Attribute Control Charts - PowerPoint PPT Presentation

1 / 63
About This Presentation
Title:

Attribute Control Charts

Description:

Attribute Control Charts Learning Objectives Defective vs Defect Binomial and Poisson Distribution p Chart np Chart c Chart u Chart Tests for Instability Shewhart ... – PowerPoint PPT presentation

Number of Views:256
Avg rating:3.0/5.0
Slides: 64
Provided by: Seaga9
Category:

less

Transcript and Presenter's Notes

Title: Attribute Control Charts


1
Attribute Control Charts
2
Learning Objectives
  • Defective vs Defect
  • Binomial and Poisson Distribution
  • p Chart
  • np Chart
  • c Chart
  • u Chart
  • Tests for Instability

3
Shewhart Control Charts - Overview
4
Defective and Defect
  • Defective
  • A unit of product that does not meet customers
    requirement or specification.
  • Also known as a non-conforming unit.
  • Example
  • A base casting that fails porosity specification
    is a defective.
  • A disc clamp that does not meet the parallelism
    specification is a defective.

5
Defective and Defect
  • Defect
  • A flaw or a single quality characteristic that
    does not meet customers requirement or
    specification.
  • Also known as a non-conformity.
  • There can be one or more defects in a defective.
  • Example
  • A dent on a VCM pole that fails customers
    specification is a defect.
  • A stain on a cover that fails customers
    specification is a defect.

6
Shewhart Control Charts for Attribute Data
  • There are 4 types of Attribute Control Charts

Defectives
p
np
(Binomial Distribution)
Defects
u
c
(Poisson Distribution)
43
7
Learning Objectives
?
  • Defective vs Defect
  • Binomial and Poisson Distribution
  • p Chart
  • np Chart
  • c Chart
  • u Chart
  • Tests for Instability

Mean defective rate
Mean defect rate
8
Types of Data and Distributions
  • Discrete Data (Attribute)
  • Binomial
  • Poisson
  • Continuous Data (Variable)
  • Normal
  • Exponential
  • Weibull
  • Lognormal
  • t
  • c2
  • F

Discrete Distributions
Continuous Distributions
9
Types of Distributions
Discrete Distributions
Continuous Distributions
10
Discrete Distributions
  • Binomial Distribution
  • Useful for attribute data (or binary data)
  • Result from inspection criteria which are binary
    in nature, e.g. pass/fail, go/nogo,
    accept/reject, etc.
  • Data generated from counting of defectives.

11
Discrete Distributions
  • Binomial Distribution
  • If a process typically gives 10 reject rate (p
    0.10), what is the chance of finding 0, 1, 2 or 3
    defectives within a sample of 20 units (n 20)?
  • Commonly used in Acceptance Sampling

12
Binomial Distribution
  • Commonly used in Acceptance Sampling, where p is
    the probability of success (defective rate), n is
    the number of trials (sample size), and x is the
    number of successes (defectives found).

13
Binomial Distribution
  • Properties
  • each trial has only 2 possible outcomes - success
    or failure
  • probability of success p remains constant
    throughout the n trials
  • the trials are statistically independent
  • the mean and variance of a Binomial Distribution
    are

14
Discrete Distributions
Binomial Distribution
The location, dispersion and shape of a binomial
distribution are affected by the sample size (n)
and defective rate (p).
15
James Bernoulli
Discrete Distributions
Binomial Distribution
16
Discrete Distributions
  • Poisson Distribution
  • Useful for discrete data involving error rate,
    defect rate (dpu, dpmo), particle count rate,
    etc.
  • Data generated from counting of defects.

17
Discrete Distributions
  • Poisson Distribution
  • If a process typically gives 4.0 defect rate (l
    4 dpu), what is the chance of finding 0, 1, 2 or
    3 defects per unit?
  • Commonly used as an approximation of the binomial
    distribution when
  • p lt 0.1 (10)
  • n is large

18
Poisson Distribution
  • This distribution have been found to be relevant
    for applications involving error rates, particle
    count, chemical concentration, etc, where ? is
    the mean number of events (or defect rate) within
    a
  • given unit of time or space.

19
Poisson Distribution
  • Properties
  • number of outcomes in a time interval (or space
    region) is independent of the outcomes in another
    time interval (or space region)
  • probability of an occurrence within a very short
    time interval (or space region) is proportional
    to the time interval (or space region)
  • probability of more than 1 outcome occurring
    within a short time interval (or space region) is
    negligible
  • the mean and variance for a Poisson Distribution
    are

20
Discrete Distributions
Poisson Distribution
The location, dispersion and shape of a Poisson
distribution are affected by the mean (l).
21
Simeon D Poisson
Discrete Distributions
Poisson Distribution
22
Summary of Approximation
Binomial
The smaller p and larger n the better
p lt 0.1
np gt 5, gt 10 p 0.5, lt 0.5
Poisson
? ? 15
The larger the better
Normal
23
Learning Objectives
?
  • Defective vs Defect
  • Binomial and Poisson Distribution
  • p Chart
  • np Chart
  • c Chart
  • u Chart
  • Tests for Instability

?
24
p Chart
  • Fraction Non-Conforming
  • Reject Rate / Defective Rate
  • Percent Fallout

0
.
5
1
0
.
4
3
.
0
S
L

0
.
3
8
8
0
n
o
i
0
.
3
t
r
o
p
o
P

0
.
2
1
4
0
r
0
.
2
P
0
.
1
-
3
.
0
S
L

0
.
0
4
0
0
0
0
.
0
2
0
1
0
0
S
a
m
p
l
e

N
u
m
b
e
r
25
p Chart
  • Fraction non-conforming (p)
  • Ratio of number of defectives (or non-conforming
    items) in a population to the number of items in
    that population.
  • Sample fraction non-conforming (p)
  • Ratio of number of defectives (d) in a sample to
    the sample size (n), i.e.

Is p a sample statistic?
26
p Chart
  • The underlying principles of the p chart are
    based on the binomial distribution.
  • This means that if a process has a typical
    fraction non-conforming, p, the mean and variance
    of the distribution for ps are computed from the
    binomial equation, giving

Xk number of defective unit in subgroup k
which has a total sample size of nk units
k number of subgroup, should be between 20 to
25 before constructing control limits.
27
p Chart
  • The p chart also assumes a symmetrical bell-shape
    distribution, with symmetrical control limits on
    each side of the center line.
  • This implies that the binomial distribution is
    approximately close to the shape of the normal
    distribution, which can happen under certain
    conditions of p and n
  • p ? 1/2 and n gt 10 implying np gt 5
  • For other values of p, the general guideline is
    to have np gt 10 to get a satisfactory
    approximation of the normal to the binomial.

28
p Chart
  • Following Shewharts principle, the Center Line
    and Control Limits of a p chart are

29
p Chart
  • If the sample size is not constant, then the
    Control Limits of a p chart may be computed by
    either method
  • a) Variable Control Limits
  • where ni is the actual sample size of each
    sampling i
  • b) Control Limits Based on Average Sample Size
  • where n is the average (or typical) sample size
    of all the samples

30
p Chart - Average Sample Size
  • When to Use Control Limits Based on Average
    Sample Size instead of Variable Control Limits
  • Smallest subgroup size, nmin, is at least 30 of
    the largest subgroup size, nmax.
  • Future sample sizes will not differ greatly from
    those previously observed.
  • When using Control Limits Based on Average Sample
    Size, the exact control limits of a point should
    be determined and examined relative to that value
    if
  • There is an unusually large variation in the size
    of a particular sample
  • There is a point which is near the control
    limits.

31
Example 1 p Chart
  • S/N Sampled Rejects
  • 1 50 12
  • 2 50 15
  • 3 50 8
  • 4 50 10
  • 5 50 4
  • 6 50 7
  • 7 50 16
  • 8 50 9
  • 9 50 14
  • 10 50 10
  • 11 50 5
  • 12 50 6
  • 13 50 17
  • 14 50 12
  • 15 50 22
  • 16 50 8
  • 17 50 10
  • 18 50 5

Frozen orange juice concentrate is packed in 6-oz
cardboard cans. A metal bottom panel is attached
to the cardboard body. The cans are inspected
for possible leak. 20 samplings of different
sampling size were obtained. Verify if the
process is in control. The data are found in
AttributeSPC.MTW.
32
Example 1 p Chart
  • MiniTab Stat ? Control Charts ? P

33
Example 1 p Chart
34
Example 1 p Chart
Minitab allows different set of control charts to
be plotted on one chart MiniTab Stat ? Control
Charts ? P
35
Example 1 p Chart
36
Establish Trial Control Limits
  • When to use it?
  • New process, modified process, no historical data
    available to calculate p
  • How to do it?
  • Calculate p based on the preliminary 20 to 25
    subgroups.
  • Calculate the trial control limits using the
    formula mentioned in slide 21 or 22.
  • Sample values of p from the preliminary subgroups
    to be plotted against the trial control limits.
  • Any points exceed the trial control limits should
    be investigated.
  • If assignable causes for these points are
    discovered, they should be discarded and new
    trial control limits to be determined.

37
np Chart
  • If the sample size is constant, it is possible to
    base a control chart on the number nonconforming
    (np), rather than the fraction nonconforming (p).
  • The Center Line and Control Limits of an np chart
    are

38
Example 2 np Chart
  • S/N Sampled Rejects
  • 1 50 12
  • 2 50 15
  • 3 50 8
  • 4 50 10
  • 5 50 4
  • 6 50 7
  • 7 50 16
  • 8 50 9
  • 9 50 14
  • 10 50 10
  • 11 50 5
  • 12 50 6
  • 13 50 17
  • 14 50 12
  • 15 50 22
  • 16 50 8
  • 17 50 10
  • 18 50 5

Frozen orange juice concentrate is packed in 6-oz
cardboard cans. A metal bottom panel is attached
to the cardboard body. The cans are inspected
for possible leak. 20 samplings of 50
cans/sampling were obtained. Verify if the
process is in control. The data are found in
AttributeSPC.MTW.
39
Example 2 np Chart
  • MiniTab Stat ? Control Charts ? NP

40
Example 2 np Chart
41
p Chart vs np Chart
  • For ease of recording, the np chart is preferred.
  • The p chart offers the following advantages
  • accommodation for variable sample size
  • provides information about process capability

42
Sample Size for p and np Charts
  • Sample Size is determined based on the 2
    criteria
  • Assumption to approximate Binomial Distribution
    to a
  • Normal Distribution
  • To ensure that the LCL is greater than zero.

For p ? 0.5
For p other values
43
Learning Objectives
?
  • Defective vs Defect
  • Binomial and Poisson Distribution
  • p Chart
  • np Chart
  • c Chart
  • u Chart
  • Tests for Instability

?
?
?
44
c Chart
  • Defects per Unit (DPU)
  • Error Rate / Defect Rate
  • Defects per Opportunity

2
0
3
.
0
S
L

1
8
.
9
7
t
n
u
o
C

1
0
e
C

9
.
6
5
0
l
p
m
a
S
-
3
.
0
S
L

0
.
3
3
0
7
0
2
0
1
0
0
S
a
m
p
l
e

N
u
m
b
e
r
45
c Chart
  • Each specific point at which a specification is
    not
  • satisfied results in a defect or nonconformity.
  • The c chart is
  • a control chart for the total number of defects
    in an inspection unit
  • based on the normal distribution as an
    approximation for the Poisson distribution, which
    can happen when
  • c or ? ? 15

46
c Chart
  • Inspection Unit
  • The area of opportunity for the occurrence of
    nonconformities.
  • e.g. a HSA, a media, a PCBA
  • This is an entity chosen for convenience of
    record-keeping.
  • It may constitute more than 1 unit of product.
  • e.g. a HSA, both surfaces of a media, 10 pieces
    of PCBA

47
c Chart
  • If the number of nonconformities (defects) per
    inspection unit is denoted by c, then
  • The Center Line and Control Limits of a c chart
    are

48
u Chart
  • In cases where the number of inspection units is
    not constant, the u chart may be used instead,
    with
  • If the average number of defects per inspection
    unit is denoted by u, then

Where ci is the count of the number of defects in
number of inspection units, ai
49
u Chart
  • The Center Line and Control Limits of a u chart
    are

50
Example 3 c and u Charts
  • S/N Units Defects
  • 1 5 10
  • 2 5 12
  • 3 5 8
  • 4 5 14
  • 5 5 10
  • 6 5 16
  • 7 5 11
  • 8 5 7
  • 9 5 10
  • 10 5 15
  • 11 5 9
  • 12 5 5
  • 13 5 7
  • 14 5 11
  • 15 5 12
  • 16 5 6
  • 17 5 8
  • 18 5 10

A personal computer manufacturer plans to
establish a control chart for nonconformities at
the final assembly line. The number of
nonconformities in 20 samples of 5 PCs are shown
here. Verify if the process is in-control.
51
Example 3 c and u Charts
  • MiniTabs Stat ? Control Charts ? C

52
Example 3 c and u Charts
  • MiniTabs Stat ? Control Charts ? U

53
Example 3 c and u Charts
54
u (or c) Chart vs p (np) Chart
  • The u (or c) chart offers the following
    advantages
  • More informative as the type of nonconformity is
    noted.
  • Facilitates Pareto analysis.
  • Facilitates Cause Effect Analysis.

55
Learning Objectives
?
  • Defective vs Defect
  • Binomial and Poisson Distribution
  • p Chart
  • np Chart
  • c Chart
  • u Chart
  • Tests for Instability

?
?
?
?
?
56
Selecting the Appropriate Chart
  • c - Chart
  • Measures the total number of defects in a
    subgroup
  • The subgroup size can be 1 unit of product if we
    expect to have a relatively large number of
    defects/unit
  • Requires a constant subgroup size
  • u - Chart
  • Measures the number of defects/unit of product
    (dpu)
  • The subgroup size can be constant or variable
  • p - Chart
  • Measures the proportion of defective units in a
    subgroup
  • The subgroup size can be constant or variable
  • np - Chart
  • Measures the number of defective items in a
    subgroup
  • Requires a constant subgroup size

57
Exercise 1
  • Strength of 5 test pieces sampled every
    hour(Xbar-R)
  • Number of defectives in 100 parts(np)
  • Number of solder defects in a printed circuit
    board assembly(C)
  • Diameter of 40 units of products sampled every
    day(Xbar-S)
  • Percent defective of a lot produced in every
    30-min period(p)
  • Surface defects of surface area of varying
    sizes(u)
  • In a maintenance group dealing with repair work,
  • the number of maintenance requests that
    require
  • a second call to complete the repair every
    week

58
Test for Instability
Suitable for all charts
_
Suitable only for X-Chart
59
Tests for Instability
  • CAUTION Do not apply tests blindly
  • Not every test is relevant for all charts
  • Excessive number of tests ? Increased ?-error
  • Nature of application

60
Variables vs Attributes Charts
  • Attributes Control Charts facilitate monitoring
    of more than 1 quality characteristics.
  • Variables Control Charts provide leading
    indicators of trouble Attributes Control Charts
    react after the process has actually produced bad
    parts.
  • For a specified level of protection against
    process drift, Variables Control Charts require a
    smaller sample size.

61
Learning Objectives
?
  • Defective vs Defect
  • Binomial and Poisson Distribution
  • p Chart
  • np Chart
  • c Chart
  • u Chart
  • Tests for Instability

?
?
?
?
?
?
62
  • End of Topic
  • What Question
  • Do You
  • Have

63
Reading Reference
  • Introduction to Statistical Quality
    Control,
  • Douglas C. Montgomery, John Wiley Sons,
  • ISBN 0-471-30353-4
Write a Comment
User Comments (0)
About PowerShow.com