Control Charts

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 Is the data continuous (aka measurement or variables data) data or attribute data (aka discreet or count data)? – 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 non- occurrences 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?

Choosing a Control Chart

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

Examples of Control Charts for Discreet Data c-chart u-chart p-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 Tests for other unnatural patterns – Test #5-Stratification occurs when 15 or more consecutive data points fall in Zone C, either above or below the centerline

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