• On a run chart the centerline is the median and the distance of a data point from the centerline is not important to interpretation
• On a control chart, the centerline is the mean and the distance a data point is from the centerline is used to define special cause variation
• The formula used to calculate the upper and lower control limits is specific to each type of control chart
– Determined in part by whether the data plotted is continuous or discreet (measurement) or attributes (discreet or count) data
– Determined in part by whether the data distribution is “normal”
(bell-shaped curve) or not (binomial, geometric, Poisson)

Selecting Which Control Chart to Use
– Continuous data is measured along a continuous scale
• Wait times
• Turnaround time for a service
• BP, cholesterol, or body weight measurements
• The duration of a procedure
• The number of procedures or transactions per day or month
– Attribute data can be classified into categories or
“buckets”
• Mortality
• Pregnancy

Selecting Which Control Chart to Use
• Attributes data are either defectives or defects
– Defectives (nonconforming units)
• Requires a count of the number of units that were acceptable and of those that were not. You know both the occurrences and the nonoccurrences
• The unacceptable units become the numerator and the total number of items observed becomes the denominator
• Either plot the number of defectives or the percentage of defectives
• The numerator and denominator have the same units
• Example: the percentage of late food trays: numerator=late food trays and the denominator is the total number of food trays passed
– Defects
• Events that occur in which the non-events are unknown and unknowable

Selecting Which Control Chart to Use
– Defects continued
• The numerator is known but the denominator cannot be known
– Example: Stains on the rug (you don’t know the number of non-stains); falls; medication errors; visits to the ED
• Expressed as rates rather than percentages. Rates are ratios in which the numerator and denominator are of different units
– Example: rate of falls has the # of falls in a month in numerator and the denominator is the average daily census for that month X 1000 also stated “falls per 1000 patient-days”
– With a rate, the numerator can be larger than the denominator (e.g. 130 falls in 100 patients (some patients fell more than once)
• Is there an equal opportunity from time period to time period for the event being measured to occur-e.g. regarding falls, is the hospital census similar from month to month?

Examples of Control Charts for
Continuous Data
XmR
X-bar &S

Examples of Control Charts for
Discreet Data u-chart c-chart p-chart

Rules for Determining Special-Cause
Variation in a Control Chart

Rules for Determining Special-Cause
Variation in a Control Chart
• Tests for instability
– Test #1-A single data point that exceeds the upper or lower control limit

Rules for Determining Special-Cause
Variation in a Control Chart
• Tests for instability
– Test #2-Two out of three consecutive data points that fall in Zone A or beyond
– Test #3-Four out of five consecutive data points that fall in Zone B or beyond

Rules for Determining Special-Cause
Variation in a Control Chart
• Tests for instability
– Test #4-Eight or more consecutive data points that fall in Zone C or beyond

Rules for Determining Special-Cause
Variation in a Control Chart

Rules for Determining Special-Cause
Variation in a Control Chart
• Tests for other unnatural patterns
– Test #6-Eight or more consecutive points on both sides of the centerline with none of the points in
Zone C

Rules for Determining Special-Cause
Variation in a Control Chart
• Tests for other unnatural patterns
– Test #7-Systematic variation will be observed when a long series of data points (usually 14 or more) are high, then low, then high, then low, without any interruption in this regular pattern

Rules for Determining Special-Cause
Variation in a Control Chart
• Tests for other unnatural patterns
– Test #8-A trend exists when there is a constantly increasing or decreasing series of data points

Rules for Determining Special-Cause
Variation in a Control Chart
• Tests that occur most often in healthcare applications
– Test #1
– Test #4
– Test #8
• Tests occurring with less frequency in healthcare applications
– Test #2
– Test #3
• Tests that do not occur very often in healthcare applications
– Test #5
– Test #6
– Test #7