Define what is meant by producer’s risk and consumer’s risk.
A system is made up of five components. There is no redundancy in the system; that is, all
system components are in series. The components have been experiencing an MTBF as
shown in Column 2 of the following table. Design analysis has shown that all components
can be redesigned to improve the individual MTBFs by a factor of 5. The estimated
development cost to redesign each component is shown in Column 3. Total development
cost is the sum of all redesign costs for those components (1–5) that the developer chooses
to improve, but it is not known which of these components should be redesigned. A costeffectiveness (CE) criterion has been defined to establish the priority for component
redesign. Cost-effectiveness is defined as the improvement (reduction) in failure rate
divided by the cost to implement the design change for each component. The component
with the highest value of CE will have the highest priority for redesign. Other components
will be listed in order of redesign priority, in accordance with its value of CE. The time
basis for all reliabilities in this problem is 1,000 hours. Cumulative cost is the total cost to
implement the design change for components 1–n.
(a) Calculate the MTBF of the entire system before redesign.
(b) Calculate the failure rate of each component before design.
(c) Calculate the CE of each redesign for each component.
(d) Prioritize these reliability improvements.
(e) Calculate the reliability after each improvement is made (in order of costeffectiveness), including the aggregate reliability if all components are redesigned. (f) Plot total system reliability as a function of total development cost. (g) Calculate the cumulative reliability over all the improvements. (h) Determine how many components should be redesigned to achieve a reliability of at least 0.8. (i) Determine how many components should be redesigned if the customer does not want to budget more than $10M to the effort.