Page 417 - Design for Six Sigma a Roadmap for Product Development

384 Chapter Ten

■ Use the following relation and solve for a single unknown: percent
down/100 MTTR/(MTTF MTTR) MTTR/MTBF.
■ Works best when you use the black belt estimate MTTR and TTR
*
distribution and use Erlang distribution for TTF (or TBF) distri-
bution with parameter based on solving the preceding equation
for MTTF (or MTBF).
5. Activity: downtime—time to repair
■ Triangular with parameters (min, mode, max)
6. Activity: downtime—time to (between) failure(s)
■ Erlang with parameters (mean, K )
†
■ Exponential with parameter (mean) ‡
7. Activity: scrap rate
■ Binomial parameters: (percent success) with success scrap part
8. Activity: interarrival time of parts
■ Erlang parameters (mean, K)
§
■ Lognormal with parameters (mean, )
■ Exponential parameter (mean)
9. Activity: assignment of part type (or other discrete attributes) to
parts
■ Binomial parameters (percent success) success first part type
¶
■ Discrete probability parameters [percent A, percent (A B), 100
percent]
An iteration of the simulation routine provides random numbers
from the assumption cells. These random numbers propagate through
the sum equation in the model to calculate the value of the total cost,
the forecast cell. When all iterations are performed, the calculated val-
ues of the forecast cell form a new statistical distribution. Six Sigma
statistical analysis takes over, and the black belt can construct confi-
dence intervals or test the hypothesis as if the data are collected from
real random experiments.
Design for life-cycle cost involves choosing the best economical alterna-
tive as we did with other costing methods (Sec. 9.6.1). Design alternatives
can be studied using ABC to select a cost optimum. However, because of

* Erlang distribution is a probability model.
† K number of exponential distributions to sum (use K 3 or K 2 for best results).
‡ Avoid when modeling with time between failures and when a very short (almost zero)
duration is impossible.
§ The black belt should avoid this unless very long delays are possible.
¶ This is an extension of the binomial for three or more choices.