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 MCHART Statement

## Constructing Median Charts

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 ni sample size of i th subgroup N the number of subgroups xij j th measurement in the i th subgroup, j = 1,2,3, ... , ni xi(j) j th largest measurement in the i th subgroup. Then weighted average of subgroup means Mi median of the measurements in the i th subgroup: average of the subgroup medians: median of the subgroup medians. Denote the j th largest median by M(j) so that . Then eM(n) standard error of the median of n independent, normally distributed variables with unit standard deviation (the value of eM(n) can be calculated with the STDMED function in a DATA step) Qp(n) 100p th percentile (0

### Plotted Points

Each point on a median chart indicates the value of a subgroup median (Mi). For example, if the tenth subgroup contains the values 12, 15, 19, 16, and 14, the value plotted for this subgroup is M10 = 15.

### Central Line

The value of the central line indicates an estimate for , which is computed as

• by default
• when you specify MEDCENTRAL=AVGMEAN
• when you specify MEDCENTRAL=MEDMED
• when you specify with the MU0= option

### Control Limits

You can compute the limits

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

The following table provides the formulas for the limits:

Table 35.22: Limits for Median Charts
 Control Limits LCLM = lower limit UCLM = upper limit

 Probability Limits LCLM = lower limit UCLM = upper limit

Note that the limits vary with ni. In Table 35.22, replace with if you specify MEDCENTRAL=AVGMEAN, and replace with if you specify MEDCENTRAL=MEDMED. Replace with if you specify with the MU0= option, and replace with if you specify with the SIGMA0= option. The formulas assume that the data are normally distributed.

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 the LIMITS= data set.
• Specify with the SIGMA0= option or with the variable _STDDEV_ in the LIMITS= data set.

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