Reliability Minitab 5jh5t

Type of observation

Description Example You know exactly when the failure Exact failure time The fan failed at exactly 500 days. occurred. You only know that the failure occurred Right censored The fan had not yet failed at 500 days. after a particular time. You only know that the failure occurred Left censored The fan failed sometime before 500 days. before a particular time. You only know that the failure occurred The fan failed sometime between 475 and 500 Interval censored between two particular times. days. Use the right-censoring options if your data are censored in either of these ways:  Time-censored - Test each unit for a preset amount of time  Failure-censored - Test the units until a preset proportion of failures occur. 1A. Example of creating a demonstration test plan: The reliability goal for a turbine engine combustor is a 1 percentile of at least 2000 cycles. The number of cycles to failure tends to follow a Weibull distribution with shape = 3. You can accumulate up to 8000 test cycles on each combustor. You must determine the number of combustors needed to demonstrate the reliability goal using a 1failure test plan. Engineers determine that early transmission failures occurring on a track-type tractor are due to the failure of a ball bearing. The failure times for this ball bearing follow a Weibull distribution with a shape of 1.3 and scale of 1,000 hours. The engineers have 3 redesigned units available for testing and must determine how long to test each unit using a 0-failure test plan. Stat > Reliability/Survival > Test Plans > Demonstration Fix  “Number of failures allowed” and one of the two “number of units to test” or “time to test each unit” Compare one of the following: Scale or location Parameter; Percentile/Reliability achieved in hours or cycles; MTTF in hours 1B. Example of creating an estimation test plan: You want to run a life test to estimate the 5th percentile for the life of a metal component used in a switch. You can run the test for 100,000 cycles. Before running this life test, you want to determine the number of units to test to ensure a precise estimate. You expect about 5% of the units to fail by 40,000 cycles, 15% by 100,000 cycles, and the life to follow the Weibull distribution. You want the lower bound of your confidence interval to be within 20,000 cycles of your estimate. Stat > Reliability/Survival > Test Plans > Estimation Multiple lower bounds can be taken. 2 out of 4 planning values should be provided. Minitab calculates the planning estimate for the parameter you want to estimate based on the planning values and distribution. If you want to estimate the 10th percentile of your failure time distribution, and the lower bound is to be no more than 25 hours less than your estimate, choose Lower bound and enter 25 as your desired precision in Sample sizes or precisions as distances from bound of CI to estimate.

If you want to estimate the reliability of your units at 200 hours, and the lower bound is to be a reliability that is no more than 0.025 below your estimate, choose Lower bound and enter 0.025 as your desired precision in Sample sizes or precisions as distances from bound of CI to estimate. 1C. Example of creating an accelerated life test plan: You want to plan an accelerated life test to estimate the 1000-hour reliability of an incandescent light bulb at the design voltage of 110 volts. You have 20 light bulbs available to test until failure. To accelerate failures, you will run the test at 120 volts and 130 volts. You believe that a power relationship will adequately model the relationship between failure time and voltage. Historical data indicate that a lognormal distribution with a scale of 50 appropriately models light bulb failure. The planning values are 1200 for the 50th percentile at 110 volts and 600 for the 50th percentile at 120 volts. Stat > Reliability/Survival > Test Plans > Accelerated Life Testing Design and sample stress levels will be different. 2A.1. Example of a Distribution ID Plot and Distribution Overview Plot for arbitrarily-censored data: Suppose you work for a company that manufactures tires. You are interested in finding out how many miles it takes for various proportions of the tires to "fail," or wear down to 2/32 of an inch of tread. You are especially interested in knowing how many of the tires last past 45,000 miles. You plan to get this information by using Parametric Distribution Analysis (Arbitrary Censoring), which requires you to specify the distribution for your data. Distribution ID Plot - Arbitrary Censoring can help you choose that distribution. You inspect each good tire at regular intervals (every 10,000 miles) to see if the tire has failed, then enter the data into the Minitab worksheet. Open the worksheet Data 1 (Col A - Col C) Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Distribution ID Plot Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Distribution Overview Plot 2A.2 Example of a parametric distribution analysis with arbitrarily censored data: Note: This exercise is not separated by exact and multiple failure modes. Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Parametric Distribution Analysis 2A.3.1.Example of non-parametric distribution analysis with arbitrarily censored data: Note: There is separate analysis for multiple failure modes Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Nonparametric Distribution Analysis

3A.1. Example of a Distribution ID Plot and Distribution Overview Plot for right-censored data: Suppose you work for a company that manufactures engine windings for turbine assemblies. Engine windings may decompose at an unacceptable rate at high temperatures. You want to know - at given high temperatures - the time at which 1% of the engine windings fail. You plan to get this information by using Parametric Distribution Analysis (Right Censoring), which requires you to specify the distribution for your data. A) Distribution ID Plot - Right Censoring can help you choose that distribution, B) but you first want to have a quick look at your data from different perspectives. First you collect failure times for the engine windings at two temperatures. In the first sample, you test 50 windings at 80° C; in the second sample, you test 40 windings at 100° C. Some of the units drop out of the test for unrelated reasons. In the Minitab worksheet, you use a column of censoring indicators to designate which times are actual failures (1) and which are censored units removed from the test before failure (0). Open the worksheet Data 1 (Col E- Col H) CE & CG are failure times when CF & CH values are (1). CF & CH (0) values indicate test was not completed till the time shown in CE & CG Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Distribution ID Plot Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Distribution Overview Plot 3A.2.1. Example of a parametric distribution analysis with exact failure/right censored data: Suppose you work for a company that manufactures engine windings for turbine assemblies. Engine windings may decompose at an unacceptable rate at high temperatures. You decide to look at failure times for engine windings at two temperatures, 80° C and 100° C. You want to find out the following information for each temperature:  

Times at which various percentages of the windings fail. You are particularly interested in the 0.1st percentile. Proportion of windings that survive past 70 months.

You also want to draw two plots: a probability plot to see if the lognormal distribution provides a good fit for your data, and a survival plot. In the first sample, you collect failure times (in months) for 50 windings at 80° C; in the second sample, you collect failure times for 40 windings at 100° C. Some of the windings drop out of the test for unrelated reasons. In the Minitab worksheet, you use a column of censoring indicators to designate which times are actual failures (1) and which are censored units removed from the test before failure (0). Again open the worksheet Data 1 (Col E - Col H) Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Parametric Distribution Analysis 3A.3.1. Example of non-parametric distribution analysis with exact failure/right censored data: You want to find out the following information for each temperature: 

The times at which half of the windings fail.



The proportion of windings that survive past various times.

You also want to know whether or not the survival curves at the two temperatures are significantly different. Again open the worksheet Data 1 (Col E - Col H) Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Nonparametric Distribution Analysis 3A.2.2 Example of a parametric distribution analysis with multiple failure modes: You are responsible for improving the overall reliability of pressure sensing circuits. Three main components could fail, leading to system failure: sensor, transmitter, and meter. You want to determine which component fails most frequently, so you can redesign it to optimize overall system reliability. You plan to get this information using Parametric Distribution Analysis (Right Censoring). You can specify a distribution for each failure mode, and Distribution ID Plot (Right Censoring) can help you choose appropriate distributions. Open the worksheet Data 1 (Col J - Col K) Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Parametric Distribution Analysis 2A.3.2. Example of non-parametric distribution analysis with multiple failure modes: Note: There is no separate analysis for Right Censoring. You work for a medical imaging company and are deg a new x-ray cassette. To be competitive in your market, the overall cassette reliability at 20,000 cycles should be at least 90%. You decide to look at each of the three failure modes (Window, Hinge, and Screen) to see which component to improve. You have interval failure times and are unsure of the distribution of failures. Open the worksheet Data 1 (Col M - Col P) Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Nonparametric Distribution Analysis 4. Example of warranty prediction: The typical steps in a warranty data analysis are: 1. Use Pre-Process Warranty Data to convert the data from triangular matrix format to arbitrary censoring format. 2. Use Distribution ID Plot, Arbitrary Censoring to choose an appropriate distribution for the existing data. 3. Use Warranty Prediction to predict the number or cost of future failures. You work for an appliance manufacturer and must use current warranty data to predict the number of refrigerator compressor warranty claims you expect to see over the next five months. Open the worksheet Data 2

Stat > Reliability/Survival > Warranty Analysis > Pre-Process Warranty Data Stat > Reliability/Survival > Warranty Analysis > Warranty Prediction 5A. Repairable System Analysis: Use nonparametric and parametric growth curves to determine whether a trend exists in times between successive failures of a repairable system; that is, to determine whether system failures are becoming more frequent, less frequent, or remaining constant. Use this information to make decisions concerning the future operation of your system, such as: setting maintenance schedules, making provisions for spare parts, assuring suitable performance, forecasting repair costs. 5A. Repairable System Analysis – Example of Parametric Growth Curve: You want to estimate the replacement rate of a certain valve on a fleet of 24 diesel engines. Open the worksheet Data 3 (Col A - Col B) Stat > Reliability/Survival > Repairable System Analysis > Parametric Growth Curve 5B. Repairable System Analysis – Example of Non-parametric Growth Curve: You want to compare two different types of a particular brake component used on a subway train. Your data include replacement times and component type for 29 trains. The final time for each train is the final failure for that train. Open the worksheet Data 3 (Col D - Col F) Stat > Reliability/Survival > Repairable System Analysis > Nonparametric Growth Curve 6. Example of Accelerated Life Testing and Regression with Life Data: Suppose you want to investigate the deterioration of an insulation used for electric motors. The motors normally run between 80 and 100° C. To save time and money, you decide to use accelerated life testing. First you gather failure times for the insulation at abnormally high temperatures - 110, 130, 150, and 170° C - to speed up the deterioration. With failure time information at these temperatures, you can then extrapolate to 80 and 100° C. It is known that an Arrhenius relationship exists between temperature and failure time. To see how well the model fits, you will draw a probability plot based on the standardized residuals. Open the worksheet Data 4 Col-D provides the variable Failure Time. Col-E shows whether the data is censored (C) or final (F). The accelerating variable temperature is listed in Col-A. Stat > Reliability/Survival > Accelerated Life Testing Stat > Reliability/Survival > Regression with Life Data