Cpk roughly double Ppk How to fix this?

Hello,

I have been collecting width measurements using a caliper for a bilateral capability study. The tolerance for our plant is 1/16 inches plus or minus. The only data that I see is throwing this off is the high end of the results in the bell curve. Even if I take this data out I am unable to get a passing Cpk and Ppk. How or why is this happening?
 
Here is the data

Number of readings
125​
Lower spec limit (LSL)
4.6125​
Nominal
4.6750​
Upper spec limit (USL)
4.7375​
Total sum
583.7540​
Average readings ( X )
4.6700​
Maximum
4.7160​
Minimum
4.6310​
Readings below LSL
0​
Readings above USL
0​
Average Range (R)
0.0229​
D2 Valuen =5
2.3260​
Upper capability index (CPU)
2.2863​
Lower capability index (CPL)
1.9496​
Capability index (Cp)
2.1179​
Process Capability (Cpk)
1.9496​
Capability ratio (CR)
0.4722​
Std Deviation (n-1)
0.0206​
Std Deviation (n)
0.0205​
Variance (n-1)
0.0004​
Variance (n)
0.0004​
Performance index (PP)
1.0110​
Performance ratio (PR)
0.9891​
Performance index (Ppk)
0.9306​
 

Miner

Forum Moderator
Leader
Admin
Without having the raw data to analyze and information on subgrouping, frequency or process type, all I can say is that your process is probably not stable as the long-term variation is much greater than the short-term variation within subgroups.
 

Bev D

Heretical Statistician
Leader
Super Moderator
OR the process is stable but naturally non-homogenous….

Please provide all of the individual data - what you have posted is not data - it is a table of statistics. Please also post the data grouped by subgroup and in time order of production - not in order of measurement…
 
n1234567891011121314151617181920
1
4.681​
4.671​
4.715​
4.678​
4.678​
4.677​
4.677​
4.708​
4.658​
4.651​
4.67​
4.698​
4.659​
4.716​
4.655​
4.678​
4.661​
4.708​
4.673​
4.671​
2
4.662​
4.646​
4.694​
4.68​
4.675​
4.65​
4.66​
4.683​
4.631​
4.634​
4.639​
4.656​
4.642​
4.69​
4.636​
4.686​
4.659​
4.705​
4.68​
4.687​
3
4.683​
4.659​
4.712​
4.681​
4.681​
4.668​
4.668​
4.687​
4.641​
4.651​
4.653​
4.677​
4.645​
4.71​
4.652​
4.682​
4.657​
4.712​
4.675​
4.699​
4
4.676​
4.66​
4.711​
4.672​
4.671​
4.664​
4.672​
4.685​
4.638​
4.644​
4.655​
4.671​
4.654​
4.672​
4.66​
4.678​
4.659​
4.705​
4.672​
4.671​
5
4.675​
4.65​
4.711​
4.662​
4.666​
4.656​
4.66​
4.679​
4.634​
4.642​
4.646​
4.656​
4.647​
4.702​
4.677​
4.672​
4.656​
4.706​
4.669​
4.678​
n2122232425
1
4.661​
4.673​
4.69​
4.635​
4.652​
2
4.673​
4.684​
4.697​
4.655​
4.659​
3
4.652​
4.666​
4.716​
4.652​
4.646​
4
4.666​
4.669​
4.687​
4.639​
4.65​
5
4.662​
4.667​
4.685​
4.666​
4.647​
 

Miner

Forum Moderator
Leader
Admin
It is as I suspected. Your process is not stable, which increases your long-term (between subgroup) variation.
You did not provide any details about your process. Have you verified that your measurement system is adequate? Are operators over adjusting the process (i.e., tampering)? How finely can you make adjustments to your process?

Cpk roughly double Ppk  How to fix this?

Cpk roughly double Ppk  How to fix this?
 
Hello,

Thank you for the feedback. Yes, measuring system is accurate. Gage R & R study was good.

The issue is that the operators are not adjusting the process unless the product falls out of the specification limits.

It is a slitting process so if you adjust one knife it will affect another measurement in the next lane unless it is on the end. We could adjust all knives to get closer to the center of the bell curve but we most likely will still have the same issue.

Maybe it is the setup of the knives that needs to be corrected?

If more of most of my results fall in the center of the bell curve would that give me a better Cpk and Ppk?
 

Miner

Forum Moderator
Leader
Admin
It is a slitting process so if you adjust one knife it will affect another measurement in the next lane unless it is on the end. We could adjust all knives to get closer to the center of the bell curve but we most likely will still have the same issue.
This raises a question of how you are setting up your subgroups as well as the potential for autocorrelation.
  1. Does your subgroup go laterally across all of the knives, or linearly down one strip?
  2. What material are you slitting, and how do you determine when to take each of the five measurements in a subgroup? Do you just take five measurements at arbitrarily determined intervals?
If you are measuring linearly down one strip, you are likely seeing the effect of autocorrelation, which screws up the basis for sub-grouped control charts. An individuals control chart will work much better. This example used the first measurement of each subgroup.

ADDED: Autocorrelation causes the Xbar chart's control limits to be based entirely on measurement variation as there is no actual within subgroup variation due to the process.

1705605344989.png
 
Last edited:

Bev D

Heretical Statistician
Leader
Super Moderator
Miner - can you plot this as a multi-vari with the spec limits? (I don't have JMP now that I'm retired and EXCEL doesn't like to make graphs anymore - well except useless pretty marketing art...)

While the control chart shows a non-homogenous condition we can't say that the process isn't naturally non-homogenous and a rational subgrouping scheme would indicate stability...certainly there are no out of spec parts so the question really is what kind of process is this and how were the data subgrouped. (ie every 2 hours, every lot, sequential pieces or randomly selected from a lot...etc.)
 

Miner

Forum Moderator
Leader
Admin
Miner - can you plot this as a multi-vari with the spec limits? (I don't have JMP now that I'm retired and EXCEL doesn't like to make graphs anymore - well except useless pretty marketing art...)

While the control chart shows a non-homogenous condition we can't say that the process isn't naturally non-homogenous and a rational subgrouping scheme would indicate stability...certainly there are no out of spec parts so the question really is what kind of process is this and how were the data subgrouped. (ie every 2 hours, every lot, sequential pieces or randomly selected from a lot...etc.)
I wasn't sure which variables you were after, but here goes.
Cpk roughly double Ppk  How to fix this?

Cpk roughly double Ppk  How to fix this?
 
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