What is the recommended minimum number of subgroups necessary to calculate the limits for a control chart?
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X Bar S charts often used control chart to examine the process mean and standard deviation over the time. These charts are used when the subgroups have large sample size and S chart provides better understanding of the spread of subgroup data than range. X
bar S charts are also similar to X Bar R Control chart, the basic difference is that X bar S charts plots the subgroup standard deviation whereas R charts plots the subgroup range Selection of appropriate control chart is very important in control charts mapping, otherwise ended up with inaccurate control limits for the data. Manually it is very easy to compute X Bar R Control chart, where as sigma chart may be difficult due to tedious calculations and large sample size. With large sample size in the subgroup, the standard deviation is better measure of variation than the range because it
considers all the data not just minimum and maximum values. It is actually a two plots to monitor the process mean and the process range (as described by standard deviation) over time and is an example of statistical process control. These combination charts helps to understand the stability of
processes and also detects the presence of special cause variation. The cumulative sum (CUSUM) and the exponentially weighted moving average (EWMA) charts are also monitors the mean of the process, but the
basic difference is unlike X bar chart they consider the previous value means at each point. Moreover these charts are considered as a reliable estimate when correct standard deviation exists. X-bar chart: The mean or average change in process over time from subgroup values. The control limits on the X-Bar brings the sample’s mean and center into consideration. S-chart: The standard
deviation of the process over the time from subgroups values. This monitors the process standard deviation (as approximated by the sample moving range) Steps to follow for X bar S chartObjective of the chart and subgroup size
Note: To demonstrate an example, we just took subgroup size 4 in the below example, but it is always recommended to take 10 and above for X bar S chart. Example: A packing organization monitoring the performance of a packing machine, each container should weigh 35 lb, during Measure phase, project team performed the process capability study and identified that the process is not capable(less than one sigma). In Analyze phase collected 12 sets of container weights with a subgroup size of 4. Compute X bar and S values
Determine the Control LimitsThe first set of subgroups are to determine the process mean and standard deviation, these values are to be consider for creation of control limits for both standard deviation and mean of each subgroup The process to be in control in the early phase of the production. Special causes to be identified if any of the points are out of control during initial phase and also the subgroup has to be removed for calculation. Sometimes in the initial phase it would be also good to have few points out of control on the x-bar portion. Otherwise, if all the values are within the control limits may be because of slop in the measurement system, team won’t focus on it. Identify appropriate Measurement System Evaluation (MSE).
The below control chart constants are approximate values to measure the control limits for X bar S chart and other control charts based on subgroup size
Example cont: In the above example n=4 Interpret X bar and S chart
Example Cont: Use the above values and plot the X bar and Sigma chart From the both X bar and S charts it is clearly evident that most of the values are out of control, hence the process is not stable Monitor the process after improvementOnce the process stabilizes and control limits are in place, monitor the process performance over the time. Example cont: Control Phase- Once the process is improved and matured, team identified the X bar S chart is one the control method in Control plan to monitor the process performance over the time period Following are the measurement values in Control phase of the project Compute X bar and Sigma Find the control limits From the both X bar and S charts it is clearly evident that the process is almost stable. During initial setup at 2nd data set both S chart and X bar chart value are out of control, team has to perform the root cause analysis for the special cause and also the process is smoothing out from the data set number 4. If that continued, the chart would need new control limits from that point.
Important notes on X Bar S Control Charts
https://www.youtube.com/watch?v=-O9Q4Z-nmfI What is the minimum number of sub groups needed for control limits calculation?Most statisticians would say you need a few hundred data points to fit a distribution. My general rule of thumb is to use 150 to 200 observations minimum for all subgroup sizes (i.e. that's 30 to 40 subgroups of size 5), and of course that data must be from a stable process for it to be useful for these purposes.
How many points are required for a control chart to be accurate?Control charts show time-ordered plotted points around a center line. The center line is determined by calculating the mean of the plot points, typically about 20 to 25 points. The upper (UCL) and lower control limits (LCL) are typically set at +/- 3 standard deviations of the plot points.
What information is needed to calculate the control limits?Control limits are calculated by: Estimating the standard deviation, σ, of the sample data. Multiplying that number by three. Adding (3 x σ to the average) for the UCL and subtracting (3 x σ from the average) for the LCL.
What is subgroup size in control chart?The subgroup size affects the sensitivity of the control chart. Smaller subgroups create a control chart that is less sensitive to changes in the process, while larger subgroups may be too sensitive to small, economically unimportant changes. When using x charts, the subgroup size should be kept small -- nine or less.
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