Scale Parameter, “Characteristic Life” Reliability Audit Lab
  30. 30. RAL VEM The Weibull Distribution This powerful and versatile reliability function is capable of modeling most real-life systems because the time dependency of the failure rate can be adjusted. β h  t  = β  t  β -1 η  β β−1 − t βt η  t = β e f η  β −t η R t =1−F  t =e Reliability Audit Lab
  31. 31. RAL VEM Weibull PDF  β β−1 − t βt Exponential when β = 1.0 • η  t = β e f Approximately normal when β = 3.44 • η • Time dependent hazard rate 0 .0 0 5 β=0.5 0 .0 0 4 η=1000 β=3.44 0 .0 0 3 η=1000 β=1.0 0 .0 0 2 η=1000 0 .0 0 1 500 1000 1500 2000 Reliability Audit Lab
  32. 32. RAL VEM β > 1: Highest failure rate later- Weibull Hazard Function “Wear-Out” f t  f t  ht  = = 1 - F t  R t  0.006 β=3.44 β=0.5 [  ]  η=1000 β−1 β η=1000 β t t exp − 0.004 h η η ht  = { [   ]} h(t) β β=1.0 t 1 - 1 - exp − η=1000 η 0.002 β  t  β -1 ht  = β 0 500 1000 1500 2000 2500 η Time β < 1: Highest failure rate early- β = 1: Constant failure rate “Infant Mortality” Reliability Audit Lab
  33. 33. Weibull Reliability Function RAL VEM Reliability is the probability that the part survives to time t. 1  β −t β=3.44 η R t =1−F  t =e η=1000 0.8 β=1.0 0.6 η=1000 R(t) β=0.5 0.4 η=1000 0.2 0 0 500 1000 1500 2000 2500 Time Reliability Audit Lab
  34. 34. RAL VEM Summary of Useful Definitions - Weibull Analysis Beta (β): The slope of the Weibull CDF when printed on Weibull paper B-life: A common way to express values of the cumulative density function - B10 refers to the time at which 10% of the parts are expected to have failed. CDF: Cumulative Density Function expresses the time-dependent probability that a failure occurs at some time before time t. Eta (η): The characteristic life, or time at which 63.2% of the parts are expected to have failed. Also expressed as the B63.2 life. This is the y-intercept of the CDF function when plotted on Weibull paper. PDF: Probability Density Function expresses the expected distribution of failures over time. Weibull plot: A plot where the x-axis is scaled as ln(time) and the y-axis is scaled as ln(ln(1 / (1-CDF(t))). The Weibull CDF plotted on Weibull paper will be a straight line of slope β and y intercept = ln(ln(1 / (1-CDF(0))) = η. Reliability Audit Lab
  35. 35. RAL VEM Weibull Analysis What is a Weibull Plot ? Log-log plot of probability of • failure versus age for a product or component Weibull Best Fit Nominal “best-fit” line, plus • Observed confidence intervals Failures Easily generated, easily • interpreted graphical read-out Confidence on Fit Comparison: test results for a • redesigned product can be plotted against original product or against goals Reliability Audit Lab
  36. 36. Weibull Shape Parameter (β ) and RAL VEM Scale Parameter (η ) Defined β is called the SLOPE For the Weibull distribution, the slope describes the steepness of the Weibull best-fit line (see following slides for more details). β also has a relationship with the trend of the hazard rate, as shown on the “bathtub curves” on a subsequent slide. η is called the CHARACTERISTIC LIFE For the Weibull distribution, the characteristic life is equal to the scale parameter, η. This is the time at which 63.2% of the product will have failed. Scale and Shape are the Key Weibull Parameters Reliability Audit Lab
  37. 37. RAL VEM β and the Bathtub Curve β<1 β=1 • Implies “infant mortality” • Implies failures are “random”, individually unpredictable • If this occurs: ­ Failed products “not to print” • An old part is as good as a new part (burn- ­ Manufacturing or assembly defects in not appropriate) ­ Burn-in can be helpful • If this occurs: • If a component survives infant mortality ­ Failures due to external stress, phase, likelihood of failure decreases with maintenance or human errors. age. ­ Possible mixture of failure modes β>4 1<β<4 • Implies rapid wearout • Implies mild wearout • If this occurs, suspect: • If this occurs ­ Material properties ­ Low cycle fatigue ­ Brittle materials like ceramics ­ Corrosion or Erosion ­ Scheduled replacement may be cost • Not a bad thing if it happens after mission effective life has been exceeded. Reliability Audit Lab
  38. 38. RAL VEM 5. DFR – System Reliability Reliability Audit Lab
  39. 39. RAL VEM System Reliability Evaluation A system (or a product) is a collection of components arranged according to a specific design in order to achieve desired functions with acceptable performance and reliability measures. Clearly, th type of components used, their qualities, and the design configuration in which they are arranged have a direct effect on the system performance an its reliability. For example, a designer may use a smaller number of high-quality components and configure them in a such a way to result in a highly reliable system, or a designer may use larger number of lower-quality components and configure them differently in order to achieve the same level of reliability. Once the system is configured, its reliability must be evaluated and compared with an acceptable reliability level. If it does not meet the required level, the system should be redesigned and its reliability should be re-evaluated. Reliability Audit Lab
  40. 40. RAL VEM Reliability Block Diagram (RBD) Technique The first step in evaluating a system's reliability is to construct a reliability block diagram which is a graphical representation of the components of the system and how they are connected. The purpose of RBD technique is to represent failure and success criteria pictorially and to use the resulting diagram to evaluate System Reliability. Benefits The pictorial representation means that models are easily understood and therefore readily checked. Block diagrams are used to identify the relationship between elements in the system. The overall system reliability can then be calculated from the reliabilities of the blocks using the laws of probability. Block diagrams can be used for the evaluation of system availability provided that both the repair of blocks and failures are independent events, i.e. provided the time taken to repair a block is dependent only on the block concerned and is independent of repair to any other block Reliability Audit Lab
  41. 41. RAL VEM Elementary models Before beginning the model construction, consideration should be given to the best way of dividing the system into blocks. It is particularly important that each block should be statistically independent of all other blocks (i.e. no unit or component should be common to a number of blocks). The most elementary models are the following Series Active parallel m-out-of-n Standby models Reliability Audit Lab
  42. 42. RAL VEM Typical RBD configurations and related formulae Simple Series and Parallel System Figure a shows the units A,B,C,….Z constituting a system. The interpretation can be stated as ‘any unit failing causes the system as a whole to fail’, and the system is referred to as active series system. Under these conditions, the reliability R(s) of the system is given by R(s) = Ra * Rb * Rc * ………Rz O A B C Z I a) Series System Figure b shows the units X and Y that are operating in such a way that the system will survive as long as At lest one of the unit survives. This type of system is referred to as an active parallel system. R(s) = 1 – (1 – Rx)(1 – Ry) X O I Y b) Parallel System Reliability Audit Lab
  43. 43. RAL VEM A Series / Parallel System When blocks such as X and Y themselves comprise sub-blocks in series, block diagrams of the type are illustrated in figure c. Rx = Ra1 * Rb1 * Rc1 *……..Rz1; Ry = Ra2 * Rb2 * Rc2 *……..Rz2 Rs = 1 – (1 – Rx)(1 – Ry) A1 B1 C1 Z1 O I A2 B2 C2 Z2 c) Series / ParallelSystem Reliability Audit Lab
  44. 44. RAL VEM m-out-of-n units The figure represents instances where system success is assured whenever at least m of n identical units are in an operational state. Here m = 2, n = 3. Rs = (Rx)^3 + 3*(Rx)^2*Fx, where Fx = 1 – Rx. X X 2/3 I O X d) m-out-of-n System Reliability Audit Lab
  45. 45. RAL VEM 6. DFR – Reliability Testing Reliability Audit Lab
  46. 46. RAL VEM Reliability Testing - Why? Reliability Testing allows us to: • Determine if a product’s design is capable of performing its intended function for the desired period of time. • Have confidence that our sample-based prediction will accurately reflect the performance of the entire population. • Provide a path to “grow” a product’s reliability by identifying weak points in the design. • Confirm the product’s performance in the field. • Identify failures caused by severe applications that exceed the ratings, and recognize opportunities for the product to safely perform under more diverse applications. Reliability Audit Lab
  47. 47. RAL VEM Reliability Testing - Measures Reliability Testing answers questions like … • What is my product’s Failure Rate? • What is the expected life? . . .. • Which distribution does my data follow? .. • What does my hazard function look like? • What failure modes are present? • How “mature” is my product’s reliability? These metrics and more can be obtained with the right reliability test Reliability Audit Lab
  48. 48. RAL VEM Four Major Categories of Reliability Testing • Reliability Growth Tests (RGT) - Normal Testing - Accelerated Testing • Reliability Demonstration Tests (RDT) • Production Reliability Acceptance Tests (PRAT) • Reliability Validation (RV) Reliability Audit Lab
  49. 49. RAL VEM Reliability Testing - Growth Testing Scope: To determine a product’s physical limitations, functional capabilities and inherent failure mechanisms. • Emphasis is on discovering & “eliminating” failure modes • Failures are welcome. . . represent data sources • Failures in development = less failures in field • Used with a changing design to drive reliability growth • Sample size is typically small • Test Types: Normal or Accelerated Testing • Can be very helpful early in process when done on competitor products which are sufficiently similar to the new design. Used early & throughout the design process Reliability Audit Lab
  50. 50. RAL VEM Reliability Testing … Demonstration Testing Scope: To demonstrate the product’s ability to fulfill reliability, availability & design requirements under realistic conditions. • Failures are no longer hoped for, because they jeopardize compliance (though it’s still better to catch a problem before rather than after launch!) • Management tool . . . provides means for verifying compliance • Provide reliability measurement, typically performed on a static design (subsequent design changes may invalidate the demonstrated reliability results) • Sample size is typically larger, due to need for degree of confidence in results and increased availability of samples. Used at end of design stages to demonstrate compliance to specification Reliability Audit Lab
  51. 51. Reliability Testing … Production Reliability RAL VEM Acceptance Testing (PRAT) Scope: To ensure that variation in materials, parts, & processes related to move from prototypes to full production does not affect product reliability • Performed during full production, verifies that predictions based on prototype results are valid in full production • Provides feedback for continuous improvement in sourcing/manufacturing • Sample size ranges from full(screen) to partial (audit) • Test Types: Highly Accelerated Stress Screens/Audits (HASS/A), Environmental Stress Screening (ESS), Burn in Screens and Audits precipitate and detect hidden defects Reliability Audit Lab
  52. 52. RAL VEM Reliability Testing … Validation Scope: To ensure that the product is performing reliably in the actual customer environment/application. • “Testing results” based on actual field data sources • Provides field feedback on the success of the design • Helps to improve future design / redesign & prediction methods • Requires effective data collection & corrective action process • Sample size depends on the customer & product type Reliability Validation tracks field data on Customer Dashboards Reliability Audit Lab
  53. 53. RAL VEM Reliability Testing … The Path NPI (New Products): Set Reliability Goals Implement Production Establish service schedule Develop Models Reliability Demonstration Keep updated dashboards NPI Pilot Readiness Initial Design Audit Programs Ensure Data Collection Mature Design Accelerated Testing Improve future design Pilot Testing Initial Design Implementation Post-Sales Service Demonstration Testing Acceptance Testing Validation Testing Growth Testing Legacy Products: Implement changes Complaint generated Revise goals Reproduce Failure Create case Clarify Redefine models Reliability Demonstration Reliability Verification Product redesign Audit Programs Field Data Verification Product Redesign Implementation Acquisition Growth Testing Demonstration Testing Acceptance Testing Validation Testing Reliability Tests are critical at all stages! Reliability Audit Lab
  54. 54. RAL VEM 7. DFR – Accelerated Testing Reliability Audit Lab
  55. 55. RAL VEM Accelerated Testing Scope : Accelerated testing allows designers to make predictions about the life of a product by developing a model that correlates reliability under accelerated conditions to reliability under normal conditions. Model: BASIC CONCEPT The model is how we extrapolate back to normal stress levels. Time to Failure . . . . Common Models: . . • Arrhenius: Thermal • Inverse Power Law: Non-Thermal Stress } } • Eyring: Combined To predict here, we test here (Elevated stress level) (Normal stress level) Results @ high stress + stress-life relationship = Results @ normal stress Reliability Audit Lab
  56. 56. RAL VEM Accelerated Testing Key steps in planning an accelerated test: • Choose a stress to elevate: requires an understanding of the anticipated failure mechanism(s) - must be relevant (temp. & vibration usually apply) • Determine the accelerating model: requires knowledge of the nature of the acceleration of this failure mechanism, as a function of the accelerating stress. • Select elevated stress levels: requires a previous study of the product’s operating & destructive limits to ensure that the elevated stress level does not introduce new failure modes which would not occur at normal operating stress levels. Applicability of technique depends on careful planning and execution Reliability Audit Lab
  57. 57. RAL VEM Parametric Reliability Models One of the most important factors that influence the design process of a product or a system is the reliability values of its components. In order to estimate the reliability of the individual components or the entire system, we may follow one or more of the following approaches. Historical Data ➢ ➢Operational Life Testing ➢Burn-In Testing ➢Accelerated Life Testing Reliability Audit Lab
  58. 58. RAL VEM Approach 1 : Historical Data The failure data for the components can be found in data banks such as GIDEP (Government-Industry Data Exchange Program), ➢ MIL-HDBK-217 (which includes failure data for components as well as ➢ procedures for reliability prediction), AT&T Reliability Manual and ➢ Bell Communications Research Reliability Manual. ➢ In such data banks and manuals, the failure data are collected from different manufacturers and presented with a set of multiplying factors that relate to different manufacturer's quality levels and environmental conditions Reliability Audit Lab
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