Clasifica lo que es el control estadístico

1. Statistical
Quality
Control
By: Torres Erick
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2. What is SQC ?
• Statistical quality control (SQC) is the
term used to describe the set of
statistical tools used by quality
professionals.
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3. Learning Objectives
1. Understand the role of statistical tools in quality improvement.
2. Understand the different types of variability, rational subgroups,
and how a control chart is used to detect assignable causes.
3. Understand control charts for variables such as X-bar, R, S, and
individuals charts.
4. Understand control charts for attributes such as P and U charts.
5. Use other statistical process control problem-solving tools.
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4. Quality Improvement and Statistics
4
• Definitions of Quality
Quality means fitness for use
- quality of design
- quality of conformance
Quality is inversely proportional to
variability.

5. Quality Improvement and Statistics 5
• Quality Improvement
Quality improvement is the reduction of
variability in processes and products.
Alternatively, quality improvement is also
seen as “waste reduction”.

6. DEFINATION-:
“Statistical quality control can be simply defined as an
economic & effective system of maintaining &
improving the quality of outputs throughout the whole
operating process of specification, production &
inspection based on continuous testing with random
samples.”
By-:
YA LUN CHOU
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7. CHARACTERISTICS OF S.Q.C.-:
 Designed to control quality standard of goods produced for marketing.
 Exercise by the producers during production to assess the quality of
goods.
 Carried out with the help of certain statistical tools like Mean Chart,
Range Chart, P-Chart, C-Chart etc.
 Designed to determine the variations in quality of the goods & limits
of tolerance.
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8. CAUSES OF VARIATIONS IN QUALITY-:
1. ASSIGNABLE CAUSES-: It refers to those changes
in the quality of the products which can be assigned
or attributed to any particular causes like defective
materials, defective labour, etc.
2. CHANCE CAUSES-: These causes take place as per
chance or in a random fashion as a result of the
cumulative effect of a multiplicity of several minor
causes which cannot be identified. These causes are
inherent in every type of production.
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9. Variation in Quality
• No two items are exactly alike.
• Some sort of variations in the two items is bound to
be there. In fact it is an integral part of any
manufacturing process.
• This difference in characteristics known as variation.
• This variation may be due to substandard quality of
raw material, carelessness on the part of operator,
fault in machinery system etc..
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10. Types Of Variations 10

11. Variation due to chance causes/common
causes
• Variation occurred due to chance.
• This variation is NOT due to defect in machine, Raw material or
any other factors.
• Behave in “random manner”.
• Negligible but Inevitable
• The process is said to be under the state of statistical control.
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11

12. Variation due to assignable causes
Non – random causes like:
• Difference in quality of raw material
• Difference in machines
• Difference in operators
• Difference of time
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12

13. 13
Variation distribution

14. METHODS OF S.Q.C.-:
1. PROCESS CONTROL-: Under this the quality of the
products is controlled while the products are in the
process of production.
The process control is secured with the technique of
control charts. Control charts are also used in the
field of advertising, packing etc. They ensures that
whether the products confirm to the specified
quality standard or not.
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15. A control chart is a time plot of a statistic, such as a sample mean, range,
standard deviation, or proportion, with a center line and upper and lower
control limits. The limits give the desired range of values for the statistic.
When the statistic is outside the bounds, or when its time plot reveals certain
patterns, the process may be out of control.
A process is considered in statistical control if it has no assignable causes,
only natural variation.
UCL
LCL
Center
Line
Time
Value
This point is out of the control limits
3
3
Control Chart
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16. Introduction to Control Charts
• A process that is operating with only
chance causes of variation present is said
to be in statistical control.
• A process that is operating in the presence
of assignable causes is said to be out of
control.
• The eventual goal of SPC is the elimination
of variability in the process.
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17. Basic Principles
A typical control chart has control limits set at values
such that if the process is in control, nearly all points
will lie within the upper control limit (UCL) and the
lower control limit (LCL).
A typical control chart.
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18. Process improvement using
the control chart.
Introduction to Control Charts 18

19. where
k = distance of the control limit from the center line
w = mean of some sample statistic, W.
w = standard deviation of some statistic, W.
Introduction to Control Charts 19

20. Important uses of the control chart
1. Most processes do not operate in a state of statistical
control
2. Consequently, the routine and attentive use of control
charts will identify assignable causes. If these causes
can be eliminated from the process, variability will be
reduced and the process will be improved
3. The control chart only detects assignable causes.
Management, operator, and engineering action will be
necessary to eliminate the assignable causes.
Introduction to Control Charts
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21. Design of a Control Chart
Suppose we have a process that we assume the true
process mean is  = 74 and the process standard
deviation is  = 0.01. Samples of size 5 are taken
giving a standard deviation of the sample average,
is
0045.0
5
01.0
n
x 


Introduction to Control Charts
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22. Design of a Control Chart
• Control limits can be set at 3 standard
deviations from the mean in both
directions.
• “3-Sigma Control Limits”
UCL = 74 + 3(0.0045) = 74.0135
CL= 74
LCL = 74 - 3(0.0045) = 73.9865
Introduction to Control Charts
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23. Design of a Control Chart
Introduction to Control Charts
X-bar control chart for piston ring diameter.
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24. Analysis of Patterns on Control Charts
• Look for “runs” - this is a sequence of
observations of the same type (all above the
center line, or all below the center line)
• Runs of say 8 observations or more could
indicate an out-of-control situation.
– Run up: a series of observations are increasing
– Run down: a series of observations are decreasing
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25. Analysis of Patterns on Control Charts
X-bar control chart.
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26. Analysis of Patterns on Control Charts
An X-bar chart with a cyclic pattern.
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27. Analysis of Patterns on Control Charts
(a) Variability with the cyclic pattern. (b) Variability with the cyclic pattern eliminated.
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28. Analysis of Patterns on Control Charts
Western Electric Handbook Rules
A process is considered out of control if any of the
following occur:
1) One point plots outside the 3-sigma control limits.
2) Two out of three consecutive points plot beyond the 2-
sigma warning limits.
3) Four out of five consecutive points plot at a distance of
1-sigma or beyond from the center line.
4) Eight consecutive points plot on one side of the center
line.
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29. Analysis of Patterns on Control Charts
The Western Electric zone rules.
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30. Basic Principles
Types of control charts
• Variables Control Charts
– These charts are applied to data that follow a
continuous distribution.
• Attributes Control Charts
– These charts are applied to data that follow a
discrete distribution.
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31. Popularity of control charts
1) Control charts are a proven technique for improving
productivity.
2) Control charts are effective in defect prevention.
3) Control charts prevent unnecessary process adjustment.
4) Control charts provide diagnostic information.
5) Control charts provide information about process
capability.
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32. PURPOSE & USES OF CONTROL CHARTS
1. Helps in determining the quality standard of the
products.
2. Helps in detecting the chance & assignable variations in
the quality standards by setting two control limits.
3. Reveals variations in the quality standards of the
products from the desired level.
4. Indicates whether the production process is in control or
not.
5. Ensures less inspection cost & time in the process
control.
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33. Types-:
Types of
Control
Charts
Control
Charts
for
Variables
Chart
Control
Charts for
Attributes
R-Chart σ-Chart p-Chart np-Chart C-Chart
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34. CONTROL CHATS FOR VARIABLES
 CHART/ MEAN CHART-: This chart is constructed for
controlling the variations in the average quality standard of the
products in a production process.
 R-CHART-: This chart is constructed for controlling the variations
in the dispersion or variability of the quality standards of the
products in a production process.
 σ Chart-: This chart is constructed to get a better picture of the
variations in the quality standard in a process than that is obtained
from the range chart provided the standard deviation(σ) of the various
samples are readily available.
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35. Control Charts for Attributes-:
 p-chart-: This chart is constructed for controlling the quality standard in the
average fraction defective of the products in a process when the observed
sample items are classified into defectives & non-defectives.
 np-chart-: This chart is constructed for controlling the quality standard of
attributes in a process where the sample size is equal & it is required to plot
the no. of defectives (np) in samples instead of fraction defectives (p).
 C-Chart-: This chart is used for the control of no. of defects per unit say
a piece of cloth/glass/paper/bottle which may contain more than one
defect. The inspection unit in this chart will be a single unit of product.
The probability of occurrence of each defect tends to remain very small.
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36. ACCEPTANCE SAMPLING
Meaning-:
Another major area of S.Q.C. is “Product Control” or “Acceptance
Sampling”. It is concerned with the inspection of manufactured
products. The items are inspected to know whether to accept a
lot of items conforming to standards of quality or reject a lot as
non- conforming.
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37. DEFINATION-:
“ Acceptance Sampling is concerned with the decision to
accept a mass of manufactured items as conforming to
standards of quality or to reject the mass as non-
conforming to quality. The decision is reached through
sampling.”
By-:
SIMPSON AND KAFKA
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38. Risks in Acceptance sampling
1. Producer’s risk-: Sometimes inspite of good quality,
the sample taken may show defective units as such
the lot will be rejected, such type of risk is known as
producer’s risk.
2. Consumer’s Risk-: Sometimes the quality of the lot is
not good but the sample results show good quality
units as such the consumer has to accept a defective
lot, such a risk is known as consumer’s risk.
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39. Types of Sampling Inspection Plan
Single Sampling Plan-: Under single sampling plan, a sample of ‘n’
items is first chosen at random from a lot of N items. If the
sample contains, say, ‘c’ or few defectives, the lot is accepted,
while if it contains more than ‘c’ defectives, the lot is rejected
(‘c’ is known as ‘acceptance number’).
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40. Single Sampling Plan
Count the no. of defectives,
‘d’ in the sample of size ‘n’
Is ‘d’ ≤ ‘c’
If yes, than accept the lot If no, then reject the lot
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41. Double Sampling Plan-:
Under this sampling plan, a sample of ‘n1’ items is first
chosen at random from the lot of size ‘N’.
If the sample contains, say, ‘c1’ or few defectives, the lot
is accepted; if it contains more than ‘c2’ defectives, the
lot is rejected.
If however, the number of defectives in the sample
exceeds ‘c1’, but is not more than ‘c2’, a seco
nd sample of ‘n2’ items is take from the same lot. If now,
the total no. of defectives in the two samples together
does not exceed ‘c2’, the lot is accepted; otherwise it is
rejected. (‘c1’ is known as acceptance no. for the first
sample & ‘c2’ is the acceptance no. of both the samples
taken together)
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42. Double Sampling Plan-:
Count the no. of defectives,
d1in the first sample of size n1
Is d1 ≤ c1 ?
Draw another sample of
size n2
If No, then check
If c1 ≤ d1 ≥ c2 ?
Count the no. of defectives d2 in
this sample
Is d1 + d2 ≤ c2
If No, reject the lot
If yes, accept the lot
If yes, then accept
the lot.
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43. Multiple Sampling Plan-:
Under this sampling plan, a decision to accept or reject a lot is
taken after inspecting more than two samples of small size each.
In this plan, units are examined one at a time & after examining
each unit decision is taken. “However, such plan are very
complicated & hence rarely used in practice.”
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44. ADVANTAGES OF S.Q.C.-:
Helpful in controlling quality of a product
Eliminate Assignable causes of variation
Better quality at lower inspection cost
Useful to both consumers & producers
It makes workers quality conscious
Helps in earn goodwill
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45. LIMITATIONS-:
Does not serve as a ‘PANACEA’ for all quality evils.
It cannot be used to all production process.
It involves mathematical & statistical problems in the process
of analysis & interpretation of variations in quality.
Provides only an information services.
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46. Conclusions
1. SQC is a series of tools used to identify the variation and quality of products
and services, which means QUALITY IMPROVEMENT
2. There are two types of causes of bad quality assignable and chance causes.
3. A control Chart can be used to detect assignable causes.
4. For variables such quantities a X-bar, R, S, are used.
5. For attributes a chart such as P and U, and C charts are used.
6. This is useful in sampling process, which can be done simple, double or
multiple
7. This are not the only tools available we have:
Histogram
Pareto Chart
Cause and Effect Diagram
Defect Concentration Diagram
Control Chart
Scatter Diagram
Check Sheet
More…
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