The seven tools of quality – Statistical Fundamentals – Measures of central Tendency and Dispersion, Population and Sample, Normal Curve, Control Charts for variables Xbar and R chart and attributes P, nP, C, and u charts, Industrial Examples, Process capability, Concept of six sigma – New seven Management tools.

1. Presented by
Dr. R. RAJA, M.E., Ph.D.,
Assistant Professor, Department of EEE,
Muthayammal Engineering College, (Autonomous)
Namakkal (Dt), Rasipuram – 637408
16EEE20 -TOTAL QUALITY MANAGEMENT
MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC, NBA & Affiliated to Anna University),
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu.
Unit-III Statistical Process Control (SPC)

2. Unit-III Statistical Process Control (SPC)
The seven tools of quality – Statistical Fundamentals – Measures of central
Tendency and Dispersion, Population and Sample, Normal Curve, Control Charts for
variables Xbar and R chart and attributes P, nP, C, and u charts, Industrial Examples,
Process capability, Concept of six sigma – New seven Management tools.
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3. The Seven Tools of Quality
"The Old Seven." "The First Seven." "The Basic Seven."
Quality pros have many names for these seven basic tools of quality, first
emphasized by Kaoru Ishikawa, a professor of engineering at Tokyo University and
the father of "quality circles." Start your quality journey by mastering these tools,
and you'll have a name for them too: indispensable.
 Cause-and-effect diagram (also called Ishikawa or fishbone diagrams):
Identifies many possible causes for an effect or problem and sorts ideas into
useful categories.
 Check sheet: A structured, prepared form for collecting and analyzing data; a
generic tool that can be adapted for a wide variety of purposes.
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 Control chart: Graph used to study how a process changes over time.
Comparing current data to historical control limits leads to conclusions about
whether the process variation is consistent (in control) or is unpredictable (out
of control, affected by special causes of variation).
 Histogram: The most commonly used graph for showing frequency
distributions, or how often each different value in a set of data occurs.
 Pareto chart: A bar graph that shows which factors are more significant.
 Scatter diagram: Graphs pairs of numerical data, one variable on each axis, to
look for a relationship.
 Stratification: A technique that separates data gathered from a variety of
sources so that patterns can be seen (some lists replace stratification with
flowchart or run chart).
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5. Statistical Fundamentals
 Every day, you encounter numerical information that describes or an alyzes
some aspect of the world you live in. For example, here are some news items
that appeared in the pages of The New York Times during a one-month period:
 Between 1969 and 2001, the rate of forearm fractures rose 52% for girls and
32% for boys, with the largest increases among children in early puberty,
according to a recent Mayo Clinic study.
 Across the New York metropolitan area, the median sales price of a single
family home has risen by 75% since 1998, an increase of more than$140,000.
 Astudy that explored the relationship between the price of a book and the
number of copies of a book sold found that raising prices by 1%reduced sales
by 4% at BN.com, but reduced sales by only 0.5% atAmazon.com.
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 Such stories as these would not be possible to understand without statistics, the
branch of mathematics that consists of methods of processing and analyzing
data to better support rational decision-making processes.
 Using statistics to better understand the world means more than just producing a
newest of numerical information you must interpret the results by reflecting on
the significance and the import process you face.
 Interpretation also means knowing when to ignore results, either because they
are misleading, are produced by incorrect methods, or just restate the obvious,
as this news story “reported” by the comedian David Letterman illustrates.
“USA Today has come out with a new survey. Apparently,
3 out of every 4 people make up 75% of the population”
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 As newer technologies allow people to process and analyze ever increase in
amounts of data, statistics plays an increasingly important part of many decision
making processes today.
 Reading this chapter will help you understand the fundamentals of statistics and
introduce you to concepts that are used throughout this book.
The Five Basic Words of Statistics
 The five words population, sample, parameter, statistic(singular), and variable
form the basic vocabulary of statistics.
 You cannot learn much about statistics unless you first learn the meanings of
these five words
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The five words population, sample, parameter, statistic(singular), and variable form
the basic vocabulary of statistics.
You cannot learn much about statistics unless you first learn the meanings of these
five words.
Population
 All the members of a group about which you want to draw a conclusion.
Sample
 The part of the population selected for analysis
Parameter
 A numerical measure that describes a characteristic of a population.
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Statistic
 A numerical measure that describes a characteristic of a sample.
 Calculating statistics for a sample is the most common activity, because
collecting population data is impractical for most actual decision making
situations.
Variable
 A characteristic of an item or an individual
 All the variables taken together form the data of an analysis. Although you may
have heard people saying that they are analyzing their data, they are, more
precisely, analyzing their variables.
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Variables can be divided into the following types.
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Categorical Variables Numerical Variables
Concept The values of these variables
are selected from an
established list of categories.
The values of these variables
involve a counted or measured
value.
Subtypes None. Discrete values are counts of
things. Continuous values are
measures, and any value can
theoretically occur, limited only
by the precision of the measuring
process.

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Branches of Statistics
 Two branches, descriptive statistics and inferential statistics, comprise the field
of statistics.
Descriptive Statistics
 The branch of statistics that focuses on collecting, summarizing, and presenting
a set of data.
Inferential Statistics
 The branch of statistics that analyzes sample data to draw conclusions about a
population.
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Sources of Data
 All statistical analysis begins by identifying the source of the data.
 Among the important sources of data are published sources, experiments, and
surveys.
Published Sources
 Data available in print or in electronic form, including data found on Internet
Web sites.
 Primary data sources are those published by the individual or group that
collected the data.
 Secondary data sources are those compiled from primary sources.
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Experiments
 A process that studies the effect on a variable of varying the value(s) of another
variable or variables, while keeping all other things equal. A typical experiment
contains both a treatment group and a control group. The treatment group
consists of those individuals or things that receive the treatment(s) being
studied. The control group consists of those individuals or things that do not
receive the treatment(s) being studied
Surveys
 A process that uses questionnaires or similar means to gather values for the
responses from a set of participants
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Sampling Concepts
Sampling
 The process by which members of a population are selected for a sample.
Probability Sampling
 A sampling process that takes into consideration the chance of occurrence of
each item being selected. Probability sampling increases your chances that the
sample will be representative of the population.
Simple Random Sampling
 The probability sampling process in which every individual or item from a
population has the same chance of selection as every other individual or item.
Every possible sample of a certain size has the same chance of being selected as
every other sample that has that size.
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Frame
 The list of all items in the population from which samples will be selected.
Sample Selection Methods
 Proper sampling can be done with or without replacement.
Sampling With Replacement
 Sampling method in which each selected item is returned to the frame from
which it was selected so that it has the same probability of being selected again.
Sampling Without Replacement
 Sampling method in which each selected item is not returned to the frame from
which it was selected. Using this technique, an item can be selected no more
than one time.
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16. Measures of Central Tendency and Dispersion
Overview:
 A partial description of the joint distribution of the data is provided here. Three
aspects of the data are of importance, the first two of which you should already
be familiar with from univariate statistics. These are:
Central Tendency: What is a typical value for each variable?
Dispersion: How far apart are the individual observations from a central value for a
given variable?
Association: This might (or might not!) be a new measure for you. When more than
one variable are studied together, how does each variable relate to the remaining
variables? How are the variables simultaneously related to one another? Are they
positively or negatively related?
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Measures of Central Tendency
Throughout this course, we’ll use the ordinary notations for the mean of a variable.
That is, the symbol is used to represent a (theoretical) population mean and the
symbol is used to represent a sample mean computed from observed data. In the
multivariate setting, we add subscripts to these symbols to indicate the specific
variable for which the mean is being given.
 For instance, represents the population mean for variable denotes
a sample mean based on observed data for variable
 The population mean is the measure of central tendency for the population.
Here, the population mean for variable j is
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 The notation E stands for statistical expectation; here E(Xj) is the mean of Xj
over all members of the population, or equivalently, overall random draws from
a stochastic model. For example, mj=E(Xj) may be the mean of a normal
variable.
 The population mean mj for variable j can be estimated by the sample mean
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Note that the squared residual is a function of the random variable .
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Variance
A variance measures the degree of spread (dispersion) in a variable’s values.
Theoretically, a population variance is the average squared difference between a
variable’s values and the mean for that variable. The population variance for variable
Xj is

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 Note that the squared residual is a function of the random variable Xj .
 Therefore, the squared residual itself is random and has a population mean.
 The population variance is thus the population mean of the squared residual.
 We see that if the data tend to be far away from the mean, the squared residual
will tend to be large, and hence the population variance will also be large.
 Conversely, if the data tend to be close to the mean, the squared residual will
tend to be small, and hence the population variance will also be small.
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 The first expression in this formula is most suitable for interpreting the sample
variance.
 We see that it is a function of the squared residuals; that is, take the difference
between the individual observations and their sample mean, and then square the
result.
 Here, we may observe that if observations tend to be far away from their sample
means, then the squared residuals and hence the sample variance will also tend
to be large.
 If on the other hand, the observations tend to be close to their respective sample
means, then the squared differences between the data and their means will be
small, resulting in a small sample variance value for that variable.
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 The last part of the expression above gives the formula that is most suitable for
computation, either by hand or by a computer! Since the sample variance is a
function of the random data, the sample variance itself is a random quantity,
and so has a population mean. In fact, the population mean of the sample
variance is equal to the population variance:
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26. Population and Sample
What Is Population?
 In statistics, a population is the entire pool from which a statistical sample is
drawn. A population may refer to an entire group of people, objects, events,
hospital visits, or measurements.
 A population can thus be said to be an aggregate observation of subjects
grouped together by a common feature.
 Unlike a sample, when carrying out statistical analysis on a population, there
are no standard errors to report that is, because such errors inform analysts
using a sample how far their estimate may deviate from the true population
value. But since you are working with the true population you already know the
true value.
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The Basics of Population
 A population can be defined by any number of characteristics within a group that
statisticians use to draw conclusions about the subjects in a study. A population
can be vague or specific. Examples of population (defined vaguely) include the
number of newborn babies in North America, total number of tech startups in
Asia, average height of all CFA exam candidates in the world, mean weight of
U.S. taxpayers and so on.
 Population can also be defined more specifically, such as the number of newborn
babies in North America with brown eyes, the number of startups in Asia that
failed in less than three years, the average height of all female CFA exam
candidates, mean weight of all U.S. taxpayers over 30 years of age, among others.
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 Most times, statisticians and researchers want to know the characteristics of
every entity in a population, so as to draw the most precise conclusion possible.
This is impossible or impractical most times, however, since population sets
tend to be quite large.
 For example, if a company wanted to know whether each of its 50,000
customers serviced during the year was satisfied, it might be challenging,
costly and impractical to call each of the clients on the phone to conduct
a survey. Since the characteristics of every individual in a population cannot be
measured due to constraints of time, resources, and accessibility, a sample of
the population is taken.
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Population Samples
 A sample is a random selection of members of a population.
 It is a smaller group drawn from the population that has the characteristics of
the entire population.
 The observations and conclusions made against the sample data are attributed to
the population.
 The information obtained from the statistical sample allows statisticians to
develop hypotheses about the larger population.
 In statistical equations, population is usually denoted with an uppercase N while
the sample is usually denoted with a lowercase n.
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Population Parameters
 A parameter is data based on an entire population. Statistics such as averages
and standard deviations, when taken from populations, are referred to as
population parameters.
 The population mean and population standard deviation are represented by the
Greek letters µ and σ, respectively.
 The standard deviation is the variation in the population inferred from the
variation in the sample.
 When the standard deviation is divided by the square root of the number of
observations in the sample, the result is referred to as the standard error of the
mean.
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 While a parameter is a characteristic of a population, a statistic is a
characteristic of a sample.
 Inferential statistics enables you to make an educated guess about a population
parameter based on a statistic computed from a sample randomly drawn from
that population.
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Real World Example of Population
 For example, let's say a denim apparel manufacturer wants to check the quality
of the stitching on its blue jeans before shipping them off to retail stores.
 It is not cost effective to examine every single pair of blue jeans the
manufacturer produces (the population).
 Instead, the manufacturer looks at just 50 pairs (a sample) to draw a conclusion
about whether the entire population is likely to have been stitched correctly.
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33. Normal Curve
Normal Curve or Normal Distribution (Bell Curve)
What are the properties of the normal distribution?
 The normal distribution is a continuous probability distribution that is symmetrical on
both sides of the mean, so the right side of the center is a mirror image of the left side.
 The area under the normal distribution curve represents probability and the total area
under the curve sums to one.
 Most of the continuous data values in a normal distribution tend to cluster around the
mean, and the further a value is from the mean, the less likely it is to occur. The tails
are asymptotic, which means that they approach but never quite meet the horizon (i.e.
x-axis).
 For a perfectly normal distribution the mean, median and mode will be the same value,
visually represented by the peak of the curve.
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 The normal distribution is often called the bell curve because the graph of its
probability density looks like a bell. It is also known as called Gaussian distribution,
after the German mathematician Carl Gauss who first described it.

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Why is the normal distribution important?
The bell-shaped curve is a common feature of nature and psychology
 The normal distribution is the most important probability distribution in
statistics because many continuous data in nature and psychology displays this
bell-shaped curve when compiled and graphed.
 For example, if we randomly sampled 100 individuals we would expect to see a
normal distribution frequency curve for many continuous variables, such as IQ,
height, weight and blood pressure.
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Parametric significance tests require a normal distribution of the samples' data
points
 The most powerful (parametric) statistical tests used by psychologists require
data to be normally distributed. If the data does not resemble a bell curve
researchers may have to use a less powerful type of statistical test, called non-
parametric statistics.
Converting the raw scores of a normal distribution to z-scores
 We can standardized the values (raw scores) of a normal distribution by
converting them into z-scores.
 This procedure allows researchers to determine the proportion of the values that
fall within a specified number of standard deviations from the mean (i.e.
calculate the empirical rule).
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Probability and the normal curve: What is the empirical rule formula?
 The empirical rule in statistics allows researchers to determine the proportion of
values that fall within certain distances from the mean. The empirical rule is
often referred to as the three-sigma rule or the 68-95-99.7 rule.
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 If the data values in a normal distribution are converted to z-scores in a standard
normal distribution the empirical rule describes the percentage of the data that
fall within specific numbers of standard deviations (σ) from the mean (μ) for
bell-shaped curves.
 The empirical rule allows researchers to calculate the probability of randomly
obtaining a score from a normal distribution.
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 68% of data falls within the first standard deviation from the mean. This means
there is a 68% probability of randomly selecting a score between -1 and +1
standard deviations from the mean.

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 95% of the values fall within two standard deviations from the mean. This means
there is a 95% probability of randomly selecting a score between -2 and +2
standard deviations from the mean.

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 99.7% of data will fall within three standard deviations from the mean. This
means there is a 99.7% probability of randomly selecting a score between -3
and +3 standard deviations from the mean.
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How can I check if my data follows a normal distribution?
 Statistical software (such as SPSS) can be used to check if your dataset is
normally distributed by calculating the three measures of central tendency.
 If the mean, median and mode are very similar values there is a good chance
that the data follows a bell-shaped distribution (SPSS command here).
 It is also advisable to a frequency graph too, so you can check the visual shape
of your data (If your chart is a histogram, you can add a distribution curve using
SPSS: From the menus choose: Elements > Show Distribution Curve).
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 Normal distributions become more apparent (i.e. perfect) the finer the level of
measurement and the larger the sample from a population.
 You can also calculate coefficients which tell us about the size of the
distribution tails in relation to the bump in the middle of the bell curve. For
example, Kolmogorov Smirnov and Shapiro Wilk tests can be calculated using
SPSS.
 These tests compare your data to a normal distribution and provide a p-value,
which if significant (p < .05) indicates your data is different to a normal
distribution (thus, on this occasion we do not want a significant result and need
a p-value higher than 0.05).
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46. Control Charts for variables Xbar and R chart and
attributes P, nP, C, and u charts
1. Variables Control Charts
1.1. X bar chart using R chart or X bar chart using s chart
 The X bar chart indicates the changes that have occured in the central tendency
of a process. These changes might be due to such factors as tool wear, or new
and stronger materials.
 R chart values or s chart values indicate that a gain or loss in dispersion has
occured.
 Such change might be due to worn bearings, a loose tool, an erratic flow of
lubricants to a machine or sloppines on the part of the machine operator.
 The two types of charts go hand in hand when monitoring variables, because
they measure the two critical parameters: central tendency and dispersion.
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1.2. X & MR (moving range) chart
 An X & MR chart is used when only one observation per subgroup is taken and
process variability needs to be determined.
 The moving range (MR) is used to estimate variation.
Examples include but are not limited to:
 Destructive sampling
 Testing of the process characteristics is costly
 Long production times
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2. Attributes Control Charts
2.1. The p chart
 The p chart is for the fraction of defective items in a sample.
 The fraction defective is the number of defective items in a sample divided by
the total number of items in a sample.
 The fraction defective chart is used when the sample size varies. If we have a
high percentage of good items, say 99%, the fraction defective is small, 0.01. In
order to get any defectives in as sample from a high quality population, the
sample size must be large.
 In many cases the sample size is all the daily production. In this situation the
sample size will vary from day to day. The only statistical measure of quality
would be the fraction rejected.
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2.2. The np chart
 The np chart is for the number of defective items in a sample.
 The number of defective, np, chart shows the number of defective items in
samples rather than the fraction of defective items.
 It requires that the sample size remains constant.
 It has two benefits over the p chart: there is no calculation required of each
sample result; it easier for some people to understand.
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2.3. The c chart
 The c chart is for the number of defects in an item.
 The number of defects, c, chart is based on the Poisson distribution. It is a plot
of the number of defects in items.
 The item may be a given length of steel bar, a welded tank, a bolt of cloth and
so on. For the control chart, the size of the item must be constant.
 If the chart is for the number of defects in a bolt of cloth, all the cloths must be
of the same size.
 The c chart can also be used for the number of defects in a fixed number of
items. The number of defects per 10 bolts of cloth can be plotted on c charts just
as well as the number of defects per single roll. The essential factor for using c
charts is that each sample has the same opportunity for defects.
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2.4. The u chart
 The u chart is for the number of defects in a sample.
 The symbol u is used to represent defects per unit.
 The u chart is used in cases where the samples are of different size.
 If the sample size varies significantly, each sample value must be plotted within
its own u chart limits.
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52. Industrial Examples - Process capability
What is Process Capability?
 Process capability is defined as a statistical measure of the inherent process
variability of a given characteristic. You can use a process-capability study to
assess the ability of a process to meet specifications.
 During a quality improvement initiative, such as Six Sigma, a capability
estimate is typically obtained at the start and end of the study to reflect the level
of improvement that occurred.
 Several capability estimates are in widespread use, including:
 Potential capability (Cp) and actual capability during production (Cpk) are
process capability estimates. Cp and Cpk show how capable a process is of
meeting its specification limits, used with continuous data.
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 They are valuable tools for evaluating initial and ongoing capability of parts
and processes.
 "Sigma" is a capability estimate typically used with attribute data (i.e., with
defect rates).
 Capability estimates like these essentially reflect the nonconformance rate of a
process by expressing this performance in the form of a single number.
 Typically this involves calculating some ratio of the specification limits to
process spread.
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Assessing Process Capability
 Assessing process capability is not easy. Some textbooks teach users to wait
until the process reaches equilibrium, take roughly 30 samples and calculate
their standard deviation; however, it is difficult to know when the process
reaches a state of equilibrium and if the recommended samples are
representative of the process. The measurement of process capability is more
complicated than that.
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For example, suppose you have a rotary tablet press that produces 30 tablets, one
from each of 30 pockets per rotation. If you’re interested in tablet thickness, you
might want to base your estimate of process capability on the standard deviation
calculated from 30 consecutive tablets. Better yet, you might assure representation
by taking those 30 consecutive tablets repeatedly over eight time periods spaced
evenly throughout a production run (Table 1). You would pool the eight individual
standard deviations yielding a thickness capability estimate based on (8 X (30 - 1)) =
232 degrees of freedom.
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 For greater assurance yet, you might want to include several production runs
with perhaps fewer sampling times per production run.
 Estimates of the process capability made this way would be representative and
independent of process mean changes that might take place from one sampling
time to the next.
 Because the pooled, within-group standard deviation is calculated on
observations taken close together in time, there is no opportunity for it to be
contaminated by assignable sources of variation.
 It is as close to pure capability as you’re likely to get.
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Practical Concerns when Conducting Capability Studies
 There are both positive and negative aspects to capability estimates. For
example, Cp and Cpk estimates are highly sensitive to the assumption that one is
sampling from a normal distribution that is, most of the data points are
concentrated around the average (mean), forming a bell shaped curve.
 Furthermore, sampling from a stable system is essential to obtaining meaningful
estimates of process performance for future production.
 Many quality practitioners report solely the numerical values of the capability
estimates. Others, however, note that the capability estimates are themselves
merely statistics, or point estimates of the true capability of a process. As such,
the use of confidence intervals for the true capability values may also be
reported.
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 When sampling from stable, but non-normal distributions, other strategies to
obtain meaningful capability estimates may be appropriate, including:
 Transforming the data to be approximately well modeled by a Normal
distribution.
 Using an alternative probability distribution, such as Weibull or lognormal
distributions.
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59. Industrial Examples - Concept of six sigma
How Six Sigma is Used in Different Industries.
 Originating with Motorola in the 1980s, Six Sigma initially focused on
eliminating defects in manufacturing processes.
 It worked. Motorola reported record profits. Other companies soon followed.
Nothing breeds success quite like success.
 But as Six Sigma became familiar to more organizations, it eventually was
adopted by some for work outside of manufacturing.
 Software engineering and technology firms began using some of its practices.
More mature industries, such as healthcare and energy, also have implemented
Six Sigma.
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 The creation of Lean, a complementary methodology with Six Sigma, attracted
even more companies. Lean focuses on creating value for customers and
eliminating wasted steps in a process.
 It also emphasizes working quickly. Nonprofit and government organizations
have adopted Lean methods to squeeze productivity out of every bit of money
they receive.
 The following looks at some of the industries that use Six Sigma, Lean or a
combination of the two.
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Healthcare
 Healthcare faces unique challenges. Large hospitals are incredibly complex. The
daily challenges involve many different processes. Just creating a proper
schedule for healthcare workers that maximizes productivity and doesn’t
overwork nurses and other staff members is daunting.
 But they also work under complex government and industry regulations, deal
with technology issues involving patient records, buy and maintain sophisticated
medical machinery and must ensure safety for all employees, patients and
visitors.
 Healthcare also is a mature industry where things have been done a certain way
for decades.
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 Change can prove difficult. A 2017 HealthLeaders Media Patient Experience
survey found that the main stumbling block to implementing healthcare is
changing the culture.
 Yet the study also found 87% of healthcare organizations saw improvements in
patient scores after implementing process improvement methodologies.
 Pharmaceutical companies also have turned to practices such as quality by
design to ensure the best results in manufacturing drugs, including meeting
safety standards and product effectiveness.
 Here are some examples of the ways companies have adopted Lean Six Sigma
in healthcare.
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Software
 Technology companies striving to remain competitive in a constantly evolving
market must focus on efficient processes and speed-to-market. Worldwide,
many have implemented process improvement, including Lean and Six Sigma.
 One early adaptor was Wipro. In 1997, the company began implementing Six
Sigma into every phase of the business, including software and hardware
development, according to the Community for Human Resource Management.
Initial results included a 91% on-time project completion rate as compared to
the industry average of only 55% at the time. In the years since, many
companies have incorporated Lean, which allows for continuous improvements
while keeping the experience of end users in mind.
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Oil and Gas
 Another mature industry turning to Six Sigma is the oil and gas industry. With
the overall industry facing a downturn in recent years, Six Sigma
methodologies have helped keep some businesses profitable in tighter economic
times.
 One example is Colorado-based UECompression, which uses Lean Six Sigma
to reduce process cycle time and improve the quality of its air and gas
compression products, according to Boss Magazine.
 With a global market for its products, the company uses Lean Six Sigma to
identify and eliminate defects in production and supply chain.
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Government
 Six Sigma has also caught the attention of government leaders, especially those
trying to maintain quality services in areas where tax revenue is down.
 One example is Kern County in California. Faced with declining tax revenue
from the oil and gas industry in and around the county seat of Bakersfield, the
county has started an ambitious project to introduce Lean into many county
departments. The county has even created a website about its initiative to keep
taxpayers informed. There, people can view individual projects, including one
such project completed by the Treasure-Tax Collector’s office. After realizing a
growing issue with incorrect and duplicate payments, the department redesigned
payment forms with the consumer in mind. The result, a projected savings of
nearly $120,000 in labor costs.
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66. New Seven Management Tools.
The Seven New Management and Planning Tools
 New management planning tools are defined as the method(s) for achieving
expected outcomes that previously have not been used.
 In 1976, the Union of Japanese Scientists and Engineers (JUSE) saw the need
for tools to promote innovation, communicate information, and successfully
plan major projects. A team researched and developed these seven new quality
control tools, often called the seven management and planning tools, or simply
the seven management tools:
Affinity diagram: Organizes a large number of ideas into their natural relationships.
Interrelationship diagram: Shows cause-and-effect relationships and helps analyze
the natural links between different aspects of a complex situation.
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Tree diagram: Breaks down broad categories into finer and finer levels of detail,
helping to move step-by-step thinking from generalities to specifics.
Matrix diagram: Shows the relationship between two, three, or four groups of
information and can give information about the relationship, such as its strength, the
roles played by various individuals, or measurements.
Matrix data analysis: A complex mathematical technique for analyzing matrices,
often replaced by the similar prioritization matrix. A prioritization matrix is an L-
shaped matrix that uses pairwise comparisons of a list of options to a set of criteria in
order to choose the best option(s).
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Arrow diagram: Shows the required order of tasks in a project or process, the best
schedule for the entire project, and potential scheduling and resource problems and
their solutions.
Process decision program chart: Systematically identifies what might go wrong in
a plan under development.
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69. Thank You
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