Control Chart for Attributes
Post on 24-Jan-2016
232 Views
Preview:
DESCRIPTION
Transcript
Control Charts for Attributes
Ronald Sukwadi, Ph.D.
Department of Industrial Engineering
TKI 329 Quality Control
Introduction
Data that can be classified into one of several
categories or classifications is known as attribute
data.
Classifications such as conforming and
nonconforming are commonly used in quality
control.
Another example of attributes data is the count of
defects.
Ronald Sukwadi TKI 329 Quality Control
Control Charts for Fraction
Nonconforming
Fraction nonconforming is the ratio of the
number of nonconforming items in a
population to the total number of items in that
population.
Control charts for fraction nonconforming are
based on the binomial distribution.
Ronald Sukwadi TKI 329 Quality Control
Control Charts for Fraction
Nonconforming
Recall: A quality characteristic follows a binomial distribution if:
1. All trials are independent.
2. Each outcome is either a “success” or “failure”.
3. The probability of success on any trial is given as p. The probability of a failure is 1-p.
4. The probability of a success is constant.
Ronald Sukwadi TKI 329 Quality Control
Control Charts for Fraction
Nonconforming
The binomial distribution with parameters n
0 and 0 < p < 1, is given by
The mean and variance of the binomial
distribution are
xnx )p1(px
n)x(p
)p1(npnp 2
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Design of Fraction Nonconforming
Chart
Three parameters must be specified
1. The sample size
2. The frequency of sampling
3. The width of the control limits
Common to base chart on 100% inspection of
all process output over a period of time
Rational subgroups may also play role in
determining sampling frequency
Ronald Sukwadi TKI 329 Quality Control
Sample size
If p is very small, we should choose n sufficiently
large to find at least one nonconforming unit
Otherwise the presence of only one non-conforming
in the sample would indicate out-of-control
condition (example)
To avoid this, choose n such that the probability of
finding at least one nonconforming per sample is at
least γ (example)
Ronald Sukwadi TKI 329 Quality Control
Example
p = 0.01 and n = 8
If there is one nonconforming in the sample, then
p =1/8=0.125
and we conclude that the process is out of control
1155.08
)01.01(01.0301.0
)1(3
n
pppUCL
Ronald Sukwadi TKI 329 Quality Control
Sample size
The sample size can be determined so that the
probability of finding at least one nonconforming
unit per sample is at least γ
Example p = 0.01 and γ = 0.95
Find n such that P(D ≥ 1) ≥ 0.95
Using Poisson approximation of the binomial with
λ =np
From cumulative Poisson table λ must exceed 3.00
np ≥ 3 n ≥ 300
Ronald Sukwadi TKI 329 Quality Control
Sample size
The sample size can be determined so that a shift of some
specified amount, can be detected with a stated level of
probability (50% chance of detection).
UCL = pout
If is the magnitude of a process shift, then n must satisfy:
Therefore,
n
)p1(pL
)p1(pL
n
2
Ronald Sukwadi TKI 329 Quality Control
Positive Lower Control Limit
The sample size n, can be chosen so that the
lower control limit would be nonzero:
and
0n
)p1(pLpLCL
2Lp
)p1(n
Ronald Sukwadi TKI 329 Quality Control
Interpretation of Points on the Control
Chart for Fraction Nonconforming
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Variable Sample SizeVariable-Width Control Limits
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Variable Sample SizeControl Limits Based on an Average Sample Size
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Variable Sample SizeThe Standardized Control Chart
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
The Opening Characteristic Function
and Average Run Length Calculations
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Control Charts for Nonconformities
(Defects)Procedures with Constant Sample Size
Ronald Sukwadi TKI 329 Quality Control
There are many instances where an item will contain nonconformities but the item itself is not classified as nonconforming.
It is often important to construct control charts for the total number of nonconformities or the average number of nonconformities for a given “area of opportunity”. The inspection unit must be the same for each unit.
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Control Charts for Nonconformities
(Defects)Procedures with Variable Sample Size
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
Ronald Sukwadi TKI 329 Quality Control
top related