[Chapter 7] Quantitative Process Analysis

Question 1

What is the definition of cycle time and cycle time efficiency? Explain all the values used in the formulas.

Answer 1

CT = PT + WT
CTE = PT/CT

Question 2

How is calculated the cycle time for a sequence, XOR gate, AND gate and loop?

Answer 2

CT = T1 + T2 + … + TN
CT = p1T1 + p2T2 + … + pNTN
CT = max(T1 + T2 + … + TN)
CT = T [-A] /(1-r) [+A]
When talking about the effort, is used the sum in the AND gate and not the maximum.
Where A is the time of a task done in the repetition of the loop.
If we know that the loop can only be repeated 1x, then we can alternatively assume that as a “XOR gate” and do not forget to add the main activity time.

Question 3

Explain the Little’s Law.

Answer 3

WIP = λ CT
- λ (if 2 patients arrive at the hospital in 1 hour, then λ=2)

Question 4

Taking into consideration the queuing theory, explain the following values λ, μ, p, c, Lq, Wq, L, W and how they are related in the formulas.

Answer 4

λ - average number of arrivals per time unit
μ - average number of jobs that can be handled by one server per time unit
c - number of servers
p = λ/μ - resource utilization
Lq = p^2/(1-p) - average number of instances in the queue
Wq = Lq/λ - average time one instance spends in the queue
L = λW - average number of instances in the system (WIP)
W = Wq + 1/μ - average time one instance spends in the entire system

Question 5

Explain the simulation concept, and the pitfalls.

Answer 5

Run a large number of process instances, gather performance data (cost, time, resources usage) and calculate statistics from the calculated data.
The pitfalls are stochasticity, data quality, simplifying assumption.