# Multiple failure mode analysis for Parametric Distribution Analysis (Arbitrary Censoring)

## Multiple failure mode analysis – parameter estimates

The parameter estimates define the best-fitting parameter estimates for the distribution that you selected for each failure mode. All other parametric distribution analysis graphs and statistics are based on the selected distribution. Therefore, to ensure accurate results, the distribution that you select must adequately fit the data.

You cannot determine from the estimated distribution parameters whether the distribution that you selected fits the data well. Use the distribution ID plot, probability plot, and goodness-of-fit measures to determine whether the distribution adequately fits the data.

### Example output

Variable Start: Start End: End Frequency: Freq Failure Mode: Failure = Bearing
Parameter Estimates Standard 95.0% Normal CI Parameter Estimate Error Lower Upper Location 11.4289 0.0661986 11.2991 11.5586 Scale 0.386879 0.0579657 0.288430 0.518932
Variable Start: Start End: End Frequency: Freq Failure Mode: Failure = Gasket
Parameter Estimates Standard 95.0% Normal CI Parameter Estimate Error Lower Upper Location 11.6318 0.150306 11.3372 11.9264 Scale 0.805358 0.139971 0.572863 1.13221

### Interpretation

For the water pump data, the engineers selected a lognormal distribution to model bearing failures and a lognormal distribution to model gasket failures. The parameters that define the best-fitting distribution for each failure mode are as follows:
• Location = 11.4289 and Scale = 0.386879 for bearing failures
• Location = 11.6318 and Scale = 0.805358 for gasket failures

## Multiple failure mode analysis – percentiles

The percentiles indicate the age by which a percentage of the population is expected to fail. Use the percentile values to determine whether your product meets reliability requirements, or to determine which failure modes impact the overall reliability.

Use these values only when the distribution fits the data adequately. If the distribution fits the data poorly, these estimates will be inaccurate. Use the distribution ID plot, probability plot, and goodness-of-fit measures to determine whether the distribution adequately fits the data.

### Example output

Variable Start: Start End: End Frequency: Freq Failure Mode: Failure = Bearing
Table of Percentiles Standard 95.0% Normal CI Percent Percentile Error Lower Upper 1 37378.2 4186.55 30010.9 46554.0 2 41535.6 4092.37 34241.6 50383.3 3 44409.9 4013.16 37201.5 53015.1 4 46702.6 3946.01 39575.0 55113.9 5 48654.4 3888.53 41600.0 56905.2 6 50380.0 3839.15 43390.3 58495.5 7 51943.2 3796.83 45010.0 59944.3 8 53383.9 3760.85 46499.1 61288.2 9 54728.9 3730.71 47884.3 62552.0 10 55997.0 3706.03 49184.7 63752.8 20 66386.7 3718.13 59485.1 74089.2 30 75055.2 4143.21 67358.5 83631.3 40 83353.3 4935.88 74219.5 93611.2 50 91937.0 6086.10 80749.9 104674 60 101405 7648.66 87468.9 117560 70 112616 9795.13 94965.1 133547 80 127321 12976.5 104266 155473 90 150944 18744.6 118335 192540 91 154441 19655.9 120346 198197 92 158332 20685.5 122564 204539 93 162724 21866.6 125046 211756 94 167773 23248.6 127871 220128 95 173723 24908.8 131163 230094 96 180984 26979.2 135130 242398 97 190327 29711.7 140159 258452 98 203498 33685.8 147115 281490 99 226132 40821.4 158746 322123
Variable Start: Start End: End Frequency: Freq Failure Mode: Failure = Gasket
Table of Percentiles Standard 95.0% Normal CI Percent Percentile Error Lower Upper 1 17295.9 4302.95 10621.3 28164.9 2 21542.1 4636.31 14128.3 32846.1 3 24761.7 4823.69 16903.0 36274.2 4 27497.1 4951.31 19320.3 39134.5 5 29943.6 5047.87 21518.3 41667.6 6 32196.6 5126.84 23565.1 43989.8 7 34311.2 5195.83 25499.7 46167.4 8 36322.0 5259.66 27347.1 48242.5 9 38253.0 5321.66 29123.9 50243.8 10 40121.1 5384.33 30841.8 52192.2 20 57180.0 6349.04 45997.1 71081.8 30 73823.8 8397.15 59071.2 92260.7 40 91833.4 11825.7 71349.1 118199 50 112619 16927.3 83882.5 151200 60 138109 24362.1 97740.3 195152 70 171802 35634.2 114413 257976 80 221809 54607.2 136906 359366 90 316119 95637.2 174716 571965 91 331557 102872 180491 609060 92 349183 111286 186970 652131 93 369648 121249 194350 703061 94 393925 133323 202921 764718 95 423565 148416 213139 841741 96 461250 168122 225778 942306 97 512205 195607 242312 1082708 98 588758 238527 266124 1302535 99 733300 324105 308366 1743799
Variable Start: Start End: End Frequency: Freq Failure Mode: Failure = Bearing, Gasket
Table of Percentiles 95.0% Normal CI Percent Percentile Lower Upper 1 17291.8 10624.0 27909.5 2 21511.5 14143.5 32140.0 3 24665.9 16938.5 35023.7 4 27287.4 19376.3 37286.9 5 29566.8 21584.1 39192.7 6 31599.2 23619.6 40869.3 7 33441.6 25513.6 42388.0 8 35132.0 27285.1 43791.9 9 36698.1 28948.1 45108.3 10 38160.4 30513.6 46355.3 20 49496.0 42607.7 56673.6 30 58169.3 51495.7 65176.2 40 66025.7 59190.3 73260.0 50 73846.8 66445.5 81745.1 60 82224.8 73737.4 91377.7 70 91908.0 81606.5 103179 80 104331 91022.7 119199 90 123832 104763 145869 91 126682 106692 149894 92 129844 108814 154393 93 133401 111178 159496 94 137476 113860 165393 95 142259 116972 172382 96 148072 120708 180967 97 155514 125421 192100 98 165939 131908 207946 99 183695 142684 235557

### Interpretation

The table of percentiles for the water pump data indicates the following:
• 1% of the pumps fail because of bearing failures by 37378.2 miles
• 1% of the pumps fail because of gasket failures by 17295.9 miles

Overall, by 17291.8 miles, 1% of the water pumps will fail. For the greatest improvement in water pump reliability, the engineers should focus on minimizing gasket failures.

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