% Proportion Defective Calculation

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• #30080

YSQuek
Member

I would appreciate it if someone can advise me on this. Thanks  & RegardsJames
Calculation for % Proportion Defective for Each Overdue Invoice Categories; CAT 1 ¨C 4, and the Overall Overdue Invoice for the month of Jul.
<<                Number of Invoice Count                >>                                                                              < Overdue Invoice Count  >                                    MONTH  TOTAL  CURRENT  CAT1  CAT2  CAT3  CAT4Jun              225            90                50         20       25        40  Jul               300           137               60         35       18        50
* CURRENT : 0  Day Overdue* CAT 1 : 1 ¨C 30 Days Overdue* CAT 2 : 31 ¨C 60 Days Overdue* CAT 3 : 61 ¨C 90 Days Overdue* CAT 4 : > 90 Days Overdue
Defect = Overdue Invoice

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#77977

Erik L
Participant

James,
Some quick questions regarding the data.  You have a metric that would allow you to do much more powerful analysis, yet you’re proceeding with an analysis that takes the data to a lower overall power (e.g. ordinal).  What’s the reason for that?  If you’re looking at subsequently charting the categories, I’d be wary of using an attribute methodology-p chart.  This would look to the binomial as a basis of the distribution and looking from the data provided there’s already a violation of one of the assumptions that is a pre-requisite for that distribution.  You do not have an equal probability of the data falling into categories of lateness due to the fluctuations in the overall population from month-to-month.  Look to the IX-MR to help you out here if that’s a tool that you’ll be looking at to gain process knowledge.
Regards,
Erik

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#77978

Carl H
Participant

James,
Please be more specific on your question.  Do you want to calculate proportion defective (late) for cat 1-4 combined (late 1+ days)?  By month?
As Erik stated, if you have the actual continuous days late (or early) by item available, you should consider using it versus discrete ordinal categories.
Carl

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#77994

YSQuek
Member

Erik / Carl
Thank you for your fast response. Sorry guys, I should have provided more information to the problem.
So, here it is …
[ Background ]The monthly Account Receivable Report classifies all Invoices into 4 Categories :
1  CURRENT (0 Day Overdue)2  CAT 1 (1-30 Days Overdue)3  CAT 2 (31-60 Days Overdue)4  CAT 3 (61-90 Days Overdue)
* Assuming All Payment Terms are the same – 30 Days;i.e. All Invoices would remain in CURRENT for 30 Days.
The Objective of this project is to Reduce the No. of Overdue Invoices (Defects).% Proportion Defective is selected as the Process Metric.( I would also like to discuss about the Rational behind this, Project Objectives, etc later )
But firstly, I wish to clarify the calculation for % Proportion Defect; for each Categories & Overall.
<>      TOTAL CURRENT <>   MONTH   CAT 1 CAT 2 CAT 3 CAT 4Jun 150 50 30 15 15 40Jul 100 40 20 10 10 20
% Proportion Defective = No. of Overdue Invoices / Total Number of Invoices ?          [Formual 1]                         OR                       = No. of Overdue Invoices / Opportunities for Overdue Invoice ? [Formula 2]
Assuming we are Caculating the % Proportion Defective for CAT1 for Jul …  * Defect Count for CAT 1 = 20* Total No. of Invoices for Jul = 100* Opportunities for Overdue CAT1 Invoices for Jul = No. of Current Invoices for Jun = 50
As for caculating the % Proportion Defective for all Categories (CAT1-4) for Jul … * Total Defect Count for All CATs = 60* Total No. of Invoices for Jul = 100* Opportunities for All Overdue Invoices for Jul = No. of Current Invoices for Jun = 150
Somehow, Formula 1 was chosen or derived by someone. All BBs, Process Owners, Team Members & MBB for this projectdo not seem to have problem with it. But, I’m having 2nd thought …
Another question that I have is that :For Transactional Project like this, what’s the min. acceptable Sample Size for Data Analysis, setting ofBaselines, Targets, etc. I thought all the last 12 months Historical Data should be used, since Financial Figures” Behave Differently ” from Quarter to Another. Does using Data from only one Month make any sense ?
James

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#78019

Carl H
Participant

To me, you should worry about the project metric after you decide what \$ problems you are having.  Do you lose \$ when you are at Cat 1or higher or do you lose significantly more \$ as you go to Cat 2,3,……?  This may direct you to worry about measuring % defective as anything >30 overdue or to categorize them as you have done.
I would suggest that the % overdue / # opprtunities by month is OK.  Careful how you count defects – do they become defects at 31 days or only after they are “closed out”.  # opportunities might be total # “initiated” that month.  Seems like the defects are going to spread themselves over the next 1+ months.  Again, I think this makes your categorizing them 1-4 even less reliable.
If you have the data on ACTUAL days to pay by item (instead of cat 0-4) , this is even better.  This data may tell you a lot more about what is going on (mean, median, spread, SD, distribution, run charts…).
If you are looking to baseline the process, one month of historical data seems pretty light.  If you think performnace changes throughout the year, then consider going back a year.  If you have to stay with discrete data (cat 0-4), then you certainly need more than a months data (150 invoices) to see any trends or have confidence in baseline performance.
We did a project on on time shipping performance and changed from discrete on time vs late to continuous days early (0).  Made baslineing, initial capability analysis, analysis for ciritcal Xs and control charting (monthly) much easier.

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#78031

YSQuek
Member

Hello, Carl ! Glad to hear from again.
The problem is we’re incurring cost by financing the Overdue Invoices. More as Invoices progress from Category to another.Categorizarion of the Invoices is an existing financial process that the Management looks at. Cat 1 =(Current+1) to (Current+30)days. Cat 2 =(Cat1+1) to (Cat1+30)Days, Cat3=(Cat2+1)Days to (Cat3+1)Days and Cat4=(> Cat3+1) Days. Once payment is made, the Overdue Invoice / defect would “cleared”. Every month we have about 700 – 900 Invoices, ranging from S\$10 to S\$200,000 each. COPQ ( Cost of Financing the Overdue amount is about S\$200K for last year).
The existing MIS / Financial System doesn’t offer reports based on ACTUAL Days- only Months; unimaginable to derive them manually. I suppose for our kind of business / industry, it’s acceptable.
My opinion on the sample size is that one month only offer a “Snap-Shot” of that particular month. To use that for formulating the Baselines & Targets would not make much sense … does it ? Unless we can prove that it represent the “patterns” for the entire year; there’s Significance Difference, Financially & Operationally.
% Proportion Defective = No. of Overdue Invoices / Total Number of InvoicesOR% Proportion Defective = No. of Overdue Invoices / Opportunities for Overdue Invoice Using Total No. of Invoices or Opportunities for Overdue Invoices make a Great Difference. Assuming, we calculating for Jul %,its 100 or 150 as the denominator … My fear is that when “Wrong” % Proportion Defectives is derived, and they direct all the efforts in the wrong direction. A case of Data analyzed incorrectly, information mis-interpreted, unsuitable solutions initiated, unpredictable results achieved, and finally un-sustainability set in … …  I’m not sure whether, I’m “over-acting” … … the Project is going to Control Phase and we’ve spend more than a year … Hmm … …
If I have the chance, I’ll do this project differently, most likely, as per your suggestion. ” changed from discrete on time vs late to continuous days early ”
Thanks & RegardsJames

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#78041

Ron
Member

I would uti8lize a 12 month rolling average as my metric this damps a lot of the variation and gives a true picture of your situation.
I would also offer that most companies offer an incentive to pay off early. If yours does not it is a way to cut losses by increasing fees the longer an invoice is out there.

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#78047

Carl H
Participant

James,
The metrics you choose are probably going to be estimates anyway since there is interaction between the months.
A measure for costs might be total overdue costs \$ / total invoiced \$ for tha month.  This might be good since it expresses the problem in \$s.  The denominator you use may be noisy from month to month so maybe pick a quarterly or annual average for this.  Lower is better in any case.
Since you are in control phase, setting up ongoing metric like this is a good idea.
Again, 1 month baseline data is probably not enough.
Dont worry, your project is not the first to ask these questions this late in the project – I ve been in them too!
Carl

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#78051

Saherngu
Participant

Hi, Ron. Thanks for confirming my understandings on this. It’s always encouraging to find someone who share similar opinion. As for your suggestions, we have in fact looked into them seriously. It was documented as some of the Action Plans. However, from observations or tracking, these 2 options are never exercised or didn’t meet its intent. Perhaps, for the following reasons :
1  Offering Incentives for Prompt or early payments cause EBIT erosions. This wouldn’t go down too well for the Management; especially, at times like these, everybody’s struggling to “stay afloat”.
2  The proposed Incentive has to be ” Attractive Enough ” for the Customer to bite the bait; especially for the Construction Industry that we’re in, most of them if not all customers expect us to ” Finance their Projects ” as long as they could possibly delay. Especially so, when the Market is in Recession for the last 3 years.
3  As for charging higher \$ for delaying payment, it has been clearly stipulated in our Invoices. But nobody is willing to demand for that, simplifying because of “Relationship Issues ” or ” Customer Satisfaction Reasons “. Such issues are more difficult to handle in Asian Context & with Fierce Competitions in bad Market Conditions.
I suppose this is the Collateral Y for the Process Y. Like what the Management puts it : The Challenge is to Manage a set of ” Parameters with Conflicting Interests “.
Cheers !
James

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