Scientific Programming

Research Article

A New Variant of JM Software Reliability Model

Table 1

Proposed model vs. JM model.


N	t_n	JM model					Proposed model
N	t_n	N′			MTTF	R = 1 − f(t)	N′			MTTF	R = 1 − f(t)

1	3	1	0.333300	0.000000	∞	1.000000	1	0.333333	0.333333	3	0.367879
2	30	2	0.055600	0.000000	∞	1.000000	2	0.036263	0.059414	16.831049	0.168230
3	113	3	0.016500	0.000000	∞	1.000000	3	0.009324	0.018380	54.406556	0.125311
4	81	4	0.009800	0.000000	∞	1.000000	4	0.004840	0.014483	69.0432864	0.309382
5	115	6	0.004600	0.004600	218.600000	0.959700	6	0.002671	0.011844	84.430767	0.256131
6	9	11	0.002100	0.010500	95.233300	0.979200	6	0.002871	0.011980	83.469009	0.897785
7	2	∞	0.000000	0.019800	50.428600	0.164600	7	0.002838	0.013825	72.332568	0.972728
8	91	28	0.000742	0.014800	67.368800	0.189700	8	0.002414	0.012989	76.983480	0.306642
9	112	16	0.001400	0.009900	100.746000	0.861700	11	0.001567	0.012004	83.300114	0.260660
10	15	46	0.000424	0.015300	65.505600	0.121600	12	0.001471	0.012387	80.726542	0.830429
11	138	20	0.001100	0.009800	102.181800	0.613000	NaN	NaN	NaN	NaN	NaN
12	50	27	0.000756	0.011300	88.216700	0.417800	12	0.001353	0.009844	101.574951	0.611251
13	77	29	0.000695	0.011100	89.932700	0.765800	13	0.001233	0.010802	92.573668	0.435278
14	24	61	0.000300	0.014100	70.835900	0.217700	14	0.001175	0.010457	95.6241495	0.778035
15	108	39	0.000494	0.011800	84.416700	0.352600	15	0.001079	0.009997	100.022048	0.339676
16	88	38	0.000509	0.011200	89.335200	0.000600	16	0.000978	0.009748	102.584017	0.424079
17	670	18	0.001400	0.001500	686.235300	0.839600	17	0.000665	0.007561	132.245087	0.006305
18	120	20	0.001200	0.002300	429.944400	0.941300	18	0.000554	0.006507	153.677753	0.458014
19	26	23	0.000899	0.003600	278.236800	0.663800	22	0.000463	0.007150	139.855327	0.830351
20	114	25	0.000782	0.003900	255.740000	0.280600	20	0.000515	0.006244	160.132492	0.490705
21	325	24	0.000844	0.002500	395.047600	0.870000	21	0.000458	0.005896	169.592304	0.147141
22	55	27	0.000684	0.003400	292.281800	0.436900	23	0.000408	0.005975	167.343635	0.719884
23	242	28	0.000639	0.003200	312.773900	0.804600	25	0.000363	0.006200	161.274074	0.223007
24	68	31	0.000541	0.003800	263.910700	0.202100	24	0.000377	0.005658	176.711764	0.680581
25	422	29	0.000608	0.002400	410.950000	0.645300	30	0.000281	0.005879	170.070077	0.083631
26	180	31	0.000538	0.002700	372.084600	0.973500	28	0.000290	0.004883	204.750312	0.415148
27	10	35	0.000439	0.003500	285.060200	0.017900	27	0.000304	0.005190	192.65184	0.949417
28	1146	30	0.000576	0.001200	867.339300	0.500700	28	0.000249	0.004452	224.595888	0.006081
29	600	31	0.000529	0.001100	944.913800	0.984300	29	0.000208	0.003817	261.922210	0.101189
30	15	33	0.000462	0.001400	721.477800	0.951300	34	0.000175	0.003886	257.306309	0.943370
31	36	35	0.000412	0.001600	606.540300	0.993400	31	0.000197	0.004052	246.749856	0.864246
32	4	38	0.000354	0.002100	471.322900	1.000000	35	0.000180	0.004712	212.192154	0.981325
33	0	41	0.000312	0.002500	400.609800	0.980200	39	0.000166	0.004508	221.801057	1
34	8	46	0.000259	0.003100	321.838200	0.493900	34	0.000196	0.004231	236.344719	0.966717
35	227	47	0.000251	0.003000	331.804800	0.822100	40	0.000167	0.004566	219.000994	0.354685
36	65	52	0.000215	0.003400	290.074700	0.545100	36	0.000186	0.004050	246.873528	0.768516
37	176	54	0.000204	0.003500	287.804500	0.817500	37	0.000182	0.004212	237.414285	0.476484
38	58	60	0.000176	0.003900	258.077800	0.170200	44	0.000154	0.004847	206.272099	0.754890
39	457	55	0.000200	0.003200	313.152200	0.383700	46	0.000143	0.004333	230.744445	0.137993
40	300	56	0.000194	0.003100	322.792200	0.740400	NaN	NaN	NaN	NaN	NaN
41	97	60	0.000175	0.003300	300.445400	0.416700	41	0.000155	0.004072	245.535290	0.673642
42	263	61	0.000171	0.003200	308.000000	0.230500	51	0.000124	0.004525	220.977867	0.304171
43	452	58	0.000185	0.002800	360.924000	0.493400	53	0.000155	0.004254	235.032626	0.146147
44	255	60	0.000175	0.002800	357.265600	0.576100	52	0.000155	0.004091	244.438673	0.352323
45	197	62	0.000167	0.002800	352.882400	0.578700	46	0.000129	0.003872	258.217142	0.466301
46	193	65	0.000155	0.002900	339.527500	0.982500	47	0.000126	0.003811	262.382299	0.479233
47	6	71	0.000137	0.003300	304.892700	0.771700	50	0.000120	0.004016	248.944067	0.976186
48	79	77	0.000122	0.003500	282.576900	0.055700	48	0.000127	0.003553	281.394045	0.755220
49	816	67	0.000149	0.002700	373.731300	0.026900	49	0.000118	0.003763	265.736415	0.046388
50	1351	59	0.000183	0.001600	607.193300	0.783700	52	0.000100	0.003386	295.265642	0.010300
51	148	61	0.000173	0.001700	578.515700	0.964400	51	0.000098	0.003147	317.685879	0.627589
52	21	65	0.000155	0.002000	497.463000	0.626000	56	0.000091	0.003221	310.373974	0.934577
53	233	67	0.000147	0.002100	485.574100	0.758800	53	0.000096	0.003241	308.498330	0.469883
54	134	70	0.000137	0.002200	456.072900	0.457100	54	0.000095	0.003194	312.990824	0.651728
55	357	71	0.000134	0.002100	466.751100	0.661300	NaN	NaN	NaN	NaN	NaN
56	193	74	0.000125	0.002300	443.803600	0.587600	56	0.000090	0.003282	304.614060	0.530683
57	236	76	0.000120	0.002300	438.064600	0.931700	NaN	NaN	NaN	NaN	NaN
58	31	81	0.000109	0.002500	398.967800	0.396600	58	0.000087	0.003455	289.420777	0.898426
59	369	81	0.000109	0.002400	416.571600	0.166000	70	0.000072	0.003446	290.145967	0.280333
60	748	78	0.000116	0.002100	481.008300	1.000000	60	0.000082	0.002949	339.070155	0.110136
61	0	82	0.000107	0.002200	444.750200	0.593500	72	0.000067	0.003388	295.134138	1
62	232	85	0.000101	0.002300	429.852700	0.464100	62	0.000079	0.002638	379.051733	0.542236
63	330	86	0.000099	0.002300	437.323000	0.434000	69	0.000070	0.003359	297.657092	0.330001
64	365	87	0.000098	0.002200	445.354600	0.064300	65	0.000074	0.003250	307.669056	0.305336
65	1222	81	0.000109	0.001700	572.519200	0.387300	65	0.000070	0.002786	358.894706	0.033210
66	543	81	0.000109	0.001600	610.210100	0.983700	66	0.000066	0.002768	361.168940	0.222361
67	10	85	0.000101	0.001800	551.660000	0.971400	67	0.000066	0.002500	399.861661	0.975301
68	16	89	0.000094	0.002000	508.892200	0.353600	68	0.000065	0.002919	342.534350	0.954363
69	429	89	0.000094	0.001900	534.642800	0.492200	69	0.000064	0.002675	373.720337	0.242804
70	379	90	0.000092	0.001800	543.980000	0.922300	70	0.000062	0.002393	417.854376	0.403727
71	44	94	0.000086	0.002000	506.655200	0.775200	71	0.000062	0.002759	362.371404	0.885659
72	129	98	0.000080	0.002100	478.508000	0.184000	NaN	NaN	NaN	NaN	NaN
73	810	95	0.000084	0.001900	538.806400	0.583800	73	0.000059	0.002668	374.698345	0.115124
74	290	97	0.000082	0.001900	532.678600	0.569400	74	0.000058	0.002778	359.874367	0.446713
75	300	99	0.000079	0.001900	527.241700	0.366700	75	0.000057	0.002715	368.299667	0.442836
76	529	99	0.000079	0.001800	550.189400	0.600100	76	0.000055	0.002621	381.517830	0.249931
77	281	101	0.000077	0.001800	544.009700	0.745200	77	0.000054	0.002564	389.939847	0.486448
78	160	105	0.000072	0.001900	514.758800	0.200200	78	0.000054	0.002684	372.443989	0.650772
79	828	102	0.000075	0.001700	576.648300	0.173200	79	0.000052	0.002524	396.126421	0.123657
80	1011	99	0.000079	0.001500	664.027600	0.511600	80	0.000050	0.002304	433.903508	0.097294
81	445	101	0.000076	0.001500	654.198100	0.636100	81	0.000048	0.002689	371.789765	0.302125
82	296	103	0.000074	0.001600	643.633600	0.065400	82	0.000047	0.002356	424.331389	0.497794
83	1755	98	0.000081	0.001200	827.210400	0.276300	83	0.000045	0.002230	448.354358	0.019954
84	1064	97	0.000082	0.001100	935.631900	0.148700	NaN	NaN	NaN	NaN	NaN
85	1783	95	0.000086	0.000856	1168.300000	0.479000	85	0.000040	0.001948	513.315339	0.031008
86	860	96	0.000084	0.000836	1195.900000	0.439600	NaN	NaN	NaN	NaN	NaN
87	983	96	0.000084	0.000754	1326.000000	0.586700	NaN	NaN	NaN	NaN	NaN
88	707	97	0.000082	0.000738	1354.900000	0.975900	88	0.000035	0.001920	520.822995	0.257311
89	33	100	0.000077	0.000845	1183.700000	0.480300	92	0.000034	0.001999	500.222704	0.936158
90	868	100	0.000077	0.000770	1298.200000	0.572500	94	0.000033	0.002061	485.139850	0.167098
91	724	101	0.000075	0.000755	1325.000000	0.173200	NaN	NaN	NaN	NaN	NaN
92	2323	100	0.000077	0.000615	1625.800000	0.164900	99	0.000029	0.001955	511.391098	0.010646
93	2930	99	0.000079	0.000471	2123.100000	0.502500	105	0.000026	0.001861	537.187177	0.004277
94	1461	99	0.000079	0.000394	2539.200000	0.717500	94	0.000028	0.001583	631.710908	0.098986
95	843	101	0.000075	0.000448	2233.200000	0.994600	104	0.000024	0.001666	599.918456	0.245320
96	12	102	0.000073	0.000439	2275.400000	0.891600	96	0.000027	0.001485	673.395806	0.982337
97	261	104	0.000070	0.000489	2044.300000	0.414600	116	0.000022	0.001836	544.648991	0.619273
98	1800	104	0.000070	0.000420	2382.100000	0.695500	121	0.000021	0.001641	609.064039	0.052060
99	865	106	0.000067	0.000466	2145.700000	0.512300	99	0.000021	0.001656	603.577182	0.238562
100	1435	106	0.000067	0.000401	2495.100000	0.988000	NaN	NaN	NaN	NaN	NaN
101	30	108	0.000064	0.000447	2236.700000	0.938100	116	0.000021	0.001310	762.984731	0.961443
102	143	110	0.000061	0.000490	2042.500000	0.948500	110	0.000022	0.001477	677.017482	0.809595
103	108	112	0.000059	0.000529	1890.100000	1.000000	103	0.000024	0.001442	693.326793	0.855755
104	0	114	0.000057	0.000566	1766.100000	0.171900	134	0.000018	0.001799	555.814849	1
105	3110	113	0.000058	0.000461	2169.600000	0.562800	105	0.000023	0.001441	693.594304	0.011289
106	1247	114	0.000056	0.000451	2215.900000	0.653400	106	0.000022	0.001402	712.758614	0.173853
107	943	115	0.000055	0.000443	2259.600000	0.733600	131	0.000017	0.001575	634.876873	0.226428
108	700	116	0.000054	0.000435	2301.000000	0.683700	108	0.000021	0.001388	720.189902	0.378338
109	875	118	0.000052	0.000469	2134.000000	0.891500	109	0.000020	0.001355	737.558886	0.305334
110	245	119	0.000051	0.000462	2166.700000	0.714300	110	0.000020	0.001413	707.414134	0.707277
111	729	121	0.000049	0.000493	2028.800000	0.392600	121	0.000018	0.001203	830.853083	0.415857
112	1897	121	0.000049	0.000444	2252.900000	0.820000	112	0.000019	0.001380	724.616992	0.072953
113	447	123	0.000047	0.000475	2106.100000	0.832500	118	0.000018	0.001553	643.567841	0.499291
114	386	124	0.000047	0.000468	2137.400000	0.811700	NaN	NaN	NaN	NaN	NaN
115	446	126	0.000045	0.000497	2014.000000	0.941200	115	0.000019	0.001209	826.530574	0.582978
116	122	128	0.000044	0.000524	1908.000000	0.595200	116	0.000019	0.001299	769.428084	0.853372
117	990	129	0.000043	0.000516	1938.900000	0.613300	117	0.000018	0.001422	702.849012	0.244496
118	948	131	0.000041	0.000539	1854.200000	0.557900	118	0.000019	0.001006	993.772526	0.385220
119	1082	132	0.000041	0.000531	1884.200000	0.988400	119	0.000018	0.001129	885.207957	0.294548
120	22	134	0.000040	0.000555	1802.500000	0.959200	120	0.000020	0.001302	767.619405	0.971746
121	75	136	0.000039	0.000578	1731.300000	0.757000	121	0.000018	0.000978	1021.98930	0.929241
122	482	138	0.000037	0.000598	1672.000000	0.037100	122	0.000018	0.001441	693.576499	0.499100
123	5509	134	0.000040	0.000436	2292.400000	0.957300	123	0.000017	0.001153	866.636866	0.001734
124	100	136	0.000038	0.000461	2169.400000	0.995400	124	0.000016	0.001434	697.121298	0.866366
125	10	138	0.000037	0.000485	2063.700000	0.595100	125	0.000016	0.000697	1433.87795	0.993050
126	1071	139	0.000037	0.000477	2094.700000	0.837700	126	0.000016	0.001357	736.891254	0.233773
127	371	141	0.000036	0.000499	2004.600000	0.674300	127	0.000016	0.001108	902.406476	0.662905
128	790	143	0.000035	0.000518	1929.700000	0.041300	NaN	NaN	NaN	NaN	NaN
129	6150	139	0.000037	0.000367	2723.300000	0.295400	129	0.000015	0.000894	1118.172980	0.004086
130	3321	139	0.000037	0.000330	3031.000000	0.708400	130	0.000014	0.001045	956.790792	0.031086
131	1045	140	0.000036	0.000325	3079.800000	0.810300	159	0.000011	0.001370	729.439350	0.238685
132	648	141	0.000036	0.000320	3125.400000	0.172900	NaN	0.000008	NaN	NaN	NaN
133	5485	140	0.000036	0.000253	3953.600000	0.745700	206	0.000004	0.001080	925.678922	0.002670
134	1160	141	0.000036	0.000249	4020.900000	0.629000	373	0.000004	0.001466	681.741222	0.182405
135	1864	142	0.000035	0.000244	4094.400000	0.365900	NaN	NaN	NaN	NaN	NaN
136	4116	142	0.000035	0.000209	4777.000000	0.000000	NaN	NaN	NaN	NaN	NaN