kristof,

Let me follow up on Dave's comments.

There are three components of variation in a part, within-piece, piece-to-piece, and time-to-time variation. These are composed of process, material, operator, and miscellaneous components. There are typically two schemes for selecting subgroup samples:

1) Select subgroup samples from product produced at one instant of time or as close to one instant as possible - instant time method.

2) Select product produced over a period of time so that it represents all products - period of time method.

The instant time method will have a minimum of within part variation and a maximum of variation among subgroups. Period of time will have a maximum of within part variation while a minimum of subgroup to subgroup variation. Instant time is the most common used method.

Deciding on the subgroup size is more of a management than a technical decision. As the subgroup size increases, the control limits become closer to the central value which makes the subgroup more sensitive to small variations in the process average. Also, as the subgroup size increases the inspection/test cost increases. When the subgroup size exceeds 10, a sigma chart is used instead of the range chart. Sigma is more sensitive but more difficult to calculate. Range is normally used simply for calculating simplicity.

There is no rule for frequency of subgroups. The inconveniences of factory layout and the cost involved in taking the subgroups have to be balanced against the value of more frequent information. A rule of thumb is to used a variables sampling plan (such as the old MIL-STD-414) to determine the sample size based on daily production. For example, if you produce 3,201 to 8,000 units per day you would take 60 samples per day. If the subgroup size is 5, then the number of subgroups per day would be 60 divided by 5 or 12 subgroups.

With regard to the A2, A3, B4, d2 factors, you need to understand the derivation of the factors to understand why the tables stop at 25. The formula substitutions do not work well in the text based forum format otherwise I would try to show it to you. If you can get hold of a copy of Acheson Duncan's book, Quality Control and Industrial Statistics you can find the background material. Never the less, for the A2 factor for a sample larger than 25 the formula is 3 multiplied times d2 divided by the squart root of the sample size

. The d2 factor for samples larger than 25 is equal to R divided by sigma. My formula come from an American Society for Testing and Materials standard, ASTM-STP-15D.

Hope this helps.

Regards,

Rick