The Bell Shaped Curve

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The Bell Shaped Curve

• By the definition of the bell shaped curve, we
  expect to find certain percentages of the
  population between the standard deviations on the
  curve.

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Critical Regions

• When decisions are made with regards to
  inferential statistics, these critical levels are
  often used.
• To determine the points that 95 percent of the
  population lies between, an assumption that the
  curve equals 100 percent is made and that when
  equally distributed to both sides of the curve,
  there should 2.5 percent of the population above
  and 2.5 percent of the population below.

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Control Chart

• A statistical device that can be used for the
  study and control of safety performance in the
  workplace.
• Assumes the data distribution to approximate the
  normal bell-shaped curve.

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Assumptions

• Plotting measurements over time, one would expect
  to obtain measurements over time that fall in the
  ranges depicted on the bell shaped curve.

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Use of Control Charts

• Methodology to detect significant changes in
  safety performance measures.
• Charts include a baseline average line, and
  control limits.
• The control limits act as alarm values.

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Theoretical Basis for the Control Chart
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Control Charts

• A control chart has a line indicating the running
  average and two lines indicating the upper and
  lower control limits.
• Common control limits are three standard
  deviations above the mean and three standard
  deviations below the mean.
• The calculation of the control limits depends on
  the type of control chart.

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Trends and Control

• Purpose of a control chart is to graphically
  identify trends.
• When using control charts, data may be considered
  a trend or out of control.

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Out-of-Control Criteria

• One or more points outside the limits on a
  control chart.
• One or more points in the vicinity of a warning
  limit.
• A run of 7 or more points. This might be a run up
  or run down or simply a run above or below the
  central line on the control chart.
• Cycles or other nonrandom patterns in the data.
• Other criteria that are sometimes used are the
  following
• A run of 2 or 3 points outside of 2-sigma limits.
• A run of 4 or 5 points outside of 1-sigma limits.

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Interpreting Control Charts

• When data points are consistently above the upper
  control limit, the control chart indicates that
  the data is significantly different from what
  would be expected.
• Points above the upper control limit could
  indicate problem if the data represents
  recordable injuries while they may indicate a
  good thing if the data represents the number of
  positive safety contacts made between supervisors
  and employees.

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Trends Outside the Control Limits

• If the points consistently lie outside of the
  upper or lower control limits, and by doing so
  represent a positive aspect, one should consider
  reconstructing the control chart using the
  current data.
• The average, upper control limit and lower
  control limit will shift so that ranges on the
  control chart will more closely reflect the
  current data being collected.

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Trends Outside the Control Limits

• Points consistently lie outside of the upper or
  lower control limits, and by doing so represent a
  negative aspect, it is imperative for the safety
  professional to evaluate the circumstances that
  are causing the results and implement the
  appropriate corrective measures.

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Out-of-Control Charts

• Out-of-control Wide fluctuations that randomly
  place data points above the upper control limit
  and below lower control limit,
• If the data on the control chart indicates that
  the chart is out of control, it is up to the
  safety manager to analyze the circumstances
  behind the situations that resulted in the data.

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Treatment of Significant Changes

• If any of the criteria for out of control data
  exist in constructing a new control chart, the
  average control limits may need to be calculated.
  

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Attribute Control Charts

• Used when the data being measured meet certain
  conditions or attributes.
• Any situation where the safety measures can be
  considered categorical.
• Examples of categorical data include the
  departments in which accidents are occurring, the
  job classification of the injured employee, and
  the type of injury sustained.
• The type of attribute control chart used depends
  on the data format of the specific attribute
  measured.
• Examples of attribute control charts include the
  p-chart, c-chart, and u-chart.

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p Chart

• The p-chart is used with "binomial" data.
• P-charts are used for results of two possible
  outcome data.
• For example, a p-chart may be used to chart the
  percentage or fraction of each sample that is
  nonconforming to the safety requirements.

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Guidelines

• When calculating the upper and lower control
  limits is that one should not plot the UCL on a
  p-chart if it exceeds 100 and one should not
  plot the LCL on a p-chart if it is below 0.

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Sample p-chart
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c Chart

• The c-chart is also used for "Poisson" processes.
  
• Occurrence reporting data (i.e. number of
  accidents per month) empirically appear to fit
  the "Poisson" model.
• The number of nonconformities per "unit" and is
  denoted by c with the "unit" being commonly
  referred to as an inspection unit such as "per
  month."

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Figure 8 Sample c Chart