How Do I Create P' Charts (Laney) in Excel Using SigmaXL?

P' and U' (Laney) Control Charts are attribute control charts that should be used when the subgroup/sample size is very large (i.e. > 5,000) and assumptions are not met. Typically you will see that the control limits do not “look right”, being very tight with many data points appearing to be out-of-control. This problem is also referred to as “overdispersion”. This occurs when the assumption of a Binomial distribution for defectives or Poisson distribution for defects is not valid. Individuals charts are often recommended in these cases, but Laney’s P’ and U’ charts are a preferred alternative.

P'-Charts

1. Open Laney – Quality Digest – Defectives.xlsx. This data is used with permission from David Laney.


2. We will begin with the creation of a regular P-Chart for this data. Select SigmaXL > Control Charts > Attribute Charts > P. Ensure that the entire data table is selected. If not, check Use Entire Data Table. Click Next.


3. Select Defectives as the Numeric Data Variable (Y) >>, N as the Subgroup Column or Size >>. Click OK. The resulting P-Chart is shown:
   
   
   
   At first glance, this chart suggests that the process is out of control. The problem here is actually due to the Binomial assumption not being valid (also known as overdispersion). This problem becomes evident when the sample sizes are large.
   
   
4. Select Sheet Defectives (or press F4). Click SigmaXL > Control Charts > Attribute Charts > P’ (Laney). Click Next.


5. Select Defectives, click Numeric Data Variable (Y) >>; select N, click Subgroup Column or Size >>. (If we had a fixed subgroup size, the numerical value of the subgroup size could be entered instead of Column N.) Check Test for Special Causes.
   
   

 



6. Click OK. The resulting P'-Chart is shown:





7. Now we see that the process is actually “in-control.” Laney’s Sigma (Z) is a measure of the overdispersion. See referenced articles for further details.

References:

1. Laney, David B., P-Charts and U-Charts Work (But Only Sometimes), Quality Digest, http://www.qualitydigest.com/currentmag/departments/what_works.shtml
2. Laney, David B., Improved Control Charts for Attribute Data, Quality Engineering 2002;14:531–7.
3. M A Mohammed and D Laney, Overdispersion in health care performance data: Laney’s approach, Qual. Saf. Health Care 2006;15;383-384.