CONTROL CHART METHODOLOGY

Transcription

1 Center for Performance Sciences, 2001

2 CONTROL CHART METHODOLOGY

3 Statistical Process Control (SPC) Analysis Statistical process control is a tool (e.g., control chart) used to help understand any process that generates products, services, or information Identifies processes behind a measure that are either: 1. Stable, predictable 2. Unstable, chaotic (variation due to common causes) (variation due to a special cause)

4 Statistical Process Control (SPC) Theory Developed by Walter Shewhart in the 1920 s at Bell Laboratories and began as a quality control tool for manufacturing Other control chart supporters and experts: W. Edwards Deming Eugene Grant and Richard Leavenworth Douglas Montgomery Thomas Pyzdek Donald J. Wheeler Introduced in the service industry and in health care, specifically, within the last 15 years.

5 Control Charts Control chart benefits: Monitors process variation Tells whether a planned improvement was successful Plan-Do-Check-Act Process improvement cycle Originated by Shewhart To be used with SPC

6 American Society of Quality Statistics Division System Thinking Statistical Methods Process Variation Data Improvement Philosophy Analysis Action 3 Principles of Statistical Thinking 1. All work occurs in a system of interconnected process 2. Variation exists in all processes It is a fact of life 3. Understanding and reducing variation are keys to success (Deming s management philosophy in reducing variation)

7 Control Chart Basics

8 Line graphs are often used to display data over time.

9 A Control Chart is a line graph of the monthly data points with the following additions: Center Line Overall process mean of the monthly data points Upper Control Limit Set at 3 standard deviations above center line Lower Control Limit Set at 3 standard deviations below center line

10 Control Chart with UCL and LCL Cesarean Section Rate Upper Control Limit +3 Sigma Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Measure Rate Lower Control Limit +2 Sigma +1 Sigma Centerline -1 Sigma -2 Sigma -3 Sigma

11 Normal Distribution Std. Dev = 5.18 Mean = 21.3 N =

12 Control Chart Analysis Std. Dev = 5.18 Mean = N =

13 Control Charts Generally: Look at data from shorter time periods Help to determine how past performance can influence future performance

14 The Value of Measuring, Analyzing, and Controlling Process Variation Control charts help determine: 1. When to respond to data 2. How to respond to data 3. The results of actions taken to improve the process as reflected by the data

15 Types of Variation Common Causes of Variation Inherent in virtually all process. Comprised of a myriad of small sources always present in the process. They are endogenous to the process Special Causes of Variation Not present in processes that are under control. Created by causes that are outside the routine process. They may appear relatively infrequently, but can destabilize a process, and are therefore important to detect. They are exogenous to a process In statistical control Out of statistical control

16 Type I errors When people make Type I errors, they tamper with a process that is already stable They think there s a problem when there really isn t!

17 Type II errors When people make Type II errors, they conclude that a data point indicates no need for action when a special-cause actually exists They fail to intervene in the process when they should!

18 Tampering (Type I Error) Undercontrolling (Type II Error) High The combined total risk of Type I and Type II Error is minimuzed when 3 sigma limits are used. Low ± 1 SD ± 2 SD ± 3 SD ± 4 SD ± 5 SD ± 6 SD

19 Problems Associated with Common Cause and Special Cause Variation 1. Taking action on common cause variation tampering or over adjustment 2. Taking no action on special cause variation Under adjustment

20 Elimination of Special Causes Stabilizes a Process When processes are in control: The capability of the process is known Can predict future performance levels Productivity maximized/costs minimized Process is suitable for improvement efforts

21 Since Performance Measures are Calculated in Different Ways Proportion (Rate) Measures Ratio Measures Continuous Variable Measures So are Their Control Charts!

22 Proportion (Rate) Definition A rate is a quantitative measure that shows how often an event occurs in a population at risk for experiencing the event during a particular time period. - A rate has a numerator, which is a straight count of the event in question. - A rate has a denominator, which is the population at risk for experiencing the event

23 p-chart a control chart for proportion data p-bar refers to the center line and is the average of all the monthly proportions (measure rates) Center Line = overall process mean p is called p-bar

24 u-chart a control chart for ratio data u-bar refers to the center line and is the average of all the monthly ratio units Ratio measures are often stated as the number of falls per 100 resident days, for example, and the unit of measure would be the 100 resident days) Center Line = overall process mean u is called u-bar

25 Control chart interpretation is similar for the different types of control charts.

26 The UCL and LCL are calculated based on the following underlying data distribution types: Proportion; p-chart Binomial (Bernoulli) No Ratio; u-chart Poisson Distribution Continuous; x-bar S chart Normal Distribution Yes Control charts can accommodate for skewed data because they are the averages of samples and the mean of rates/values tend to be normally distributed if the number of cases is large.

27 Decision Rules Test for Outliers Trends Shifts Patterns (Oscillations)

28 Control Chart Zones

29 Control Chart Zones Zone A from 2-sigma to 3-sigma Zone B from 1-sigma to 2-sigma Zone C from centerline to 1-sigma Centerline Zone C from centerline to 1-sigma Zone B from 1-sigma to 2-sigma Zone A from 2-sigma to 3-sigma

30 Tests 1. One point beyond zone A, that is, 3-sigma 2. Nine points in a row in zone C or beyond, that is, on either side of the centerline 3. Six points in a row (including endpoints) steadily increasing or decreasing 4. Fourteen points in a row alternating up or down 5. Two out of three points in a row in zone A or beyond, that is, outside the same 2-sigma 6. Four out of five points in a row in zone B or beyond, that is, outside the same 1-sigma 7. Fifteen points in a row in zone C (above or below the centerline), that is, within 1-sigma 8. Eight points in a row on both sides of the centerline with non in zone C, that is, none within 1-sigma

31 One point beyond zone A, that is, 3- sigma

32 Nine points in a row in zone C or beyond, that is, on either side of the centerline

33 Six points in a row (including endpoints) steadily increasing or decreasing

34 Fourteen points in a row alternating up or down

35 Two out of three points in a row in zone A or beyond, that is, outside the same 2-sigma

36 Four out of five points in a row in zone B or beyond, that, outside the same 1-sigma

37 Fifteen points in a row in zone C (above or below the centerline), that is, within 1-sigma

38 Eight points in a row on both sides of the centerline with non in zone C, that is, none within 1-sigma

39 Application of Tests Due to large α-risks, it is recommended that for the evaluation of a process (i.e. identification of special-cause variation) only the 3-sigma test be used However, when improving performance, the false alarm risk is of little importance For process improvement, all criteria may be used