Control chart with one limit

[#1]

Hi all,
could anyone in the community possibly help me with my question regarding the control?

I have a process with just one limit.
And I want to carry out analyses like process capability. How can I carry out such analyses and build a control chart with one limit?

I am using JMP 16.1.0

[#2]

Welcome to the community.  I'm not sure what you mean by "I have a process with just one limit.?  What is a limit?  Is this a specification limit?  If so, control limits have nothing to do with specification. Capability is simple, just enter the one limit and use the Cpl/Cpu or Ppl/Ppu(depending on the limit).

[#3]

Adding to @statman 's response, if you have a one-sided spec limit and also want a one-sided control chart, you can turn off either the upper or lower control limit via the control panel in the Control Chart Builder (red circle in pic below).

[#4]

Sorry, because you can doesn't mean you should.  That is an inappropriate use of a control chart.

[#5]

@statman Some data should only have an upper control limit, especially when the lower control limit is below zero, or anyother value that is logically impossible. For example, count data.  In addition, measurement data that is right-skewed, maybe even exponentially, might be plotted on a control chart. In this case, the lower limit can again, be less than zero, something that is logically impossible. 

Adding the lower control limit, and displaying it confuses the consumers of the data, it also formats the axis so that half of the graph shows the illogical, less than zero range, (all white space) making the chart harder to read. 

Remember, the whole purpose of the control chart is to make it clear when the user should react to process behavior changes. Generating charts that obscure the intent are not helpful. 

In this particular case, the original question made an equivocation between "control limit" and "spec limit".   This is the larger issue. Control limits are for assessing process behavior and Specification limits are for assessing process performance.   Originally answering the question by differentiating between the two and noting that process capability analysis only needs one specification limit, might have been more helpful. 

[#6]

Admittedly, I could also have chosen a better data set for my example. Great discussion!

[#7]

With all due respect, if the software is plotting control limits of an implausible value (for your example, count data) then that is a problem.  For some data, 0 may be the appropriate LCL. There is no requirement data be normally distributed to properly use control charts (See Shewhart and Wheeler). 

There are two functions (purposes) of a control chart (as defined by Shewhart):

1. Assess the consistency/stability of the within subgroup sources of variation (this is typically quantified by using a range of the within subgroup data).  This is the function of the range chart.  This is done first, because the second function of the control chart method is to do a comparison of the components of variation (the within sources to the between sources).  Of course, a comparison would be irrational if the basis for comparison *the within subgroup variation) was inconsistent.

2. Compare the components of variation to determine where the greatest source of variation lies.  This is done using the X-bar chart.  The plotted data (averages) are biased to the between sources of variation (the x's that vary at the sampling frequency).  These are plotted against the control limits which are a function of the within sources of variation (again, the x's that vary at the subgroup frequency).

The limits are intended to provide guidance to the user for determining consistency and evaluating leverage.  They were originally derived based on empirical data with economic risks.  Not properly using control charts as they were intended confuses many users.  I'll add, having control limits on the X-bar chart automatically calculated by the software when the range demonstrates inconsistency (e.g., out-of-control), is inappropriate and confuses the user.

Now, this does not mean there are not a host of other graphical techniques to display data and make other decisions.  I refer only to control chart method.

[#8]

Control limit is not the same with spec limit.

Process capability (Cpk or Ppk) is based on spec limit. Control limits used in control chart.

Cpu/Ppu if you need only the upper limit, Cpl/Ppl if you need only the lower limit.

Otherwise, the  Cpk/Ppk is the minimum of Cpu/Cpl or Ppu/Ppl.

Just take note that Cpk is using short term sigma (estimated based on subgroup variation - in @Jed_Campbell , the method for Cpk is based on average of moving range) & Ppk is based on long term sigma (overall standard deviation - this value similar to standard deviation computed in distribution platform)