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SPC (Statistical Process Control) for Unilateral Tolerance - Questions

Re: SPC for Unilateral tolerance

The only difference is that one could only calculate a Ppk. This is the difference between the process average and the specification limit divided by 3 estimated standard deviations. That's about it.

One would have the same sample size -minimum 30 parts, etc.

Dear Sir ,

Mysefl Shivashankar from India , i have atatched few problem in excell shet which contains SPC quentioneries and request anyone can solve and send me back.


Dear Quality Guru’s

I have Few doubt /Question on SPC study and request you all to Clarify the same.
  • One sided Tolerance (Unilateral Tolerance ) has been categorised as a two Category as below .
  • Unilateral tolerance on Geometrical Tolerances like Perpendicularity , Run out , Symmetrycity etc..
  • Unilateral tolerance on Target Dimensions like Dia 2.5+0.02, Dimn 2.3-0.03, Dimn 2.45+0.02/-0.05 etc..
  • Q1. What is the Cpk formula for ‘a’ Category ?
  • Q2. Do we required Cp as well as Cpk for both for ‘b’ category ?
  • Q3. What is the Cp /Cpk formula for ‘b’ category?
  • We do Batch process like Sintering/Heat treatment etc.. and once after completing this process we collect 50Pcs for Inspection. Here my Question is ,
Q1. What type of SPC study we need to conduct here ?

Q2. What is the Subgroup size need to consider here ?
  • As you all know there is a Hole Basis System /Shaft Basis System (HBS/SBS) like 5H6, 12f6, 7K8, etc.. My Question here is
Q1. Dia 10H6 (Dia 10+0.009mm ) , do we need Cp /Cpk both here or Cpk is enough .

Q2. What is the Cp/Cpk formula for the Above Q1.

Q3.What is the Cp/Cpk formula for 10h6 (Dia 10-0.009mm ) .

Q4. What is the Cp/Cpk formula for 10+0.005 /-0.008mm .

Please have look over these question and if you need further data , clarity , please send queries and solve these question .

It will help us to learn the process excellence.
SPC only considers specifications such as parallelity, perpendicularity, etc. as unilateral.
For unilateral tolerances such as Perpendicularity, parallelity, etc. calculate only Cpk/Ppk, since our target here is 0 and there can't be any reading less than 0. Cp/Pp is of no significance here, since the specification can only be more than 0. Therefore we want to check only shift(location) of the process.
Cpk formula would be USL-Xdbar/3s

For specifications such as 20 +0.02, Cp/Pp, Cpk/Ppk both should be calculated, since there is a possibility of specification being less than 20.
Cp = USL-LSL/6s
Cpk= Minimum of : USL-Xdbar/3s or Xdbar-LSL/3s

For processes where batch production happens, such as heat treatment, pressing, IMR (XMR) chart can be used. Subgroup size is considered as 2 here for calculating and plotting MR (Moving Range).

For specifications such as Dia 10H6, Cp/Pp, Cpk/Ppk both should be calculated. Eg. in case of 10H6, LSL is 10.000 and USL is 10.009. But the results can be less than 10.000 as well. Cp helps us to identify ratio of tolerance to process variation i.e. USL-LSL/6s. In this case, it can happen that the ratio is good .i.e. Variation is less than tolerance. But the results might be nonconforming (Out of specification), hence we need to calculate Cpk/Ppk to understand shift (Location) of the process.

Proud Liberal

Quite Involved in Discussions
Amit, I don't think this chart is easy to interpret.

Realizing that my changes are purely cosmetic, here's a modified version of test 6 Xbar chart (see attached Excel file for all changes) :

Removing the legend, adjusting the Y-axis scaling, and having the line labels automatically populate make it easier to see patterns in the data and focus on the story being told. I would also advocate excluding the ± 1 sigma and ± 2 sigma lines on the charts. In my option, a good chart should be able to be interpreted from "across the room".


Thank you so much proud liberal for help. I appreciate.
I've added 1 sigma and 2 sigma limits in order to be able to apply control chart rules to detect special causes. It depends on the user whether he wants to use it or not (depending upon application).
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