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

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40 CHAPTER 2. MODELLING QUALITY AND WARRANTY COST 300 Component Failure Rate: 100*q1 300 Infant Mortality Factor: 1+q2 300 Diagnostics Capability: 100*q3 200 200 200 100 100 100 0 0 Working Environment 100 Range: q4 300 0 1 300 Software Development Environment: q5 0 0 1 Code Complexity: q6 300 200 200 200 100 100 100 0 0 1 Stability Index: q7 300 0 0 1 Coverage Testing: 100*q8 300 0 0 300 Fault Density: 1000*q9 200 200 200 100 100 100 0 0 1 0 0 100 0 0 1000 Figure 2.7: Simulated data drawn from normal distributions. In detail, + K-,/.1032!465!782!462!9!: , + N;,!782!462!9!: , + P , .1032!46?!782!462!9!: , + g , .=032!469!782!462!9!: , + v , .=032!46?!782!462!9!: , + w , .1032!4 @¥782!462!9!: , + x , .=032!46?!782!462!9!: , + y,A.1032!46?!782!462B@¥: , + S;,C.=032!462!9!782!462!2B@¥: . Any normalization to the respective variables is indicated.
2.9. SUMMARY, FUTURE DIRECTIONS AND SUGGESTIONS 41 250 Overall Failure Rate 100 Severity Levels 90 200 80 70 150 60 50 100 40 30 50 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Failure Rate 0 2 2.5 3 3.5 4 4.5 5 Severity Levels Figure 2.8: Effect of FRN and SLN on simulated data using a normal distribution: most instances of the product have a low failure rate. towards the lower end. We expect that with most products being built to high quality specifications the warranty costs will be low while the cost of implementation will be high. This is borne out in Figure 2.11. In Figure 2.12 we see that at least for this test data, the simplified objective function described in Section 2.6 captures most of the behaviour of the complicated objective function (2.11). Û 2.9 Summary, Future Directions and Suggestions We conclude this report by noting again that the models developed were based solely on discussions and heuristic arguments. In the absence of data, survival and hazard models, indeed even product information from Lucent, this report should not be interpreted as representative. Instead, we hope that the arguments will provide the basis for a more careful modelling effort by Lucent. We note that despite the identification of nine quality attributes J>c , not all of these attributes are equally important. This is a crucial step in any modelling process: identifying the key elements. Based on the preceding discussion we can conclude that the most significant independent attributes are the component failure rates J K and the software development environment JTv . These indices seem to outweigh the others. In fact, most of the other attributes are affected by these two. Thus, any further work should focus on the careful estimation of these attributes. The attributes associated with diagnostics capability JTP , coverage testing JOy and fault density JOS are the least significant. Indeed, these do not even appear in the constraints. Neither the constraint functions FR and SL nor the objective function contain complicated functional forms; the resultant model is nonlinear and awkward, but none of the individual components is more complicated than a quadratic or an exponential. These forms are deliberately chosen since the associated parameters can be easily fit, using real data and standard statistical software. We suggest that the parameters be located based on true data which may be available to the industry.
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Page 5 and 6: 2.3. HOW DO WE MODEL THE RELIABILIT
Page 7 and 8: 2.3. HOW DO WE MODEL THE RELIABILIT
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Page 11 and 12: J 2.5. THE WARRANTY COSTS 35 fail
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Page 19 and 20: 2.9. SUMMARY, FUTURE DIRECTIONS AND
Page 21 and 22: 2.9. SUMMARY, FUTURE DIRECTIONS AND
Page 23: Bibliography [1] Mendiratta, V.B. (

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