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

In This Topic

Multiple failure mode analysis – parameter estimates
Multiple failure mode analysis – percentiles

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 Error	95.0% Normal CI
Parameter	Estimate	Standard 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 Error	95.0% Normal CI
Parameter	Estimate	Standard 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 Error	95.0% Normal CI
Percent	Percentile	Standard 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 Error	95.0% Normal CI
Percent	Percentile	Standard 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.