Multiple failure mode analysis for Parametric Distribution Analysis (Right 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 distribution. Therefore, to ensure that the results are accurate, the distribution that you select must adequately fit the data.

You cannot determine from the estimated distribution parameters whether the distribution 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

Parameter Estimates Standard 95.0% Normal CI Parameter Estimate Error Lower Upper Shape 1.97672 0.276587 1.50260 2.60044 Scale 891.929 90.8270 730.552 1088.96
Parameter Estimates Standard 95.0% Normal CI Parameter Estimate Error Lower Upper Location 5.75328 0.271171 5.22179 6.28476 Scale 1.95933 0.238720 1.54311 2.48780

Interpretation

For the dishwasher data, the engineers selected a Weibull distribution to model spray arm breaks, and a lognormal distribution to model spray arm obstructions. The following parameters define the best-fitting distributions for each failure mode:

Shape = 1.97672 and Scale = 891.929 for spray arm breaks

Location = 5.75328 and Scale = 1.95933 for spray arm obstructions

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 if the distribution adequately fits the data.

Example output

Table of Percentiles Standard 95.0% Normal CI Percent Percentile Error Lower Upper 1 87.0276 30.6339 43.6548 173.493 2 123.896 37.7877 68.1466 225.252 3 152.497 42.3555 88.4796 262.833 4 176.847 45.7243 106.541 293.548 5 198.502 48.3870 123.105 320.077 6 218.260 50.5811 138.583 343.746 7 236.594 52.4406 153.227 365.317 8 253.812 54.0493 167.205 385.279 9 270.130 55.4632 180.636 403.963 10 285.703 56.7217 193.608 421.606 20 417.625 64.8194 308.086 566.111 30 529.457 69.7943 408.905 685.548 40 634.964 74.3928 504.686 798.871 50 740.979 79.9464 599.746 915.471 60 853.343 87.6525 697.736 1043.65 70 979.746 99.1411 803.489 1194.67 80 1134.71 117.529 926.234 1390.11 90 1360.10 152.029 1092.51 1693.23 91 1391.24 157.433 1114.50 1736.69 92 1425.26 163.497 1138.28 1784.59 93 1462.89 170.393 1164.31 1838.05 94 1505.19 178.371 1193.22 1898.73 95 1553.77 187.816 1226.02 1969.15 96 1611.28 199.369 1264.30 2053.50 97 1682.59 214.223 1311.01 2159.50 98 1778.36 235.032 1372.53 2304.18 99 1931.34 270.138 1468.25 2540.49
Table of Percentiles Standard 95.0% Normal CI Percent Percentile Error Lower Upper 1 3.30424 1.78563 1.14571 9.52940 2 5.63679 2.72980 2.18177 14.5631 3 7.91050 3.55915 3.27511 19.1066 4 10.2074 4.33709 4.43857 23.4741 5 12.5595 5.08849 5.67682 27.7867 6 14.9838 5.82646 6.99250 32.1079 7 17.4916 6.55916 8.38765 36.4772 8 20.0913 7.29230 9.86408 40.9221 9 22.7896 8.03022 11.4236 45.4641 10 25.5926 8.77646 13.0681 50.1206 20 60.5984 17.2863 34.6455 105.993 30 112.822 29.6226 67.4371 188.749 40 191.884 49.8160 115.359 319.171 50 315.222 85.4790 185.266 536.337 60 517.841 152.725 290.505 923.079 70 880.729 291.401 460.480 1684.51 80 1639.73 627.451 774.563 3471.28 90 3882.58 1807.19 1559.26 9667.69 91 4360.12 2080.97 1710.97 11111.0 92 4945.69 2424.60 1892.04 12927.8 93 5680.72 2866.84 2112.69 15274.7 94 6631.50 3454.60 2388.85 18409.2 95 7911.58 4269.92 2747.04 22785.7 96 9734.61 5470.91 3235.47 29288.6 97 12561.2 7407.95 3953.98 39904.9 98 17628.0 11054.7 5157.08 60256.0 99 30072.1 20656.8 7824.62 115575

Interpretation

For the dishwasher data, based on the distributions fitted to each failure mode, the engineers conclude the following:
  • 1% of the spray arms fail due to breakage by 87.0276 cycles
  • 1% of the spray arms fail due to obstruction by 3.30424 cycles

Overall, by 3.30048 cycles, 1% of the spray arms will fail. For the greatest improvement in reliability, the engineers should focus improvement efforts on minimizing spray arm obstructions.

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