© 2016 Minitab, Inc. Reliability for Your Company's Survival Bonnie Stone, Minitab October 19,

© 2016 Minitab, Inc. Agenda ►Introduction to Reliability Why Reliability Analysis is Different Censoring ►Reliability Distributions Probability Plots Choosing Distributions Hazard Functions Weibull Distributions ►Reliability Analysis ►Other Tools 2

© 2016 Minitab, Inc. What is Reliability? ►Reliability: The probability (0 ~ 1) that a system or product will perform its intended function under normal operating conditions for a specified period of time ►Reasons: Predicting product reliability Predicting warranty costs (downtime, spares, repairs, etc.) Assessing the effect of proposed design changes 3

© 2016 Minitab, Inc. What is Reliability? ►Some examples: Mileage before auto part failure Time until bulb burnout Load before part breakage Temperature until circuit failure

© 2016 Minitab, Inc. Why is Reliability Analysis Different? ►Censored data ►Interested in lower percentiles instead of mean ►Apply distributions other than normal ►Small sample sizes ►Accelerate and extrapolate 5

© 2016 Minitab, Inc. Example: Pacemaker Battery Life What is the 5-year and 10-year reliability of a pacemaker battery? ►1970 pacemakers have been tracked ►1019 batteries replaced, 951 still using original battery ►Reliability goals: 95% last at least 5 years 50% last at least 10 years 6

© 2016 Minitab, Inc. Censoring ►Censoring: the exact failure time is not observed ►Three common types of censoring: Right censoring Interval censoring Left censoring ►Censoring is common because we cannot always run tests until products fail 7

© 2016 Minitab, Inc. Censoring Consider 5 failure times:

© 2016 Minitab, Inc. Censoring ►Add a censored value; say at time = 6: ►Mean of the data: 21/6 = 3.5 ►Mean time until failure (exponential distribution): 9

© 2016 Minitab, Inc. Probability Plots ►Handle censoring appropriately ►Provide percentile estimation ►Allow for non-normal data ►Work for small sample sizes ►Allow for extrapolation 10

© 2016 Minitab, Inc. Probability Plots and Percentile Estimation Data Rank (i) Percentile (i-.3)/(n+.4) ** 11

© 2016 Minitab, Inc. Probability Plots and Distribution Fit 12

© 2016 Minitab, Inc. Choosing a Distribution ►Weibull distribution ►Known to be appropriate for the situation ►Simplest distribution that adequately fits 2-parameter distributions over 3 3-parameter distribution only if no 2-parameter distributions fit and/or an engineering reason for third parameter ►Familiar to your organization ►Most conservative 13

© 2016 Minitab, Inc. Hazard Function and the Bathtub Curve 14 Hazard = Instantaneous rate of failure

© 2016 Minitab, Inc. Weibull Shape Parameter and Hazard Function Shape = 0.8 (Infant Mortality)Shape = 1 (Useful Life) Shape = 3 (Early Wearout)Shape = 10 (Rapid Wearout) 15

© 2016 Minitab, Inc. Weibull Shape Parameter 16 Shape valueMode of failureRate of failure over time Shape < 1Infant mortalityDecreasing Shape ≈ 1Useful lifeConstant (random) Shape > 1WearoutIncreasing

© 2016 Minitab, Inc. Parametric Distribution Analysis What is the 5-year and 10-year reliability of a pacemaker battery? Reliability goals: ►95% last at least 5 years ►50% last at least 10 years 17

© 2016 Minitab, Inc. Analysis Results ►95% confident at least 95.9% of units will survive 5 years (Acceptable) ►95% confident at least 43.9% of units will survive 10 years (Unacceptable) 18

© 2016 Minitab, Inc. Failure Modes ►Analysis may also include “failure modes” Different types of failure ►Each mode modeled independently ►Distributions “combined” into survival/hazard data

© 2016 Minitab, Inc. Failure Modes ►Example – Circuit board failures Meter, Sensor, or Transmitter might fail

© 2016 Minitab, Inc. Failure Modes

© 2016 Minitab, Inc. Other Reliability Tools ►Similar to Sample Size calculation ►How many parts/what conditions to demonstrate “minimum” reliability ►How many units to estimate percentiles with certain interval/confidence

© 2016 Minitab, Inc. Other Reliability Tools ►Uses production and warranty claim data ►Predict future warranty claims ►Also predict cost of future claims

© 2016 Minitab, Inc. Other Reliability Tools ►Useful when component failure does not mean total failure ►Estimate: Frequency of repair # parts to stock Future repair costs

© 2016 Minitab, Inc. Other Reliability Tools ►Predict reliability under typical conditions by using more extreme conditions ►Good for long-life products where testing could be impractically long ►Example: Light bulb failure ►Must know accelerating factor(s)

© 2016 Minitab, Inc. Other Reliability Tools ►Similar to GLM but allows for: Censoring Alternate residual distributions ►Model failure times or stresses using other factors ►Can be used to shorten data collection time

© 2016 Minitab, Inc. Other Reliability Tools ►Similar to Binary Logistic Regression ►For responses that are binary Broke / didn’t break Fail / no fail ►Output includes percentile information

© 2016 Minitab, Inc. Testing Equipment ►What detailed testing equipment should exist for testing my product. Thermal and thermal shock Vibration Mechanical shock Thermal shock Computer test equipment Electrical and magnetic stress 28

© 2016 Minitab, Inc. Product Testing ►How do I test product to the application and meet customer expectations. Find out from customer what their Reliability requirements are. To know specifically, we must ask the customer what stresses the product will see. We must correlate the test equipment parameters to the stresses the product will see so that we exactly test to the Reliability and timing the customer wants. 29

© 2016 Minitab, Inc. Summary ►Reliability Analysis describes the times-to-failure for components, subassemblies, assemblies, or systems. ►Useful for Repairable and Non-Repairable Systems ►Estimate failure costs caused by system downtime, cost of spares, repair equipment, personnel, and cost of warranty claims ►Assess the effect of proposed design changes 30 Thank you for attending today’s session

© 2016 Minitab, Inc. Reliability for Your Company's Survival Bonnie Stone