Estimating the Distribution of Total Defects over Time

Based on the discussions in the previous section, it is apparent that for software maintenance planning, we should (1) use the reliability models to estimate the total number of defects or defect rate only and (2) spread the total number of defects into arrival pattern over time based on historical patterns of field defect arrivals.

The field defect arrival patterns, in turn , can be modeled by the same process. Our experience with several operating systems indicates that the arrival curves follow the Rayleigh, the exponential, or the S models. Figure 8.5 shows the field defect arrival patterns of a major release of both the System/38 and the AS/400 operating systems. As discussed in Chapter 7, Figure 7.6 shows the field defect arrivals pattern of another IBM system software, which can be modeled by the Rayleigh curve or the Weibull distribution with the shape parameter, m, equal to 1.8.

Figure 8.5. Field Defect Arrival Pattern ”System/38 and AS/400 Operating Systems

The field defect arrival pattern may differ for different types of software. For example, in software for large systems it takes longer for latent defects to be detected and reported . The life of field defect arrivals can be longer than three years. For applications software, the arrival distribution is more concentrated and usually last about two years . We call the former the slow ramp-up pattern and the latter the fast ramp-up pattern. Based on a number of products for each category, we derived the distribution curves for both patterns, as shown in Figure 8.6. The areas under the two curves are the same, 100%. Tables 8.3 and 8.4 show the percent distribution by month for the two patterns. Because the defect arrival distribution pattern may depend on the type of software and industry segment, one should establish one's own pattern based on historical data. If the defect arrival patterns cannot be modeled by a known reliability model, we recommend using a nonparametric method (e.g., 3-point moving average) to smooth the historical data to reveal a pattern and then calculate the percent distribution over time.

Figure 8.6. Two Patterns of Field Defect Arrivals ”Areas Under the Curves Are the Same

Table 8.3. Monthly Percent Distribution of Field Defect Arrivals ”Slow Ramp-up Pattern

Month	%	Month	%	Month	%	Month	%
1	0.554	13	4.505	25	1.940	37	0.554
2	1.317	14	4.366	26	1.802	38	0.416
3	2.148	15	4.158	27	1.594	39	0.416
4	2.911	16	3.950	28	1.386	40	0.347
5	3.465	17	3.742	29	1.247	41	0.347
6	4.019	18	3.465	30	1.178	42	0.277
7	4.366	19	3.188	31	1.040	43	0.277
8	4.643	20	2.980	32	0.970	44	0.208
9	4.782	21	2.772	33	0.832	45	0.208
10	4.851	22	2.495	34	0.762	46	0.138
11	4.782	23	2.287	35	0.693	47	0.138
12	4.712	24	2.079	36	0.624	48	0.069
Year 1	42.550	Year 2	82.537	Year 3	96.605	Year 4
Cumulative		Cumulative		Cumulative		Cumulative	100.000

Table 8.4. Monthly Percent Distribution of Field Defect Arrivals ”Fast Ramp-up Pattern

Month	%	Month	% Month	%
1	1.592	13	5.398	25	0.277
2	3.045	14	4.706	26	0.208
3	4.429	15	4.014	27	0.128
4	5.536	16	3.391	28	0.069
5	6.505	17	2.768	29	0.069
6	7.128	18	2.215	30	0.069
7	7.474	19	1.730
8	7.612	20	1.384
9	7.474	21	1.038
10	7.197	22	0.761
11	6.713	23	0.554
12	6.090	24	0.415
Year 1	70.795	Year 2	99.169	Year 2.5	99.999
Cumulative		Cumulative		Cumulative