npmle

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V
1	Table 1. Please enter your ships in column B and failure counts from each cohort in columns C-T
2	Period	Units Shipped	Peroid 1	Period 2	Period 3	Period 4	Period 5	Period 6	Period 7	Period 8	Period 9	Period 10	Period 11	Period 12	Period 13	Period 14	Period 15	Period `6	Period 17	Period 18	Row Sums
3	1	47	1	3	7	8	13	5	4	2	2	2	0	0	0	0	0	0	0	0	47
4	2	41		4	3	4	7	6	5	6	1	2	1	1	0	0	0	0	1	0	41
5	3	45			2	4	9	6	7	5	6	0	2	3	1	0	0	0	0	0	45
6	4	39				1	6	4	7	7	3	3	2	4	1	0	0	0	1	0	39
7	5	43					2	6	6	6	8	5	5	2	2	1	0	0	0	0	43
8	6	48						1	4	7	8	8	7	5	3	2	2	1	0	0	48
9	7	41							0	5	13	8	4	7	1	1	1	0	1	0	41
10	8	40								2	3	7	10	5	7	2	3	0	0	0	39
11	9	45									0	10	6	6	8	8	4	3	0	0	45
12	10	41										2	7	7	5	3	9	3	0	1	37
13	11	37											2	2	8	6	10	3	1	2	34
14	12	39												2	3	6	7	10	5	3	36
15	13	36													2	2	6	3	6	6	25
16	14	27														1	1	4	5	6	17
17	15	30															1	3	4	6	14
18	16	38																1	5	6	12
19	17	32																	0	6	6
20	18	42																		1	1
21	Column Sums	711	1	7	12	17	37	28	33	40	44	47	46	44	41	32	44	31	29	37
22
23	Table 2. Kaplan-Meier nonparametric max. likelihood reliability estimate from ships and grouped failure or return counts in body of table 1
24	Age t	Installed base	Withdrawn	Deaths	At risk	K-M R(t)	S&R R(t) table 4
25	0	711				1	1
26	1	645	41	25	711	0.964838256	0.9787234043
27	2	546	26	73	645	0.8556395076	0.8292682927
28	3	416	26	104	546	0.6926605538	0.7333333333
29	4	302	16	98	416	0.5294857118	0.5641025641
30	5	191	10	101	302	0.3524060532	0.2857142857
31	6	105	11	75	191	0.2140267129	0.2857142857
32	7	59	3	43	105	0.1263776781	0.1951219512
33	8	37	3	19	59	0.08567978178	0.01176470588
34	9	17	4	16	37	0.04862906533	0.01176470588
35	10	7	0	10	17	0.02002373278	0
36	11	2	1	4	7	0.008581599765	0
37	12	2	0	0	2	0.008581599765	0
38	13	2	0	0	2	0.008581599765	0
39	14	1	0	1	2	0.004290799882	0
40	15	1	0	0	1	0.004290799882	0
41	16	0	0	1	1	0	0
42	17	0	0	0	0	0	0
43	18	0	0	0	0	0	0
44
45	Table 3. Ratios of sums of ships and returns for "pool adjacent violators" majorization
46	Period	Ships	Returns
47	1	47	1		0.02127659574
48	2	41	7		0.09090909091	0.1707317073
49	3	45	12		0.1503759398	0.2209302326	0.2666666667
50	4	39	17		0.2151162791	0.288	0.3452380952	0.4358974359
51	5	43	37		0.3441860465	0.4345238095	0.5196850394	0.6585365854	0.8604651163
52	6	48	28		0.3878326996	0.4675925926	0.5371428571	0.6307692308	0.7142857143	0.5833333333
53	7	41	33		0.4440789474	0.5214007782	0.587962963	0.6725146199	0.7424242424	0.6853932584	0.8048780488
54	8	40	40		0.5087209302	0.5858585859	0.65234375	0.7345971564	0.8023255814	0.7829457364	0.9012345679	1
55	9	45	44		0.5629820051	0.6374269006	0.7009966777	0.77734375	0.8387096774	0.8333333333	0.9285714286	0.9882352941	0.9777777778
56	10	41	47		0.6186046512	0.6919060052	0.7543859649	0.8282828283	0.8875968992	0.8930232558	0.9820359281	1	1	1
57	11	37	46		0.6680942184	0.7404761905	0.8021108179	0.874251497	0.9322033898	0.9444444444	1	1	1	1	1
58	12	39	44		0.7035573123	0.7734204793	0.8325358852	0.9008042895	0.9550898204	0.9690721649	1	1	1	1	1	1
59	13	36	41		0.7324723247	0.8	0.8568281938	0.9217603912	0.972972973	0.9877675841	1	1	1	1	1	1	1
60	14	27	32		0.7539543058	0.8199233716	0.8752598753	0.9380733945	0.9874055416	1	1	1	1	1	1	1	1	1
61	15	30	44		0.7896494157	0.8550724638	0.9099804305	0.9721030043	1	1	1	1	1	1	1	1	1	1	1
62	16	38	31		0.7912087912	0.8525423729	0.9034608379	0.9603174603	1	1	1	1	1	1	1	1	1	1	1	0.8157894737
63	17	32	29		0.7967115097	0.8553054662	0.9036144578	0.9570895522	0.9979879276	1	1	1	1	1	1	1	1	1	1	0.8571428571	0.90625
64	18	42	37		0.8016877637	0.8569277108	0.9020866774	0.9515570934	0.9888682746	1	1	1	1	1	1	1	1	1	0.9929577465	0.8660714286	0.8918918919	0.880952381
65
66
67	Table 4. Maximum likelihood estimates of cumulative distribution function G(t), S&R reliability function R(t), and actuarial return rate function a(t)
68	Ages don't have to be equally spaced; actuarial return rate a(t) computation is per age unit
69	Age t	actuarial a(t)	cdf G(t)	S&R R(t)	<-Ships and Returns reliability function
70	1	0.02127659574	0.02127659574	0.9787234043	0.02127659574
71	2	0.1527041357	0.1707317073	0.8292682927	0.09090909091	0.1707317073
72	3	0.1156862745	0.2666666667	0.7333333333	0.1503759398	0.2209302326	0.2666666667
73	4	0.2307692308	0.4358974359	0.5641025641	0.2151162791	0.288	0.3452380952	0.4358974359
74	5	0.4935064935	0.7142857143	0.2857142857	0.3441860465	0.4345238095	0.5196850394	0.6307692308	0.7142857143
75	6	0	0.7142857143	0.2857142857	0.3878326996	0.4675925926	0.5371428571	0.6307692308	0.7142857143	0.5833333333
76	7	0.3170731707	0.8048780488	0.1951219512	0.4440789474	0.5214007782	0.587962963	0.6725146199	0.7424242424	0.6853932584	0.8048780488
77	8	0.9397058824	0.9882352941	0.01176470588	0.5087209302	0.5858585859	0.65234375	0.7345971564	0.8023255814	0.7829457364	0.9012345679	0.9882352941
78	9	0	0.9882352941	0.01176470588	0.5629820051	0.6374269006	0.7009966777	0.77734375	0.8387096774	0.8333333333	0.9285714286	0.9882352941	0.9777777778
79	10	1	1	0	0.6186046512	0.6919060052	0.7543859649	0.8282828283	0.8875968992	0.8930232558	0.9820359281	1	1	1
80	11	#DIV/0!	1	0	0.6680942184	0.7404761905	0.8021108179	0.874251497	0.9322033898	0.9444444444	1	1	1	1	1
81	12	#DIV/0!	1	0	0.7035573123	0.7734204793	0.8325358852	0.9008042895	0.9550898204	0.9690721649	1	1	1	1	1	1
82	13	#DIV/0!	1	0	0.7324723247	0.8	0.8568281938	0.9217603912	0.972972973	0.9877675841	1	1	1	1	1	1	1
83	14	#DIV/0!	1	0	0.7539543058	0.8199233716	0.8752598753	0.9380733945	0.9874055416	1	1	1	1	1	1	1	1	1
84	15	#DIV/0!	1	0	0.7896494157	0.8525423729	0.9020866774	0.9515570934	0.9888682746	1	1	1	1	1	1	1	1	1	0.9929577465
85	16	#DIV/0!	1	0	0.7912087912	0.8525423729	0.9020866774	0.9515570934	0.9888682746	1	1	1	1	1	1	1	1	1	0.9929577465	0.8157894737
86	17	#DIV/0!	1	0	0.7967115097	0.8553054662	0.9020866774	0.9515570934	0.9888682746	1	1	1	1	1	1	1	1	1	0.9929577465	0.8571428571	0.8918918919
87	18	#DIV/0!	1	0	0.8016877637	0.8569277108	0.9020866774	0.9515570934	0.9888682746	1	1	1	1	1	1	1	1	1	0.9929577465	0.8660714286	0.8918918919	0.880952381
88
89
90
91
92
93
94
95
96
97
98
99
100