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 XCHART Statement

## Constructing Charts for Means

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) mean of measurements in i th subgroup Ri range of measurements in i th subgroup ni sample size of i th subgroup N number of subgroups weighted average of subgroup means zp 100p th percentile of the standard normal distribution

### Plotted Points

Each point on an chart indicates the value of a subgroup mean (). For example, if the tenth subgroup contains the values 12, 15, 19, 16, and 14, the value plotted for this subgroup is

### Central Line

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

### Control Limits

You can compute the limits in the following ways:

• as a specified multiple (k) of the standard error of 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 exceeds the limits

The following table provides the formulas for the limits:

Table 42.22: Limits for Charts
 Control Limits LCL = lower limit UCL = upper limit

 Probability Limits LCL = lower limit UCL = upper limit

Note that the limits vary with ni. If standard values and are available for and , respectively, replace with and with in Table 42.22.

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 a constant nominal sample size for the control limits 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 a LIMITS= data set.
• Specify with the SIGMA0= option or with the variable _STDDEV_ in a LIMITS= data set.

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