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.
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.
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, cchart, 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
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