Statistical quality control presentation

Submitted by
Raju Kumar Sharma
Suchitra Sahu
Mayank Bisht
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Statistical Quality Control (SQC)
Submitted to
Prof. I Ajit Kumar Reddy
National Institute of Technology, Warangal
Telangana State, 506004

What is Statistical Quality Control??
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 A method of quality control which uses statistical methods.
 a collection of strategies, techniques, and actions taken by an organization
to ensure they are producing a quality product or providing a quality service.
 The objective of statistical quality control is to monitor production through
many stages of manufacturing
 The general category of statistical tools used to evaluate organizational
quality.

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Walter Andrew Shewhart (1891-1967)
US Physicist and Statistician
Father of Statistical Quality Control

Introduction
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 Statistics:
Statistics means the good amount of data to obtain reliable results. Its
techniques find extensive applications in quality control, production
planning and control, business charts, linear programming etc.
 Quality:
Quality is a relative term and is generally explained with reference to the
end use of the product. Quality is thus defined as fitness for purpose
(defined by Juran)
 Control:
Control is a system for measuring and checking or inspecting a
phenomenon. It suggests when to inspect, how often to inspect and how
much to inspect, how often to inspect

SQC : Three broad categories
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 Descriptive statistics Statistics used to describe quality characteristics
and relationships.
 Statistical process control (SPC) A statistical tool that involves
inspecting a random sample of the output from a process and deciding
whether the process is producing products with characteristics that fall
within a predetermined range.
 Acceptance sampling the process of randomly inspecting a sample of
goods and deciding whether to accept the entire lot based on the results.

Sources Of Variation: Common And Assignable Causes
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 Common causes of Variation Random causes that cannot be identified.
 Assignable causes of variation Causes that can be identified and
eliminated.
Descriptive statistics
 Descriptive statistics can be helpful in describing certain characteristics of
a product and a process.
 The most important descriptive statistics are measures of central tendency
such as the mean, measures of variability such as the standard
deviation and range, and measures of the distribution of data.

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The Mean
A statistic that measures the central tendency of a set of data.
where x = the mean
xi =observation i= 1, . . . , n
n =number of observations
The Range and Standard Deviation
 Range The difference between the largest and smallest observations in a
set of data.
 Standard deviation A statistic that measures the amount of data
dispersion around the mean.
where ϭ = standard deviation of a sample
x = the mean
xi = observation i = 1, . . . , n
n = the number of observations in the sample

Distribution of Data
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o A third descriptive statistic used to measure quality characteristics is the
shape of the distribution of the observed data.
o When a distribution is symmetric, there are the same number of
observations below and above the mean.
o This is what we commonly find when only normal variation is present in
the data.
o When a disproportionate number of observations are either above or
below the mean, we say that the data has a skewed distribution.

Histogram
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 A histogram is a graphical representation of the distribution of
numerical data. It is an estimate of the probability distribution of a
continuous variable (quantitative variable) and was first introduced
by Karl Pearson

Pareto Chart
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 A Pareto chart, named after Vilfredo Pareto, is a type of chart that
contains both bars and a line graph, where individual values are
represented in descending order by bars, and the cumulative total is
represented by the line.

Fish-Bone Chart
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 This diagram is useful to help organize ideas and to identify relationships.
The usual approach to a fishbone diagram is to consider four
problem areas, namely, methods, materials, equipment, and
personnel The effect is usually a particular problem, or perhaps a
goal, and it is shown.

Cause-and-Effect Diagram
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 A graphic tool that helps identify, sort, and display possible causes of
a problem or quality characteristic

Defect Concentration Diagram
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The defect concentration diagram (also problem concentration diagram) is a graphical tool that is
useful in analyzing the causes of the product or part defects. It is a drawing of the product (or other
item of interest), with all relevant views displayed, onto which the locations and frequencies of
various defects are shown.

Developing Control Charts
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 A control chart (also called process chart or quality control chart) is a
graph that shows whether a sample of data falls within the common or
normal range of variation. The common range of variation is defined by
the use of control chart limits.
 We say that a process is out of control when a plot of data reveals that
one or more samples fall outside the control limits.
 The center line (CL) of the control chart is the mean, or average.
 The upper control limit (UCL) is the maximum acceptable variation.
 The lower control limit (LCL) is the minimum acceptable variation

Control chart A graph that shows whether a sample of data falls within the
common or normal range ofvariation.
Out of control The situation in which a plot of data falls outside preset control
limits.
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Types of Control Charts
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 Variable A product characteristic that can be measured and has
continuum of values (e.g., eight, weight, or volume).
 x-bar chart
 Range (R) chart
 Attribute A product characteristic tha has a discrete value and can be
counted.
 P-chart
 C-chart

Mean (x-Bar) Charts
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A mean control chart is often referred to as an x-bar chart. It is used to
monitor changes in the mean of a process
To construct the upper and lower control limits of the chart, we use the
following formulas
 Where X = the average of the sample means
 z = standard normal variable (2 for 95.44% confidence, 3 for 99.74% confidence)
 ϭ x = standard deviation of the distribution of sample means, computed as
 ϭ = population (process) standard deviation
 n = sample size (number of observations per sample)

Constructing a Mean (x-Bar) Chart:
Statistical Software, Inc., offers a toll-free number where customers can call from 7 A.M. until 11 P.M. daily with
problems involving the use of their products. It is impossible to have every call answered immediately by a
technical representative, but it is important customers do not wait too long for a person to come on the line.
Customers become upset when they hear the message “Your call is important to us. The next available
representative will be with you shortly” too many times. Statistical Software decides to develop a control chart
describing the total time from when a call is received until the representative answers the caller’s question.
Yesterday, for the 16 hours of operation, five calls were sampled each hour.
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Based on this information, develop a control chart for the mean duration
of the call. Does there appear to be a trend in the calling times? Is there
any period in which it appears that customers wait longer than others?
(Given: A2 = 0.577)

Range (R) Charts
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 A control chart that monitors changes in the dispersion or variability
of process.
 Range (R) charts are another type of control chart for variables.
Whereas x-bar charts measure shift in the central tendency of the
process, range charts monitor the dispersion or variability of the
process.

Constructing a R- Chart:
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 The length of time customers of Statistical Software, Inc. waited from the time their call was answered until a
technical representative answered their question or solved their problem is recorded in above table. Develop a
control chart for the range. Does it appear that there is any time when there is too much variation in the
operation? (Given: D3 = 0 and D4 = 2.115)
13.483
0.0

P-Charts
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A control chart that monitors the proportion of defects in a sample. P-charts are
used to measure the proportion that is defective in a sample.
Where
z = standard normal variable
P = the sample proportion defective
ϭp = the standard deviation of the average proportion defective
Where n is the sample size

Constructing a P- Chart:
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 The Credit Department at Global National Bank is responsible for entering
each transaction charged to the customer’s monthly statement. Of course,
accuracy is critical and errors will make the customer very unhappy! To
guard against errors, each data entry clerk rekeys a sample of 1500 of their
batch of work a second time and a computer program checks that the
numbers match. The program also prints a report of the number and size of
any discrepancy. Seven people were working last hour and here are their
results:
Inspector Number Inspected Number Mismatched
Mullins 1500 4
Rider 1500 6
Gankowski 1500 6
Smith 1500 2
Reed 1500 15
White 1500 4
Reading 1500 4

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So, from the above plot, we find the process is not under control and
‘Reed’ must be given some additional training or must be
transferred to some other department
0.00267
0.004 0.004
0.00133
0.01
0.00267
0.00267
0
0.002
0.004
0.006
0.008
0.01
0.012
mullins rider Gankowski smith reed white reading
U.C.L = 0.0087
L.C.L = 0

C-Charts
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A control chart used to monitor the number of defects per unit.
Examples are the number of returned meals in a restaurant
Example:
The publisher of the Oak Harbour Daily Telegraph is concerned about the number of misspelled words
in the daily newspaper. They do not print a paper on Saturday or Sunday. In an effort to control the
problem and promote the need for correct spelling, a control chart is to be instituted. The number of
misspelled words found in the final edition of the paper for the last 10 days is: 5, 6, 3, 0, 4, 5, 1, 2, 7,
and 4. Determine the appropriate control limits and interpret the chart. Were there any days during the
period that the number of misspelled words was out of control?

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 Process capability The ability of a production process to meet or excee
preset specifications.
 Product specifications Preset ranges of acceptable quality characteristics
 Measuring Process Capability
Simply setting up control charts to monitor whether a process is in control
does not guarantee process capability.
To produce an acceptable product, the process must be capable and in
control before production begins.
Process capability index
An index used to measure process capability.

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 Cp =1: A value of Cp equal to 1 means that the process variability just
meets specifications.
 Cp ≤ 1: A value of Cp below 1 means that the process variability is outside
the range of specification. This means that the process is not capable of
producing within specification and the process must be improved.
 Cp ≥ 1: A value of Cp above 1 means that the process variability is tighter
than specifications and the process exceeds minimal capability

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Problem:
Three bagging machines at the Crunchy Potato Chip Company are being evaluated for their capability.
The following data are recorded:
If specifications are set between 12.35 and 12.65 ounces, determine which of the machines are capable of
producing within specification.

Acceptance Sampling
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 The third branch of SQC refers to the process of randomly inspecting a
certain number of items from a lot or batch in order to decide whether to
accept or reject the entire batch
 Different from SPC because acceptance sampling is performed either before
or after the process rather than during
Sampling before typically is done to supplier material
Sampling after involves sampling finished items before shipment or
finished components prior to assembly
 Used where inspection is expensive, volume is high, or inspection is
destructive

Sampling Plans
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Goal of Acceptance Sampling plans is to determine the criteria for
acceptance or rejection based on:
Size of the lot (N)
Size of the sample (n)
Number of defects above which a lot will be rejected (c)
Level of confidence we wish to attain
 There are single, double, and multiple sampling plans
Which one to use is based on cost involved, time consumed, and cost
of passing on a defective item
 Can be used on either variable or attribute measures, but more
commonly used for attributes

Operating Characteristics (OC) Curves
• OC curves are graphs which show the
probability of accepting a lot given
various proportions of defects in the lot
• X-axis shows % of items that are
defective in a lot- “lot quality”
• Y-axis shows the probability or chance of
accepting a lot
• As proportion of defects increases, the
chance of accepting lot decreases
• Example: 90% chance of accepting a lot
with 5% defectives; 10% chance of
accepting a lot with 24% defectives
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AQL, LTPD, Consumer’s Risk (α) & Producer’s Risk
(β)
• AQL is the small % of defects that
consumers are willing to accept; order
of 1-2%
• LTPD is the upper limit of the
percentage of defective items
consumers are willing to tolerate
• Consumer’s Risk (α) is the chance of
accepting a lot that contains a greater
number of defects than the LTPD limit;
Type II error
• Producer’s risk (β) is the chance a lot
containing an acceptable quality level
will be rejected; Type I error
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OC Curve:
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• Lets develop an OC curve for a
sampling plan in which a sample of 5
items is drawn from lots of N=1000
items
• The accept /reject criteria are set up in
such a way that we accept a lot if no
more that one defect (c=1) is found
• Using Table and the row
corresponding to n=5 and x=1
• Note that we have a 99.74% chance of
accepting a lot with 5% defects and a
73.73% chance with 20% defects

Average outgoing quality
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Average outgoing quality(AOQ) The expected proportion of defective items
that will be passed to the customer under the sampling plan.
Where
Pac = probability of accepting a given lot
p = proportion of defective items in a lot
N = the size of the lot
n = the sample size chosen for inspection
Usually we assume the fraction in the previous equation to equal 1 and simplify the equation to the
following form:
AOQ = (Pac)p

Implications for Managers
• How much and how often to inspect?
• Consider product cost and product volume
• Consider process stability
• Consider lot size
• Where to inspect?
• Inbound materials
• Finished products
• Prior to costly processing
• Which tools to use?
• Control charts are best used for in-process production
• Acceptance sampling is best used for inbound/outbound
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SQC in Services
• Service Organizations have lagged behind manufacturers in the use of
statistical quality control
• Statistical measurements are required and it is more difficult to measure
the quality of a service
• Services produce more intangible products
• Perceptions of quality are highly subjective
• A way to deal with service quality is to devise quantifiable measurements
of the service element
• Check-in time at a hotel
• Number of complaints received per month at a restaurant
• Number of telephone rings before a call is answered
• Acceptable control limits can be developed and charted
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OM Across the
Organization
SQC requires input from other organizational functions, influences their
success, and used in designing and evaluating their tasks
Marketing – provides information on current and future quality standards
Finance – responsible for placing financial values on SQC efforts
Human resources – the role of workers change with SQC implementation.
Requires workers with right skills
Information systems – makes SQC information accessible for all.
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Benefits of Statistical Quality Control
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 It provides a means of detecting error at inspection.
 It leads to more uniform quality of production.
 It improves the relationship with the customer.
 It reduces inspection costs.
 It reduces the number of rejects and saves the cost of material.
 It provides a basis for attainable specifications.
 It points out the bottlenecks and trouble spots.
 It provides a means of determining the capability of the manufacturing
process.
 It promotes the understanding and appreciation of quality control.

Statistical quality control presentation

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