Chance or Common Causes of Variability

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• Chance or Common Causes of Variability
• Chance causes or common causes are numerous small
  causes of variability that are inherent to a
  system or process and operate randomly or by
  chance.
• At any time, numerous factors affect a system or
  process, causing variability. Most of these are
  not readily identifiable and yet have very small
  to moderate effects that, individually and in
  interaction with each other, cause detectable
  variability in the process and its output.

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• Chance or Common Causes of Variability
• A stable process is in a state of statistical
  control and has only chance or common causes of
  variability operating on it.
• The system of chance causes that operates on a
  process is stable and constantly present. This
  stable system of chance causes produces patterns
  of variability that follow known statistical
  distributions. If a set of data is analyzed and
  the pattern of variation of the data is show to
  conform to statistical patterns that are
  characteristic of those produced by chance, we
  can assume that only chance or common causes are
  operating on the system.
• Because a system is in a state of statistical
  control is considered to be stable we can predict
  the status of output for the process for the near
  future.

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• Assignable or Special Causes of Variability
• Assignable or special causes of variability have
  relatively large effects on the process and are
  not inherent to it. The circumstances or factors
  that cause this kind of variability can be
  identified.
• Assignable or special causes can be recognized
  and assigned or attributed to specific special
  circumstances or factors. Examples of special
  causes are
• Differences between machinery
• Differences in a machine over time
• A change in raw materials
• Differences between workers
• Differences in an individual worker over time
• Differences in the relationship among production
  equipment, materials, and workers
• a change in manufacturing conditions...

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• Assignable or Special Causes of Variability
• A process is said to be out of statistical
  control if one or more special causes are
  operating on it.
• Special causes are not inherent to the process,
  so they are considered to be outside the system.
  When patterns of variability do not conform to
  the patterns we would expect if only chance or
  common causes are operating, we know that one or
  more special causes are operating on the system.
  If special causes are operating, the system is
  considered to be out of statistical control, and
  intervention is required to eliminate the special
  causes and reduce process variability.

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• Types of Control Charts
• Control charts can be divided into two categories
  that are determined by the type of measurements
  used to monitor a process.
• If, in monitoring a process, we sample output and
  evaluate each member of the sample to see whether
  individual items or events are conforming or
  nonconforming, the frequency or proportion of
  nonconforming items are used to evaluate such
  attribute data. If our quality characteristic is
  measured on a continuous scale such as height,
  weight, temperature, or time, we employ a
  variable control chart.

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• Types of Control Charts
• Attribute control charts include
• 1. Counts of nonconforming Items Charts
• Pieces or number nonconforming charts (np
  charts)
• Fraction or proportion nonconforming charts (p
  Charts)
• 2. Area of Opportunity Charts
• Number of nonconformities charts (c charts)
• Nonconformities per unit charts (u charts)

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• Types of Control Charts
• Variables control charts contain more information
  than attribute charts and are generally used in
  pairs. One member of the pair monitors process
  variability while other monitors central tendency
  or the average quality level or the output of the
  process. The major types of variables control
  charts include the following
• 1. Charts based on means of samples
• mean and range charts (X R Charts)
• mean and standard deviation charts (X s charts)
• exponentially weighted moving average charts
  (EWMA charts)
• cumulative sum charts (CUSUM charts)
• 2. Charts based on individual measurements (X
  charts)
• individual measurements using the range
• individual measurements using the standard
  deviation

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Types of Error that Can Occur When Using Control
Charts
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Testing Hypotheses The decision risks are
measured in terms of probability. ?
P(Type I error) P(reject H0H0 is
true) Producers risk ?
P(Type II error) P(accept H0H1 is true)
Consumers risk Remark 100 ? is commonly
referred to as the significance level of a
test. Note For fixed n, ? increases as ?
decreases, and vice versa, as n increases, both ?
and ? decrease.
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Power Function Before applying a test procedure,
i.e., a decision rule, we need to analyze its
discriminating power, i.e., how good the test is.
A function called the power function enables us
to make this analysis. Power Function
P(rejecting H0true parameter value) OC
Function P(accepting H0true parameter
value) 1 - Power Function where OC is
Operating Characteristic.
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Power Function The power function of a
statistical test of hypothesis is the
probability of rejecting H0 as a function of the
true value of the parameter being tested, say ?,
i.e., PF(?) PR(?) P(reject H0?)
P(test statistic falls in CA?)
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Operating Characteristic Function The operating
characteristic function of a statistical test of
hypothesis is the probability of accepting H0 as
a function of the true value of the
parameter being tested, say ?, i.e., OC(?)
PA(?) P(accept H0?) P(test statistic
falls in CR?)
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• Runs
• One way to study the probability of false alarm
  is through the run length. A run is a series of
  consecutive points which all increases in value
  or all decrease in value. Another kind of runs
  occurs when a consecutive series of points all
  fall above the center line or all fall below the
  center line.
• Run length is the number of charts points that
  occur after a shift in parameter takes place
  before a signal is given by the chart that the
  shift has occurred.
• The average run length (ARL) is the average
  number of points that must be plotted before a
  point indicates that the process is
  out-of-control or a shift has occurred.

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• Use of Control Chart
• Control charts are a proven technique for
  improving productivity
• Control charts are effective in defect prevention
• Control charts prevent unnecessary process
  adjustment
• Control charts provide diagnostic information.
• Control charts provide information about process
  capability

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General Model for the Shewhart Control
Chart UCL ?W K?W Center Line ?W LCL
?W - K?W where W is a statistic that measures a
quality characteristic ?W is the mean of W ?W
is the standard deviation of W K is the distance
of the control limits from the center line, in
multiples of ?W
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Types of Control Chart
X
One
Moving Range
Measurement (variables)
X
Multiple
R
S
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Types of Control Chart
p
Defectives
np
Counts (attributes)
c
Defects
?