SUGI 28: Using the SAS(r) System to Construct and Operate Control Charts with Randomized Control Limits

Attribute control charts (e.g., charts for counts and proportions) have discrete jumps in the quantities plotted on the charts, which means that the chart designer has only a discrete set of unique control limits to choose from when designing a chart. These charts have a small set of in-control Average Run Lengths (ARLs) from which to determine the appropriate control scheme. In a chart with randomized control limits the operational control limit in an epoch is determined by a random choice from among a set of control limits. The resulting control chart will then have a predetermined in-control ARL. These charts can be thought of as ones with optimal ARL properties. SAS® programs for designing and operating these charts will be provided. INTRODUCTION A process is a collection of activities or occurrences that produce observable (measurable) output. Statistical Process Control (SPC) is the art and science of using observation of the process to determine, in a particular epoch, whether the process is in an in-control state or an out-of-control state. An in-control process is one that is operating in a stable and predictable manner. In this context, “stable and predictable” has a stochastic interpretation. An extreme definition of an in-control process is one which during any epoch i , observations from the process ij x for J j , , 1 K = are distributed F(x). That is, samples from in-control epochs are identically distributed. In practice it is usually sufficient for this to be only approximately so. When observation of the process produces count or categorical data, the process is said to be an attribute process (the data are attribute data). One method for controlling attribute processes is the control chart (see Montgomery (2000) for a more complete discussion of control charts). A p-chart can be used to control the rate at which non-conforming units arise in a process. Let p be the proportion of units that are nonconforming. Note that p must either be known or be estimated. The control chart limits are