Chapter 2 Modelling Quality and Warranty Cost - Mathematics in ...

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30 CHAPTER 2. MODELLING QUALITY AND WARRANTY COST 0.24 FR1 v/s q1, q2=0.3 0.5 FR1 v/s q2, q4=0.3 0.22 0.2 0.4 0.18 0.16 0.3 0.14 0.12 0.2 0.1 0.08 0.06 q4=0.1 q4=0.5 q4=0.8 0.1 q1=0.1 q1=0.5 q1=0.8 0.04 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Component Failure Rate q1 0.25 (a) FR1 v/s q4, q4=0.3 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Infant Mortality Factor q2 (b) q1=0.1 q1=0.5 q1=0.8 1 0.9 0.22 0.2 0.8 0.2 0.15 0.1 Working Environment Range 0.7 0.6 0.5 0.4 0.3 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.05 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Working Environment Range q4 (c) 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Component Failure Rate (d) 0.06 Figure 2.2: Failure Rate FRK model as a function of (a) component J K quality , (b) infant JON mortality , (c) working environment JOg range , and (d) JMK both JTg and JTNdH|]Q together, .
2.3. HOW DO WE MODEL THE RELIABILITY CONSTRAINTS? 31 0.25 FR2 v/s q1, q2=0.3 0.25 FR2 v/s q2, q4=0.3 q1=0.1 q1=0.5 q1=0.8 0.2 0.2 0.15 0.15 0.1 q4=0.1 q4=0.5 q4=0.8 0.05 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Component Failure Rate q1 (a) 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Infant Mortality Factor q2 (b) Figure 2.3: Failure Rate model FRN as a function of (a) component quality JMK , and (b) infant mortality JON . on JMK is modelled by an exponential. Second, the initial mortality rate JOg impacts the overall failure FRN rate, but even if this IMF is low, a poor-quality component will impact the failure rate adversely. The two graphs in Figure 2.3 use the failure model (2.4) for FR to describe the broad trends in the model with component failure J K rate and infant mortality JON factor and can be compared to Figure 2.2. In Section 2.8 we show the effect of inputting several instances D of , drawn from test data, into the FRN model . 2.3.2 Modelling the Severity Level Software failures are characterized in terms of varying severity levels (hereafter denoted SL), where an H _ SL is a catastrophic failure, while an Hu{ SL is a minor failure. In this section we present some models describing the relationship between the quality D vector and the SL. In the context of this specific project, we determined that the severity levels of software failure were impacted by the software development environment JOv , the code complexity JOw , the stability index JMx , the coverage testing JOy and the fault density JTS . The model we propose for the severity levels is not an additive/linear one. We believe that the chosen functional form captures well the trends in severity levels as functions of the individual attributes, as well as the relative importance amongst these factors. There are some free (nonnegative) parameters in the model, ‘’K , ‘N , ‘¦P , ‘¦g , ‘¦v . The severity level SL as a function of D is: N Q (2.5) x SLK_FDIHH SLK¤F7JOvL JOw#LMJ x.LMJOyMLMJOS_HVH|‘¢K.ˆ¦“ Š•”‹T–˜—~š y “>› ”‹Tœ•—~š K ” JTv„n F>_žn…JTwŸe J ”A— N H¡“T¢¦J w To describe the effects of coverage testing JOy , we noted that as JTy increases, the likelihood of catastrophic software error decreases since more of the software is validated. Similarly, as the number of faults per 1K lines, JTS , increases, so does the risk of catastrophic error. Keeping in mind the scale
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Page 23: Bibliography [1] Mendiratta, V.B. (

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