Forecasting and Statistical Process Control

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MBAStatistics 51-651-02COURSE 5

• Forecasting and Statistical Process Control

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• Part I Forecasting
• Part II Statistical Process Control

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Forecasting

• Uncertainty means we have to anticipate future
  events
• Good forecasting results from a combination of
  good technical skills and informed judgement

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Insulator Sales DataData sets of chapter 10
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Time Series

• Data measured over time is called a time series.
• Usually such data are collected at regular time
  periods.
• Aim is to detect patterns that will enable us to
  forecast future values.

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Forecasting Process

• Choose a forecasting model
• Apply the model retrospectively, and obtain
  fitted values and residuals
• Use the residuals to examine the adequacy of the
  model
• If model acceptable, use it to forecast future
  observations
• Monitor the performance of the model

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Time Series Components

• Long term trend
• Fundamental rise or fall in the data over a long
  period of time.
• Seasonal effect
• Regular and repeating patterns occurring over
  some period of time
• Cyclical effect
• Regular underlying swings in the data
• Random variation
• Irregular and unpredictable variations in the
  data

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Identifying the Trend
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A cycle is a regular pattern repeating
periodically with a long period (more than one
year).
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Seasonal effect is similar to cyclical effect but
with shorter period (less than 1 year).
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Random effect

• Random variations (also called noise) include all
  irregular changes not due to other effects
  (trend, cyclical, seasonal). 
• The noise is like a fog, often hiding the other
  components.
• One of the goal is to try to get rid of the
  effect (using smoothing).

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Models

•  additive model
• yt Tt Ct St Rt
•  multiplicative model
• yt Tt ? Ct ? St ? Rt

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Illustration Sales vs Quarter (ts.xls)
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Moving Averages

• Used to smooth data so we can see the trend or
  seasonality
• removes random variation
• We can take moving averages of any number time
  periods (preferable to take an odd number)
• How much smoothing?
• too little random variation not removed
• too much trend may also be eliminated

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Smoothing of Sales
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Remarks

• Considering MA over 3 periods, one can see a
  linear trend and seasonality of order 4, looking
  at peaks.
• The MA series over 5 periods is too smooth and
  seasonality almost disappeared.
• It is preferable to center the smoothed series
  with respect to the original one.

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Smoothing of Sales
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Exponential Smoothing

• Smoothing aims to remove random so as to reveal
  the underlying trend and seasonality.
• Moving averages use only the last few figures,
  and give them equal weight. We are loosing data.
• Exponential smoothing uses all the data giving
  less and less weight to data further back in time.

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Updating Procedure

• New Forecast
• a Latest Actual Value
• (1 a) Previous Forecast

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Exponential Smoothing in Excel

• In Excel we use the damping factor (1-a)
• For a 0.8, we use 0.2 in Excel
• The best value of a is found by trial and error,
  and is the one that gives the smallest MSE.

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Exponential smoothing for Sales Data
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Using Regression for estimating trend and
seasonal effects

• Can fit a linear regression model to the time
  series.
• Use dummy variables corresponding to seasonality.
• More complicated for multiplicative effects.
• Desaisonalized series corresponds to residuals
  constant!

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Regression approach

• What happens if the only explanatory variable is
  the quarter? Look at the residuals.
• Introduce 3 dummy variables S1, S2, S3,
  corresponding to the seasonality of order 4.
• Look at residuals now.
• What are the predictions for the next 10
  quarters?

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Prediction of the next 10 quarters
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Part II Statistical Process Control (SPC)
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Statistical Process Control

• Statistical process control (SPC) is a collection
  of management and statistical techniques whose
  objective is to bring a process into a state of
  stability or control
• And then to maintain this state
• All processes are variable and being in control
  is not a natural state.
• SPC is an effective way to improve product and
  service quality

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Five Stage Improvement Plan
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Aspects of SPC

• Benefits of reducing variation
• Effect of tampering
• Common cause highway
• Special and common causes
• Construction and use of control charts
• Establishment and monitoring
• Specifications and capability
• Strategies for reducing variation

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Processes
PROCESSING SYSTEM
INPUTS
OUPUTS
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Process Variability
Inputs
Outputs
Process
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Improved Process less variability in input gt
less variability in output
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Common Cause Highway
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The Key to Reducing Variation

• To distinguish between data that fall within the
  common cause highway, and data that falls outside
  the highway.
• Common cause variation indicates a systemic
  problem.
• Special cause variation is almost certainly
  worthy of separate investigation.

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Epic Video Sales
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Special Causes of Variation

• Localised in nature
• Not part of the overall system
• Not always present in the process
• Abnormalities, unusual, non-random
• Contribute greatly to variation
• Can often be fixed by people working on the
  process

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Common Causes of Variation

• In the system
• Always present in the process
• Common to all machines, operators, and all parts
  of the process
• Random fluctuations
• Events that individually have a small effect, but
  collectively can add up to quite a lot of
  variation

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Three Sigma Limits

• The arithmetic mean gives the centre line of the
  common cause highway
• The mean plus three standard deviations gives the
  upper boundary of the highway. This boundary is
  called the upper control limit (UCL)
• The mean minus three standard deviations gives
  the lower boundary of the highway. This boundary
  is called the lower control limit (LCL)
• If a point falls outside the 3-sigma limits it is
  almost certainly a special cause.

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Why 3-Sigma Limits?

• In trying to distinguish between common and
  special causes there are two mistakes that we can
  make.
• Interfering too often in the process. Thinking
  that the problem is a special cause when in fact
  it belongs to the system.
• Missing important events. Saying that a result
  belongs to the system when in fact it is a
  special cause.

too narrow 2-sigma
too wide 4-sigma
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Patterns

• Specific patterns on a control chart also
  indicate a lack of randomness
• We need rules to help us decide when we have a
  pattern
• to avoid seeing patterns when none really exist
• A pattern would indicate that special causes
  could be present

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9 Points Below the Mean
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Stability and Predictability
Stable Process
Source Ford Motor Company
Unstable process
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Stability and Predictability

• A stable process is predictable in the long run.
• In contrast, with an unstable process special
  causes dominate.
• Nothing is gained by adjusting a stable process
• A stable process can only be improved by
  fundamental changes to the system.

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Implementing SPC

• There are two stages involved in implementing SPC
• The establishment of control charts
• scpe.xls