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 IRCHART Statement

## Constructing Charts for Individual Measurements and Moving Ranges

The following notation is used in this section:
 process mean (expected value of the population of measurements) process standard deviation (standard deviation of the population of measurements) Xi the i th individual measurement mean of the individual measurements, computed as (X1+ ... +XN)/N, where N is the number of individual measurements n number of consecutive measurements used to calculate the moving ranges (by default, n=2) Ri moving range computed for the i th subgroup (corresponding to the i th individual measurement). If i

### Plotted Points

Each point on an individual measurements chart, indicates the value of a measurement (Xi).

Each point on a moving range chart indicates the value of a moving range (Ri). With n=2, for example, if the first three measurements are 3.4, 3.7, and 3.6, the first moving range is missing, the second moving range is |3.7-3.4|=0.3, and the third moving range is |3.6-3.7|=0.1.

### Central Lines

By default, the central line on an individual measurements chart indicates an estimate for , which is computed as .If you specify a known value () for , the central line indicates the value of .

The central line on a moving range chart indicates an estimate for the expected moving range, computed as where .If you specify a known value () for , the central line indicates the value of .

### Control Limits

You can compute the limits

• as a specified multiple (k) of the standard errors of Xi and Ri above and below the central line. The default limits are computed with k=3 (these are referred to as limits).
• as probability limits defined in terms of , a specified probability that Xi or Ri exceeds the limits

The following table provides the formulas for the limits:

Table 34.22: Limits for Individual Measurements and Moving Range Charts
 Control Limits Individual Measurements Chart LCL = lower control limit UCL = upper control limit Moving Range Chart LCL = lower control limit UCL = upper control limit =

 Probability Limits Individual Measurements Chart LCL = lower control limit UCL = upper control limit Moving Range Chart LCL = lower control limit UCL = upper control limit

The formulas assume that the measurements are normally distributed. Note that the probability limits for the moving range are asymmetric about the central line. If standard values and are available for and ,replace with and with in Table 34.22.

You can specify parameters for the limits as follows:

• Specify k with the SIGMAS= option or with the variable _SIGMAS_ in a LIMITS= data set.
• Specify with the ALPHA= option or with the variable _ALPHA_ in a LIMITS= data set.
• Specify n with the LIMITN= option or with the variable _LIMITN_ in a LIMITS= data set.
• Specify with the MU0= option or with the variable _MEAN_ in the LIMITS= data set.
• Specify with the SIGMA0= option or with the variable _STDDEV_ in the LIMITS= data set.

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