# Individual Moving Range (I-MR) Charts. The Swiss Army Knife of Process Charts

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1 Individual Moving Range (I-MR) Charts The Swiss Army Knife of Process Charts

2 SPC Selection Process Choose Appropriate Control Chart ATTRIBUTE type of data CONTINUOUS DEFECTS type of attribute data DEFECTIVES type of defect type of subgroups subgroup size CONSTANT VARIABLE CONSTANT VARIABLE Sample size C Chart U Chart NP Chart P Chart I MR Chart X R Chart X S Chart Number of Incidences Incidences per Unit Number of Defectives Proportion Defectives Individual s & Moving Range Mean & Range Mean & Std. Dev. 2

3 Individual Moving Range (I-MR Chart) Control charts for variables data Monitors the process over time Individual Chart Plots each measurement as a separate data point Each data point stands on its own (subgroup size = ) Moving Range Chart Uses a default value of 2, which means each data point plots the difference (range) between two consecutive data points as they come from the process in sequential order There will be one less data point in the Moving Range chart than the Individual chart 3

4 Moving Range Individual Value Sample Individual Moving Range Chart I-MR Chart of Systolic Blood Pressure UC L= X= O bser vation LC L= UC L= MR=. 0 LC L= O bser vation

5 Xbar-R Charts Control charts for variables data Monitors the process over time The distribution does not have to be approximately normal Based on the average of a series of observations, called a subgroup Monitors the variation between observations in the subgroup over time The larger the subgroup, the more sensitive the chart will be to shifts, providing a Rational Subgroup can be formed What is a rational subgroup? 5

6 What is it and where does it come from? Rational Subgroup Items which were produced under the same conditions When possible, formed by using consecutive units Each subgroup s statistics are compared to the control limits, and patterns of variation between subgroups are analyzed Picture a Stable Distribution A group of objects containing a characteristic of interest Distribution 6

7 Where do Subgroups Come From? Subgroup: A subset of the distribution of interest Subgroup Subgroup 2 Subgroup 3 Subgroup N

8 Sample Range Sample Mean Sample Xbar-R Chart Xbar-R Chart of Glucose Readings 0 UC L= X= LC L= Sample UC L= R= Sample LC L=5.2 8

9 When to Use I-MR/Xbar-R I-MR When you have a limited number of individual measurements Xbar-R When you can collect measurements in groups (subgroups) of between two and ten observations For subgroup sizes greater than ten Use Xbar / Sigma charts Must have data that is time-ordered 9

10 Interpreting R Charts Always look at the Range chart first Control limits on the I-MR are derived from the change in range (moving range) The control limits on the Xbar-R chart are derived from the average range If the Range chart is out of control, then the control limits on the Individual and X-bar chart are meaningless. Look for out of control points Special causes must be eliminated There should be more than five distinct values plotted No single value should appear more than 25% of the time 0

11 Moving Range Individual Value I-MR Chart Looking at the moving range chart, what does the out of control point tell you? I-MR Chart of Individual 8 UC L= X= LC L= Observation UC L= MR= LC L= Observation

12 Interpreting R Charts Average charts become more sensitive to process changes as the subgroup size is increased What does that mean? 2

13 Sample Range Sample Range Sample Mean Sample Mean Sensitive to Process Changes As the subgroup size increases the control limits of the range chart increase Xbar-R Chart of Glucose Readings (Subgroup Size 3) Xbar-R Chart of Glucose Readings (Subgroup Size 9) 20 UC L=6.2 0 UC L= X= X= Sample LC L= Sample LC L= UC L= UC L= R= R= Sample LC L= Sample LC L=5.2 Range Chart UCL LCL 0 Range Chart UCL LCL 5.2 3

14 Interpreting Individual/Xbar Charts Individual/Xbar Charts Interpret the points on the X-bar chart relative to the control limits and Run Tests Look for out of control points Look for obvious non-random behavior Averages in the Xbar Chart cannot be compared to requirements What does that mean? 4

15 Moving Range Sample Range Individual Value Sample Mean Xbar-R Cannot Be Compared to Requirements Both charts use same data set Look at the control limits on the Individual and Xbar Charts Individual Readings Same Readings in Subgroups of 9 I-MR Chart of Glucose Readings Xbar-R Chart of Glucose Readings 40 UC L=3. 0 UC L= X= X= Observation LC L= Sample LC L= UC L= UC L= Observation MR=.84 LC L= Sample R=28.63 LC L=5.2 UCL 3. LCL 68.2 UCL LCL

16 The Control Chart Cookbook General Steps for Constructing I-MR Charts. Select characteristic (critical X or CTQ) to be charted 2. Determine the purpose of the chart 3. Select data-collection points 4. Determine the measurement method/criteria 5. Drop the data into Minitab or other charting software 6

17 Questions?

18 Run Tests Western Electric Rules One or more observations occurring more than 3 Standard Deviations from the average, i.e. any points occurring above or below the Control Limits. UCL +2 + Average - -2 LCL Fifteen consecutive observations occurring within one Standard Deviation from the average. UCL +2 + Average - -2 LCL Two out of three consecutive observations, all on the same side of the average and occurring more than two Standard Deviations away form the average. UCL +2 + Average - -2 LCL Eight consecutive observations that are more than one Standard Deviation from the average. UCL +2 + Average - -2 LCL Four out of five consecutive observations, all on one side of the Center Line occurring more than one Standard Deviation from the average. UCL +2 + Average - -2 LCL Fourteen consecutive observations that alternate up and down. UCL +2 + Average - -2 LCL Eight consecutive observations on one side of the average. UCL +2 + Average - -2 LCL Six consecutive observations that trend downward or upward. UCL +2 + Average - -2 LCL

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