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Process control is concerned with monitoring quality while the product or service is being produced. Typical objectives of process control plans are to provide timely information on whether currently produced items are meeting design specifications and to detect shifts in the process that signal that future products may not meet specifications. Statistical Process Control (SPC) involves testing a random sample of output from a process to determine whether the process is producing items within a preselected range.
Attributes are quality characteristics that are classified as either conforming or not conforming to specifications. Goods or services may be observed to be either good or bad, or functioning or malfunctioning. For example, a lawnmower either runs or it doesn’t; it attains a certain level of torque and horsepower or it doesn’t. This type of measurement is known as sampling by attributes. Alternatively, a lawnmower’s torque and horsepower can be measured as an amount of deviation from a set standard. This type of measurement is known as sampling by variables.
Process Control with Attribute Measurements: Using p Charts
Measurement by attributes means taking samples and using a single decision – the item is good, or it is bad. Because it is a yes or no decision, we can use simple statistics to create a p chart with an upper control limit (UCL) and a lower control limit (LCL). We can draw these control limits on a graph and then plot the fraction defective of each individual sample tested. The process is assumed to be working correctly when the samples, which are taken periodically during the day, continue to stay between the control limits.
Size of the Sample: The size of the sample must be large enough to allow counting of the attribute. For example, if we know that a machine produces 1% defects, a sample size of 5 would seldom capture a defect. A rule of thumb when setting up a p chart is to make the sample large enough to expect to count the attribute twice in each sample.
Process Control with Variable Measurements: Using X-bar and R (range) Charts
X-bar and R charts are widely used in SPC. In attributes sampling, we determine whether something is good or bad, fits or doesn’t fit – it is a go/no-go situation. In variables sampling, however, we measure the actual weight, volume, number of inches, or other variable measurements, and we develop control charts to determine the acceptability or rejection of the process based on those measurements. For example, in attribute sampling we might decide that if something is over 10 pounds we will reject it and under 10 pounds, we will accept it. In variable sampling, we measure a sample and may record weights of 9.8 pounds or 10.2 pounds. These values are used to create or modify control charts and to whether they fall within the acceptable limits.
There are four main issues to address in creating a control chart: the size of the samples, number of samples, frequency of samples, and control limits.
Size of the Sample: For industrial applications in process control involving the measurement of variables, it is preferable to keep the sample size small. There are two main reasons. First, the sample needs to be taken within a reasonable length of time; otherwise, the process might change while the samples are taken. Second, the larger the sample, the more it costs to take. Sample sizes of four or five units seem to be the preferred numbers. The means of samples of this size have an approximately normal distribution, no matter what the distribution of the parent population looks like. Sample sizes greater than five give narrower control limits and thus more sensitivity. Or detecting finer variations of a process, it may be necessary, in fact, to use larger sample sizes.
Number of Samples: Once the chart has been set up, each sample taken can be compared to the chart and a decision can be made about whether the process is acceptable. To set up the charts, however, prudence and statistics suggest that 25 or so samples be taken.
Frequency of Samples: How often to take a sample is a trade-off between the cost of sampling and the benefit of adjusting the system. Usually, it is best to start off with frequent sampling of a process and taper off as confidence in the process builds. For example, one might start with a sample of five units every half hour and end up feeling that one sample per day is adequate.
Control Limits: Standard practice in statistical process control for variables is to set control limits three standard deviations above the mean and three standard deviations below. This means that 99.7% of the sample means are expected to fall within these control limits. Thus, if one sample mean falls outside this obviously wide band, we have strong evidence that the process is out of control.
