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

34 CHAPTER 2. MODELLING QUALITY AND WARRANTY COST
200
160
154
1
0.9
160
140
150
155
152
150
0.8
0.7
120
100
0 0.5 1
q1
158
150
0 0.5 1
q2
180
148
0 0.5 1
q3
156
SDE
0.6
0.5
100
80
156
154
152
160
140
154
152
0.4
0.3
60
150
0 0.5 1
q4
154
120
0 0.5 1
q5
154
150
0 0.5 1
q6
154
0.2
40
152
153
153.5
0.1
20
150
152
153
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Component Failure Rate
(a)
148
0 0.5 1
q7
151
0 0.5 1
q8
(b)
152.5
0 0.5 1
q9
Figure 2.5: Behaviour of the quality function. (a) Trend in cost of quality as a function of component
failure rate J K and SDE JTv . (b) Trend of cost of quality in individual attributes J>c .
EK Here E ªK , Ežv , E ª v , ÈTN , È ªN , ÈÉP , ÈTg , È ªg , ÈTw , Èx , ÈÉS , È ªS , are constant parameters which need to be determined
by fitting actual data to the model.
The first term of the hardware and software portions in this model capture the importance of the
component failure J K rate and the software development JOv environment in the overall cost model. As
decreases, the overall likelihood of failure decreases. This improvement costs more, especially after
JMK
a certain threshold is achieved. Improvements beyond this level are increasingly expensive, as captured
by an exponential function with the negative exponent. On the other hand, as JTv SDE increases, the
software development environment becomes better and thus costs more. These trends are captured in
Figures 2.5(a) and (b).
The terms collected in equation (2.8) under hardware describe the effects of the infant mortality
JON rate , the diagnostics JTP capability and the working environment JOg range . In terms of the overall
hardware quality costs, these are higher-order effects in the sense that their contribution may not be
as significant as that of the component failure JMK rate, . This reasoning dictated the functional relationships
as being at best quadratic. Similarly, the costs collected under software describe the effects of
controlling the code JTw complexity and the stability JMx index . These costs contribute less significantly
to the overall quality costs for the software than the software development JTv environment . Indeed,
the effects of increasing the coverage testing and decreasing the fault density are captured (to a large
extent) by the cost JTv of , and are therefore ignored in this cost model. The trends of the cost as each of
these attributes vary is pictured graphically in Figure 2.5. The results using the test data are described
in Section 2.8.
2.5 The Warranty Costs
Warranty costs can be broadly broken up into the hardware and software costs, and we thus modelled
each of these separately. As in the cost of quality, the dominant factors involved are the component