SPC Chart for One-Sided Maximum Spec

Good question.

How's your understanding of the necessary maths?

First question is "Is the process truly a unilateral/one-sided specification?" (For instance flatness cannot be less than zero.)

If so, then the following is where you can start.

Cp (Capability index) comparing process capability to allowable variation. Has no menaing for unilateral tolerances.

Cpk (Capability index) compares process location to the relevant tolerance (Depending on whether you have an upper or lower tolerance.)

Cp (upper) =(USL-Xdouble bar)/(3 x (Rbar/d2))

Cp (lower) = (xdouble bar-LSL)/(3 x (Rbar/d2))

Pp (Performance index) has no meaning for unilateral tolerance

Ppk (predictor for proportion non conforming product) again depends on whether ULS or LSL and only predicts beyond that limit.

PPU = (USL-Xdouble bar)/3s

PPL = (Xdouble bar - LSL)/3s

CR (Capability ratio) is reciprocal of Cp and as such has no meaning for unilateral tolerances.

PR (Performance Ratio) is reciprocal of Pp and also as such has no menaing for unilateral tolerances.

Now to suggest an answer to your question.

For charting a process, the measurements are your data. For unilateral tolerances, you could use an "individuals and moving range" chart.

Using that sort of chart enables the data to be seen as a continuous stream of (samples) data packets, negative movements can occur, data will be centred typically exactly on zero with known variation (From your inital measurements) and you can then use conventional control limit theory on the chart information.

I would suggest though that you include the tolerance lines on the "individuals" part of the control chart just to pick "out of spec" situations.

While answer #2 is very complete and I believe a good answer I would advise that surface finish often produces a non normal distribution pattern so walk with caution with marginal capability indicators.

Secondly depending on the application I would encourage you to verify that zero surface finish (A fictitional as that is) is desirable as well. If surface finish is specified in a wear surface that is lubricated being too smooth can cause a wringing effect depending on the design of the surfaces mating and the lubricant being used. It is not unusual to specify a max limit for surface finish with the assumption that failure will always be to the rough side based on process intentions. Then "innovation and continuiou improvement" enter the mindset of the production plant andthey take a surface to glass like finish with pride and verbosity on to have a rash of warranty. (I don't sound too bitter do I?) :) Kepp Plugging away Guys and Gals.