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I have a production process, which produces one or more goods on a certain day. For this example, assume the weight of the produced good is consistenlty measured. However, the operators can ofcourse differ on a day-to-day basis.

I want to establish control limits for this production process based on the weight. However, my research leads me to believe that I need to account for the subgroups, which, in this case, I assume is the day. The problem is that I thusfar only encountered cases in which the number of samples in each subgroup was equal. As the production varies from day to day, there exists varying subgroup size.

What is the best manner to proceed?

X-bar R charts with varying subgroup size proposed control limits per subgroup, but I desire a single control limit.

Reference example:

day1:

  • #01: 25.6 kg
  • #02: 25.8 kg
  • #03: 25.3 kg
  • #04: 25.7 kg

day2:

  • #01: 25.3 kg
  • #02: 25.4 kg
  • #03: 25.2 kg
  • #04: 25.3 kg
  • #05: 24.9 kg

day3:

  • #01: 25.4 kg
  • #02: 25.2 kg
  • #03: 25.9 kg
  • #04: 24.8 kg
  • #05: 25.2 kg
  • #06: 25.7 kg
Jigeli
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  • What is your goal here? As best I can tell I can't tell if this is strictly a statistics question or if you are asking something else. Some clarification of what you want from this data would be helpful. – Shawn Hemelstrand Nov 16 '23 at 11:39
  • The goal is to determine the control limits of the process. Given those, specification limits may be later introduced.

    While the 3σ provides some form of answer, it does not account for the variability within a group or between groups of data. The subquestion could be how to determine variability given the unequal groups of data samples.

     – Jigeli Nov 16 '23 at 15:54

0 Answers0