TECHNOLOGY OVERVIEW

# Individuals and Moving Range Control Charts

The Individuals Control Chart is used when rational subgrouping has little effect. One example is fast automatic filling lines. Another is when sampling is expensive requiring sample size to be kept to a minimum.

The Individuals Control Chart is usually based on a moving two period range but using larger periods or moving standard deviation charts are also used occasionally. The benefit is however dubious.

The average moving range to estimate the process standard deviation is normally used to calculate control limits instead of the total standard deviation, as the latter can be affected by outliers and process variation over time. Various counter arguments can be applied to this reasoning. Control limits based on the median moving range have also been proposed. The benefit of this approach over the average is debatable.

The classical Individuals and Control chart assumes a normal distribution.

For this classical mainstream control charts section accepted formulae are used.

#### Control Limits for the Individuals Chart

Control limits are calculated such that there is a small probability of points falling outside these limits. If a point falls outside the limits it is assumed that the event is of such small probability that we can reasonably assume it is not a false alarm, but due to an assignable cause. To ensure there is a small probability a control chart factor of 3 is used.

Control limits are then placed around an estimate of the population mean or target. The estimate is usually obtained from the mean of all samples.

UCl = Average (or target) +2.66*Average Moving Range

LCl = Average (or target) -2.66*Average Moving Range

The value of 2.66 is derived from the control chart factor, an anti biasing factor and the moving period of 2.

Warning limits: Shewhart charts are often supplemented with warning limits. Warning limits are calculated as above, after replacing 2.66 with 1.77. A warning is signaled when one point falls outside warning limits but inside control limits. An assignable cause is signaled if two consecutive points fall outside the same warning limit.

#### Control Limits for the Moving Range Chart

UCL=3.267*Average Moving Range

LCL=0

The factor is derived from the control chart factor and constants obtained from readily available tables.

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