Assume you are managing a process making 100+ parts per hour for one of your customers. This customer requires that you control your process and ship 100% good product for a critical characteristic. Your goals for initiating a process control procedure are:
1. To maintain the process to its capability (Keep it in control.)
2. To learn about the factors that can cause the process to change.
3. To do the above in and inexpensive way and as quickly as possible.
Sample Frequency – Variable/Measurement Control Charts:
There are a number of factors that affect the frequency and size of the sample collected for a control chart.
1. The first and foremost concerns how much data can you get. If you are producing between one to five units per day, you are pretty much limited to one sample which has 5 observations (n = 5) day or five samples with one observation per sample (n = 1). If you get 500 to a 1,000 units per hour, there are many more options to consider.
2. Another factor concerns how the process typically changes (goes out of control). If the process tends to jump/shift, than a larger samples will detect the change more quickly. If the process drifts in one direction, a more frequent sampling will tend to trigger a violation of one of the run’s rule conditions. The frequency here should mirror the rate at which the process drifts and not be too frequent.
3. Another factor concerns the cost associated with the process change. If a lot of units can be made very quickly that must be scrapped or reworked, then more frequent sampling should be done – particularly if there is a high cost associated with bad units getting through to the customer.
4. Another factor concerns the costs of taking the samples. If the cost is high, then less frequent and smaller samples should be taken. If the test is destructive, then the cost of taking the sample can be high and/or be most of your production.
Assume you have a process that is producing 100 units each hour. Taking a sample of five units each hour can be viewed as a starting point. You can make adjustments to this sampling process based on the factors above. You might want to consider just starting with this sample size and frequency (if it fits your process), and just plan on adjusting it based on how it performs. If you are getting too many alarms (more than people can deal with) or too many false alarms, you can adjust the frequency down and/or the size of the sample down as well. If over some period of time, you do not get any out-of-control signals, you also might want to adjust the sample size and frequency if you think there should have been some indications of out-of-control over the period of time tested. One suggestion here is to communicate to others that you are trying it out and there will be opportunities to change the way things are sampled.
Sample Frequency – Attribute/Count Control Charts:
Attribute control charts are built based on the premise that defectives or defect do occur. They are most useful where there is automatic, 100%, “go-no go” testing of a high volume product.
For P- and nP-charts, if you have a 1% defective/nonconforming product, a sample of 100 units is expected to have 1 bad unit in the sample. The upper control limit tends to fall between 0% and 1% defective, making any sample with one bad unit in it, above the upper control limit. A sample size of 200 to 500 would be more appropriate and it frequently is based on the number of units produced that day, shift, etc. In general, I prefer to have samples that contain at least ten different numbers of defectives (say 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9), and I would still consider using the chart if there were as few as 5 different values (say 0, 1, 2, 3, and 4) occurring.
In the case where the number of defects per some unit designation (C- and U-charts) is considered, more than one defect can occur per unit. In this case as in the previous one, if the average number of defects per unit is 1 or less, any sample with a defect in it will tend to be above the upper control limit. As before, I prefer to have samples that contain at least ten different numbers of defects (say 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9), and I would still consider using the chart if there were as few as 5 different values (say 0, 1, 2, 3, and 4) occurring. Note: On a U-chart, the average number of defects per unit for a sample is frequently not an integer.
The frequency of the sample for an attribute chart is generally specified by some time period, e.g., by shift, by day, per week, etc. This makes the number of units tested different each time period which results in the P- and U-charts being the ones used more frequently. These charts are generally less sensitive and they provide less information. For example, one does not know where the process is centered (X-BarBar) when only “go-no go” information is gathered.
