Probability
Random variables and pdf's
Aplications
Counting
Models
How many cashiers should we open to reduce the waiting time to 2 minutes?
What is the expected number of days until a serious accident happen in a production line?
If we roll a die four times, what is the probability that the sequence of rolls is increasing?
If a die is rolled four times, what is the probability that the total sum is greater than 20?
+INFO
+INFO
+INFO
+INFO
BINOMIAL Bin(n,p)
X = Number of successes in n Bernoulli trials
- Two possible outcomes: Success and Failure.
- Probability of success constant.
- Independent trials.
Acceptance Sampling
Control charts p, np
Poisson Pois(λ)
X = Number of occurrences in a interval of time, area or volumen
- Occurrences are homogeneous in time, area or volumen.
Queueing systems
Control charts u, c
Exponential Exp(λ)
X = Lifetime / Durability / Waiting time
- Only continuous distribution with no memory.
Queueing systems
Reliability
Normal N(µ,σ)
X = Error magnitud / IQ / Random fluctuations
Control charts Xbar-R, Xbar-S, IMR
Linear Regression
Capacity Cp, Cpk, Pp, Ppk
Box-Jenkins
DOE
IN2032 Probability Models
Iván Pacheco Soto
Created on February 14, 2023
Usefulness of probability models
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Transcript
Probability
Random variables and pdf's
Aplications
Counting
Models
How many cashiers should we open to reduce the waiting time to 2 minutes?
What is the expected number of days until a serious accident happen in a production line?
If we roll a die four times, what is the probability that the sequence of rolls is increasing?
If a die is rolled four times, what is the probability that the total sum is greater than 20?
+INFO
+INFO
+INFO
+INFO
BINOMIAL Bin(n,p)
X = Number of successes in n Bernoulli trials
Acceptance Sampling
Control charts p, np
Poisson Pois(λ)
X = Number of occurrences in a interval of time, area or volumen
Queueing systems
Control charts u, c
Exponential Exp(λ)
X = Lifetime / Durability / Waiting time
Queueing systems
Reliability
Normal N(µ,σ)
X = Error magnitud / IQ / Random fluctuations
Control charts Xbar-R, Xbar-S, IMR
Linear Regression
Capacity Cp, Cpk, Pp, Ppk
Box-Jenkins
DOE