STATISTICAL INFERENCE

STATISTICAL CONTROL CHARTS

Constructing a Control Chart

To obtain this chart using Minitab, the 51 sample measurements would need to be entered into the worksheet. The command needs to specify that sample size is 3 and there is no known µ and s. Note that professional graphics produces a superior chart than standard graphics.

MTB> gpro

MTB> set c1

data> 8.8 9.2 9.1 ... 7.4

data> end

MTB> xbarchart c1 3

The control chart was constructed assuming that the process was in control. Recall that by the Central Limit Theorem our 's are approximately normally distributed, and that 99.7% of the normal distribution lies within 3 standard deviations of the mean. The so-called "three-sigma limits" were constructed so that any one subgroup mean from a stable process had only about three chances in 1,000 of exceeding them. Yet three averages were beyond the control limits. We have therefore solid evidence that the process is not in control. The important thing is what happens next. In companies which claim that control charts haven't helped them improve, the answer is: very little. As one SPC consultant put it, "Control charts don't improve processes, people do". Control charts can identify the presence of a special cause. People need to track down the root cause and remove it, ensuring that it does not recur.

A control chart for continuous data was constructed from m subgroups of size n with Centre line CL = Upper Control Limit UCL = + 3 Lower Control Limit LCL = - 3 where is the average of the m subgroup standard deviations, and is the average of all of the observations.

Some Comments On Control Charts

1. Every incident, change, or unusual circumstance should be logged on the control chart at the time point where it occurred. This is easy enough to do when the chart is being manually recorded, in real time. Many computer programs which claim to do SPC do not permit comments to be made on the chart - which shows they don't understand the purpose of the control chart. Control charts which are run off and filed away from the process producing the output are not being used properly.
2. Control charts do not of themselves solve problems. Properly used, they (a) identify situations most likely to contain problems (identify opportunities for improvement), and (b) impose a discipline to keep people from adjusting a process when the variability is a natural part of the process (prevent tampering). Tampering (unnecessary process adjustment) is a widespread and persistent problem. It results from people wanting to help, to have control over their process, but not understanding variation. Sometimes the first improvement that is made in a process is to keep workers from adjusting the process; the variability goes down, even though they had been trying to reduce variability with their adjustments!
3. Do not put specification limits on control charts. Specifications pertain to individual values; control limits are for averages, which vary less than individual values. In addition, specifications usually represent the minimum of what is desired, control limits attempt to estimate what is currently possible. There is no connection.

   Always remember: the customer buys individual products or services, not averages.

4. If operators are not trained in the use and purpose of control charts they may feel that this is a device to check up on (and punish) them; they may alter or remeasure data so that it will stay within the control limits.
5. Usually, try to start off the control chart with 20-25 subgroups of 4-5 observations each. The estimates of the process mean and standard deviation will be reasonably precise then. Then keep on adding points at the right. This is the mode in which control charts are most useful on the shop floor. Generally operators will not be required to calculate control limits from the initial data. Rather, this will have been done for them (e.g. by the foreman, supervisor, or TQM facilitator). The operator simply plots the points on the appropriate charts which will already have the control limits drawn in. They are then in a perfect position to react to a special cause signal as it occurs.
6. If the control charts indicate (often as a result of a deliberate process change) that the process mean has shifted ( chart) or the process variance has changed (R or s chart), then the control limits should be recalculated. Again 20-25 subgroups are recommended, and again these calculations need not be done by the operators, even though they are likely to be the ones who identified the process shift.
7. Computer generated control charts can be used for management reporting, e.g. summarising monthly production or sales performance. These charts help management appreciate the difference between, and magnitude of, common and special causes of variation. The control limits enhance the information in the data, and help management avoid the inevitable tampering which can occur when the data is presented purely as run charts (or, even, worse, as tables of numbers). Management data is typically individual numbers rather than subgroup averages. The relevant control chart is usually the individuals chart, which we discuss later in this chapter.