Frank Satherwaite was a brilliant statistician who establish the theoretical underpinnings for Pre-control. Pre-control was further developed by the consulting company of Rath and Strong. The mechanics of Pre-control can be taught and less than 10 minutes as there are only four simple rules to follow as exemplified in the “Pre-Control Example” figure:
Rule 1. Divide the specification width by four. The boundaries of the middle half of the specification then become the Pre-Control lines. The area between these Pre-Control lines is called the Green Zone. The two areas between each Pre-Control line in each specification limit or call the Yellow Zones. The two areas beyond the specification limits are called the Red Zones.
Rule 2. To determine process capability, take a sample of five consecutive units in the process. If all five fall within the Green Zone, the processes in control.(In fact, with a simple rule, usual samples of 50 to 100 units to calculate CP and CPK are not necessary. By applying the multiplication theorem of probabilities or the binomial distribution, it can be proven that a minimum CPK of 1.33 will automatically result.) Full production can now commence. If even one of the units falls outside the Green Zone, the process is not in control. Conduct an investigation, using engineering judgment or better still, using design of experiments to determine and reduce the cause of variation.
Rule 3. Once production starts, take two consecutive items from the process periodically. The following possibilities can occur:
(A) if both units fall inside the Green zone, continue production.
(B) if one unit is in the Green zone and the other unit in the yellow zones, the process is still in control. Continue production.
(C) if both units are in the Yellow zones (with both in the same Yellow zone or one in one Yellow zone and the second one in the other), stop production and conduct an investigation into the cause of variation and correct it.
(D) if even one of the units falls in the red zone, there is a known reject, and production must be stopped and the reject cause investigated. When the process is stopped, and the cause of variation identified reduced or eliminated, Rule 2, i.e., five units in a row in the Green zone, must be reapplied before production can resume.
Rule 4. The frequency a sampling of two consecutive units is determined by dividing the time period between two stoppages (i.e., between two points of yellows) by six. In other words, if there is a stoppage (two yellows) say at nine in the morning and the processes corrected and restarted soon after, followed by another stoppage at noon (again two yellows), the period of three hours between these stoppages is divided by six, to give frequency of sampling of every half hour. If, on the other hand, the period between two stoppages is three days, the frequency of sampling is every half-day.
The theory behind the effectiveness of Pre-control is based on the multiplication theorem of probabilities and the binomial distribution. Although the mathematical derivation is beyond the scope of this discussion the following is a summary of the results. The worst alpha risk, the risk of overcorrection and stopping a process when it should continue, is around 2%. The worst beta risk, the risk of allowing a process to continue when it should be stopped, is close to 1.5%. Pre-control is a method that’s extremely useful when starting up a production process coming out of a new business development or R&D project.