Multiple failure modes analysis (Kaplan-Meier estimation method) for Nonparametric Distribution Analysis (Right Censoring)

In This Topic

Characteristics of variable – Multiple failure mode (Kaplan-Meier estimation method)
Kaplan-Meier estimates – multiple failure mode analysis (Kaplan-Meier estimation method)

Characteristics of variable – Multiple failure mode (Kaplan-Meier estimation method)

The mean (MTTF, mean time to failure) and the median are measures of the center of the distribution. The IQR is a measure of the spread of the distribution.

Example output

Variable: Cycles

Failure Mode: Failure = Break

Censoring

Censoring Information	Count
Uncensored value	25
Right censored value	40

Nonparametric Estimates

Characteristics of Variable

	Standard Error	95.0% Normal CI
Mean(MTTF)	Standard Error	Lower	Upper	Q1	Median	Q3	IQR
789.412	82.1172	628.466	950.359	503.88	729.3	1055.45	551.57

Variable: Cycles

Failure Mode: Failure = Obstruction

Censoring

Censoring Information	Count
Uncensored value	40
Right censored value	25

Nonparametric Estimates

Characteristics of Variable

	Standard Error	95.0% Normal CI
Mean(MTTF)	Standard Error	Lower	Upper	Q1	Median	Q3	IQR
690.936	101.916	491.185	890.687	89.38	257.47	*	*

Variable: Cycles

Failure Mode: Failure = Break, Obstruction

Censoring

Censoring Information	Count
Uncensored value	65

Nonparametric Estimates

Characteristics of Variable

	Standard Error	95.0% Normal CI
Mean(MTTF)	Standard Error	Lower	Upper	Q1	Median	Q3	IQR
377.006	50.6908	277.654	476.358	89.38	195.94	547.25	457.87

Interpretation

For the dishwasher data, the estimated median failure times are:

729.3 cycles for breaks
257.47 cycles for obstructions
195.94 cycles for either breaks or obstructions

To maximize the overall product reliability, the engineers should focus improvement efforts on reducing spray arm obstructions.

Kaplan-Meier estimates – multiple failure mode analysis (Kaplan-Meier estimation method)

The survival probabilities are the probability that the product survives until a particular time. Use these values to determine whether your product meets reliability requirements or to determine which failure modes impact the overall reliability.

Example output

Variable: Cycles

Failure Mode: Failure = Break

Kaplan-Meier Estimates

	Number at Risk	Number Failed	Survival Probability	Standard Error	95.0% Normal CI
Time	Number at Risk	Number Failed	Survival Probability	Standard Error	Lower	Upper
98.04	45	1	0.977778	0.0219739	0.934710	1.00000
141.90	37	1	0.951351	0.0337133	0.885274	1.00000
201.78	32	1	0.921622	0.0438508	0.835676	1.00000
285.38	29	1	0.889842	0.0526091	0.786730	0.99295
292.05	27	1	0.856884	0.0601036	0.739084	0.97469
378.10	25	1	0.822609	0.0667610	0.691760	0.95346
413.05	24	1	0.788334	0.0722440	0.646738	0.92993
503.88	20	2	0.709500	0.0838103	0.545235	0.87377
508.44	18	1	0.670084	0.0879360	0.497732	0.84244
547.25	17	1	0.630667	0.0911704	0.451976	0.80936
650.18	15	1	0.588623	0.0942900	0.403817	0.77343
669.18	14	1	0.546578	0.0964746	0.357491	0.73566
729.22	13	1	0.504534	0.0977869	0.312875	0.69619
729.30	12	1	0.462489	0.0982619	0.269899	0.65508
735.90	11	1	0.420445	0.0979117	0.228541	0.61235
843.60	10	1	0.378400	0.0967274	0.188818	0.56798
941.05	9	1	0.336356	0.0946777	0.150791	0.52192
968.55	8	1	0.294311	0.0917046	0.114574	0.47405
1046.52	7	1	0.252267	0.0877142	0.080350	0.42418
1055.45	6	1	0.210222	0.0825592	0.048409	0.37204
1202.70	4	1	0.157667	0.0768478	0.007048	0.30829
1221.00	3	1	0.105111	0.0668288	0.000000	0.23609
1514.70	2	1	0.052556	0.0499757	0.000000	0.15051
1740.75	1	1	0.000000	0.0000000	0.000000	0.00000

Variable: Cycles

Failure Mode: Failure = Obstruction

Kaplan-Meier Estimates

	Number at Risk	Number Failed	Survival Probability	Standard Error	95.0% Normal CI
Time	Number at Risk	Number Failed	Survival Probability	Standard Error	Lower	Upper
7.14	65	1	0.984615	0.0152658	0.954695	1.00000
9.24	64	1	0.969231	0.0214198	0.927249	1.00000
10.02	63	1	0.953846	0.0260247	0.902839	1.00000
21.27	62	1	0.938462	0.0298075	0.880040	0.99688
23.10	61	1	0.923077	0.0330515	0.858297	0.98786
23.19	60	1	0.907692	0.0359031	0.837324	0.97806
26.78	59	1	0.892308	0.0384497	0.816948	0.96767
27.81	58	1	0.876923	0.0407486	0.797057	0.95679
41.82	57	1	0.861538	0.0428396	0.777574	0.94550
43.89	56	1	0.846154	0.0447519	0.758442	0.93387
47.87	55	1	0.830769	0.0465075	0.739616	0.92192
51.70	54	1	0.815385	0.0481236	0.721064	0.90971
55.59	53	1	0.800000	0.0496139	0.702759	0.89724
63.12	52	1	0.784615	0.0509893	0.684678	0.88455
63.20	51	1	0.769231	0.0522589	0.666805	0.87166
69.34	50	1	0.753846	0.0534303	0.649125	0.85857
89.38	49	1	0.738462	0.0545099	0.631624	0.84530
90.63	48	1	0.723077	0.0555028	0.614293	0.83186
91.28	47	1	0.707692	0.0564138	0.597123	0.81826
94.35	46	1	0.692308	0.0572468	0.580106	0.80451
99.33	44	1	0.676573	0.0580678	0.562763	0.79038
99.44	43	1	0.660839	0.0588104	0.545573	0.77611
100.23	42	1	0.645105	0.0594778	0.528531	0.76168
112.04	41	1	0.629371	0.0600722	0.511631	0.74711
122.40	40	1	0.613636	0.0605960	0.494870	0.73240
137.72	39	1	0.597902	0.0610508	0.478245	0.71756
139.72	38	1	0.582168	0.0614383	0.461751	0.70258
150.15	36	1	0.565997	0.0618233	0.444825	0.68717
155.43	35	1	0.549825	0.0621360	0.428041	0.67161
181.60	34	1	0.533654	0.0623773	0.411397	0.65591
195.94	33	1	0.517483	0.0625482	0.394890	0.64007
203.22	31	1	0.500790	0.0627185	0.377864	0.62372
257.47	30	1	0.484097	0.0628101	0.360991	0.60720
290.11	28	1	0.466807	0.0629014	0.343523	0.59009
321.20	26	1	0.448853	0.0629923	0.325391	0.57232
427.35	23	1	0.429338	0.0632043	0.305460	0.55322
437.29	22	1	0.409823	0.0632725	0.285811	0.53383
455.87	21	1	0.390307	0.0631975	0.266442	0.51417
596.67	16	1	0.365913	0.0637822	0.240902	0.49092
1149.66	5	1	0.292730	0.0829951	0.130063	0.45540

Variable: Cycles

Failure Mode: Failure = Break, Obstruction

Kaplan-Meier Estimates

	Number at Risk	Number Failed	Survival Probability	Standard Error	95.0% Normal CI
Time	Number at Risk	Number Failed	Survival Probability	Standard Error	Lower	Upper
7.14	65	1	0.984615	0.0152658	0.954695	1.00000
9.24	64	1	0.969231	0.0214198	0.927249	1.00000
10.02	63	1	0.953846	0.0260247	0.902839	1.00000
21.27	62	1	0.938462	0.0298075	0.880040	0.99688
23.10	61	1	0.923077	0.0330515	0.858297	0.98786
23.19	60	1	0.907692	0.0359031	0.837324	0.97806
26.78	59	1	0.892308	0.0384497	0.816948	0.96767
27.81	58	1	0.876923	0.0407486	0.797057	0.95679
41.82	57	1	0.861538	0.0428396	0.777574	0.94550
43.89	56	1	0.846154	0.0447519	0.758442	0.93387
47.87	55	1	0.830769	0.0465075	0.739616	0.92192
51.70	54	1	0.815385	0.0481236	0.721064	0.90971
55.59	53	1	0.800000	0.0496139	0.702759	0.89724
63.12	52	1	0.784615	0.0509893	0.684678	0.88455
63.20	51	1	0.769231	0.0522589	0.666805	0.87166
69.34	50	1	0.753846	0.0534303	0.649125	0.85857
89.38	49	1	0.738462	0.0545099	0.631624	0.84530
90.63	48	1	0.723077	0.0555028	0.614293	0.83186
91.28	47	1	0.707692	0.0564138	0.597123	0.81826
94.35	46	1	0.692308	0.0572468	0.580106	0.80451
98.04	45	1	0.676923	0.0580051	0.563235	0.79061
99.33	44	1	0.661538	0.0586915	0.546505	0.77657
99.44	43	1	0.646154	0.0593087	0.529911	0.76240
100.23	42	1	0.630769	0.0598587	0.513448	0.74809
112.04	41	1	0.615385	0.0603434	0.497114	0.73366
122.40	40	1	0.600000	0.0607644	0.480904	0.71910
137.72	39	1	0.584615	0.0611229	0.464817	0.70441
139.72	38	1	0.569231	0.0614200	0.448850	0.68961
141.90	37	1	0.553846	0.0616567	0.433001	0.67469
150.15	36	1	0.538462	0.0618336	0.417270	0.65965
155.43	35	1	0.523077	0.0619513	0.401655	0.64450
181.60	34	1	0.507692	0.0620100	0.386155	0.62923
195.94	33	1	0.492308	0.0620100	0.370770	0.61385
201.78	32	1	0.476923	0.0619513	0.355501	0.59835
203.22	31	1	0.461538	0.0618336	0.340347	0.58273
257.47	30	1	0.446154	0.0616567	0.325309	0.56700
285.38	29	1	0.430769	0.0614200	0.310388	0.55115
290.11	28	1	0.415385	0.0611229	0.295586	0.53518
292.05	27	1	0.400000	0.0607644	0.280904	0.51910
321.20	26	1	0.384615	0.0603434	0.266344	0.50289
378.10	25	1	0.369231	0.0598587	0.251910	0.48655
413.05	24	1	0.353846	0.0593087	0.237603	0.47009
427.35	23	1	0.338462	0.0586915	0.223428	0.45349
437.29	22	1	0.323077	0.0580051	0.209389	0.43676
455.87	21	1	0.307692	0.0572468	0.195491	0.41989
503.88	20	2	0.276923	0.0555028	0.168140	0.38571
508.44	18	1	0.261538	0.0545099	0.154701	0.36838
547.25	17	1	0.246154	0.0534303	0.141432	0.35088
596.67	16	1	0.230769	0.0522589	0.128344	0.33319
650.18	15	1	0.215385	0.0509893	0.115447	0.31532
669.18	14	1	0.200000	0.0496139	0.102759	0.29724
729.22	13	1	0.184615	0.0481236	0.090295	0.27894
729.30	12	1	0.169231	0.0465075	0.078078	0.26038
735.90	11	1	0.153846	0.0447519	0.066134	0.24156
843.60	10	1	0.138462	0.0428396	0.054497	0.22243
941.05	9	1	0.123077	0.0407486	0.043211	0.20294
968.55	8	1	0.107692	0.0384497	0.032332	0.18305
1046.52	7	1	0.092308	0.0359031	0.021939	0.16268
1055.45	6	1	0.076923	0.0330515	0.012143	0.14170
1149.66	5	1	0.061538	0.0298075	0.003117	0.11996
1202.70	4	1	0.046154	0.0260247	0.000000	0.09716
1221.00	3	1	0.030769	0.0214198	0.000000	0.07275
1514.70	2	1	0.015385	0.0152658	0.000000	0.04531
1740.75	1	1	0.000000	0.0000000	0.000000	0.00000

Interpretation

For the dishwasher data, the survival probabilities are as follows:

95% (or 0.951351) of the spray arms survived breaks for at least 141.90 cycles
95% (or 0.953846) of the spray arms survived obstructions for at least 10.02 cycles
95% (or 0.953846) of the spray arms survived both types of failures for at least 10.02 cycles

To have the greatest impact on improving the reliability of the dishwashers, the engineers should focus on the spray arm obstructions.