Run rules

For case (1), a group control chart could be maintained on all streams but it suffices to plot only the two streams corresponding to the highest and lowest values. The chart limits are set up for a single stream and run rules should not be used. If the output of the heads is highly correlated, then a single chart on one stream may be used as a surrogate for all streams. 

Champ, C.W. Woodall, W.H. Exact results for Shewhart control charts with supplementary runs rules. Technometrics 1987, 29 (4), 393-399. 

The X chart considers only the current data value in assessing the status of the process. Run rules have been developed to include historical information such as trends in data. The run rules sensitize the chart, but they also increase the false alarm probability. The warning limits are useful in developing additional run rules in order to increase the sensitivity of Shewhart charts. The warning limits are established at 2-sigma level, which corresponds to o /2=0.02275. Hence,... 

If r run rules are used simultaneously and rule i has a Type I error probability of Oj, the overall Type I error probability a total is... 

Run rules, also known as Western Electric Rules [323], enable decision making based on trends in data. A process is declared out-of-control if any run rules are met. Some of the run rules are ... 

There are a number of statistical run rules which are used to indicate out-of-control situations. Some laboratories use only one rule of a data point beyond 3 sigmas. This in itself may not be adequate, since it will ignore several short term and more importantly long term indications of system instability. 

A point exactly on the centerline does not cancel or count towards a run (rule 2). 

AT T Runs Rules CONTROL CHARTS FOR 1863 5.3. Control Chart for Number of Defectives c Chart 1874... 

Clearly, the term nonrandom trend must be consistently defined for the shop floor operators. Such definitions are made by the consistent adoption of rules for judging the current status of a process. Probably the most common set of rules for examining the state of the process is known as the AT T runs rules (AT T 1985). In AT T (1985), these rules are called Tests for Instability. In applying these tests, each half of the control chart (the area between the CL and UCL and the CL and LCL) is divided into three equally spaced zones, as shown in Figure 7. 

The AT T runs rules should always be employed for the X chart and should be used for the R chart when the sample size is five or more (AT T 1985). The first rule of the AT T runs rules... 

From the control charts above, the process exhibits stability using the AT T runs rules on the X chart (see zones marked on Figure 8) and for rule number 1 for the R chart therefore, the process is judged to be in a state of statistical control. 

In practice, the initial estimation of the control limits may require an iterative process in securing control limits that are statistically valid. In particular, it may be necessary to estimate the limits initially. If a given A or R plots beyond the initial control limits, it is recommended that the cause of the extraordinary point be resolved and then removed from the calculation. That is, the control limits should be recalculated with the out-of-control point(s) removed. In some extreme cases, this iterative process may be repeated several times. Once the observed data are contained within the trial limits, continued production should be used to collect more data to further validate the limits. Once process stability is obtained, that is control is maintained for an extended period, the new control limits should become the operational standard. Furthermore, once the trial limits are established, the AT T Runs Rules should be deployed in totahty.to insure protection against process disturbances. 

As demonstrated, aU points plot within the control limits therefore, these trial limits should be employed for production. Fuithermore, it is highly recommended that the production also utilize the AT T runs rules on the X chart (see zones on Figure 10) for subsequent production to monitor the state of the process. 

It is assumed that the number of observations that are defective in a subgroup of n samples follows the binomial distribution with parameters p (the true population percent nonconforming) and n. For the formrrlation presented here, n is assum to be fixed. This assirmption can be relaxed, but a modified approach for the varying sample size must be employed as demonstrated in most standard quality control textbooks (i.e., Montgomery 1996). The p chart is essentially the plotting of the observed values of p. These values are individtrally compared to the control limits (shown below) to determine the current status of the process (i.e., state of statistical control or out of control). Furthermore, the AT T runs rules should be deployed when possible. 

The LCL is truncated to 0 when the calculated value falls below 0. The AT T runs rules can be employed in situations where the control limits are reasonably symmetric (AT T 1985). 

Asynchronous transfer mode (ATM), 250 ATC, see Apparent tardiness cost ATM (Asynchronous transfer mode), 250 ATO, see Assemble to order ATP (available to promise), 2046 Attention, limited-resource model of, 1016 AT T Laboratories, 268, 913 Attribute control charts, 1844-1851 Attribute data, 1856-1857 Attribute modeling, 2279—2280 AT T runs rules, 1863—1868 Attributes ... 

J. Sancho, J. Martinez, J.J. Pastor, J. Taboada, J.I. Pineiro, P.J. Garcia-Nieto. New methodology to determine air quality in urban areas based on runs rules for functional data. Atmospheric Environment 83, 2014, pp. 185-192. 

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