iSixSigma

Steps in Constructing a Median And Range Control Chart

Median Charts

Preparing Median Charts

The primary reason for using medians is that it is easier to do on the shop floor because no arithmetic must be done. The person doing the charting can simply order the data and pick the center element. For simplicity, odd numbers of samples are chosen 3, 5, 7, etc. The major disadvantage of using a median chart is that it is less sensitive (powerful) in detecting process changes when extreme values occur.

Traditionally, all subgroup values are plotted, and only the median values are connected by line segments. One must be careful when interpreting the chart that the "out of control" rules are only applied to the median elements.

Steps in Constructing a Median Chart

  1. Either an R chart or s chart is developed as shown on the respective XBAR-r or XBAR-s charts and the process variation is shown to be in statistical control.
  2. If an R chart was used, the control limits are as follows:
  3. If an s chart was used, the control limits are as follows:
  4. Table of A(6) and A(7)
    
    n    A(6)    A(7)       n    A(6)    A(7)
    2    1.880   1.880      6    .549    .580
    3    1.187   1.067      7    .509    .521
    4     .796    .796      8    .434    .477
    5     .691    .660      9    .412    .444
    
    The centerline is XDBLBAR.  Note that it is the subgroup MEANS that determine both the centerline and the control limits.
  5. Plot the centerline XDBLBAR, LCL, UCL, and the subgroup medians.
  6. Interpret the data using the following guidelines to determine if the process is in control:
  7. a.  one pount outside the 3 sigma control limits
    b.  eight successive points on the same side of the centerline
    c.  six successive points that increase or decrease
    d.  two out of three points that are on the same side of the centerline, both at a distance exceeding 2 sigmas from the centerline
    e.  four out of five points that are on the same side of the centerline, four at a distance exceeding 1 sigma from the centerline
    f.  using an average run length (ARL) for determining process anomolies

Example:

Handpicked Content:   Control Chart Wizard - Discrete Defect Data

The following data consists of 20 sets of three measurements of the diameter of an engine shaft. An R-Chart will be used to examine variability followed by a Median Chart.

n       meas#1  meas#2  meas#3          Range   XBAR    Median  
1       2.0000  1.9998  2.0002          0.0004  2.0000  2.0000  
2       1.9998  2.0003  2.0002          0.0005  2.0001  2.0002  
3       1.9998  2.0001  2.0005          0.0007  2.0001  2.0001  
4       1.9997  2.0000  2.0004          0.0007  2.0000  2.0000  
5       2.0003  2.0003  2.0002          0.0001  2.0003  2.0003  
6       2.0004  2.0003  2.0000          0.0004  2.0002  2.0003  
7       1.9998  1.9998  1.9998          0.0000  1.9998  1.9998  
8       2.0000  2.0001  2.0001          0.0001  2.0001  2.0001  
9       2.0005  2.0000  1.9999          0.0006  2.0001  2.0000  
10      1.9995  1.9998  2.0001          0.0006  1.9998  1.9998  
11      2.0002  1.9999  2.0001          0.0003  2.0001  2.0001  
12      2.0002  1.9998  2.0005          0.0007  2.0002  2.0002  
13      2.0000  2.0001  1.9998          0.0003  2.0000  2.0000  
14      2.0000  2.0002  2.0004          0.0004  2.0002  2.0002  
15      1.9994  2.0001  1.9996          0.0007  1.9997  1.9996  
16      1.9999  2.0003  1.9993          0.0010  1.9998  1.9999  
17      2.0002  1.9998  2.0004          0.0006  2.0001  2.0002  
18      2.0000  2.0001  2.0001          0.0001  2.0001  2.0001  
19      1.9997  1.9994  1.9998          0.0004  1.9996  1.9997  
20      2.0003  2.0007  1.9999          0.0008  2.0003  2.0003  
                                                                
RBAR CHART LIMITS:                                                      
RBAR  = 0.0005                                          

UCL   =  D(4)*RBAR   =  2.574*.0005 =   0.001287                
LCL   =  D(3)*RBAR   =  0 * .0005   =   0.00            

XBAR CHART LIMITS:                                                      
XDBLBAR  = 2.0000                                       
                                                                
UCL  =  XDBLBAR + A(6)*RBAR   = 2.000+1.187*.0005  = 2.0005935
LCL   = XDBLBAR - A(6)*RBAR   = 2.000-1.187*.0005  = 1.9994065

R Chart:

Median – Chart:

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