ODC - Orthogonal Defect Classification

3. Analysis by Failure Symptom

This section addresses the question of whether the population of defects consists of sub-populations that exhibit different reliability growth characteristics. Given the nature of defect data there is no straightforward answer. We attempted a search for this answer, by trial and error, inspecting growth curves of various sub-populations identified by keys such as defect severity, symptom, component, etc. The qualitative inspection revealed that symptom held a promise. This prompted a quantitative identification of the sub-populations using estimated parameters from a reliability growth model. We first begin by describing the growth model used and then the clustering method used to identify the sub-populations of interest. We use the inflection S-shaped growth model for our analysis. The choice is motivated by the shape of the observed reliability growth curve. In this paper, the primary purpose of fitting a model is not prediction, but to provide a quantitative means to identify sub-populations. (The data used has been made available in the Appendix). The inflection S-shaped model is characterized by a growth mean value function h(t) of NHPP: h(t) = N<1-e sup(-phi t)> over <1 + psi e sup (- phi t)> where, phi is the failure detection rate (in the sense of the Jelinski-Moranda model ), psi is the inflection parameter, and h(t) is the number of failures detected up to time t. The inflection parameter is defined for a given r by, psi(r) = <1-r> over <r>, r gt 0, where r is the inflection rate. The S shape and the inflection are attributed to mutually dependent defects such that some faults are not detectable before others. Essentially, r indicates the ratio of the number of detectable faults to the total number of faults in the program. An r value of 1 reduces the model to an exponential curve, and implies that the defects are independent. A lower value of r causes the curve to be more inflected and implies, in this model, the defects are dependent. A detailed discussion on this model, its use, and algorithms for estimation of parameters can be found in . Figure 1 shows the observed and fitted reliability growth curve of the entire population of detected defects. The estimated parameters for N, phi and psi are shown against the figure. A vertical reference line is drawn in the figure at a specific instant, T, during the testing cycle. We call the percentage of total defects detected at time T, P sub T, that is about 65% in the figure. We use the parameter P sub T later in this section. The S-shaped model is a good fit for most of the testing phase. Towards the late stages of testing there is a pronounced increase in detection rate which this model is not intended to capture.

• Identification of Sub-populations