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.

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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