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Non-Normal/Normal Combined Capability Analysis

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  • #25081

    Dillon
    Participant

    I am a new BB and need some assistance with a cycle time reduction project I am working on at a healthcare facility.  Originally, my client asked me to reduce the cycle time for the “patient work up process” which is the time it takes to complete the up front documentation/chart preparation prior to being seen by a Dr. or RN.  However, after mapping the process completely,  there is a significant opportunity (backed by customer complaints), that the total patient wait time before service is provided is excessive.  The opportunities are in two areas (1. time from patient sign-in to being called to the window to start the work up process, and 2. the actual work up cycle itself), both of which I now have data for.  
     The distribution for the “work up process” is Normally distributed (GOF test verified), however, I went through the same process for the up front “patinet wait time” and the best fit with a p-value of .469 was Exponential.  
    Can these two be combined for capability analysis, long term dpm, sigma level etc., and if so, what is the preferred/least painful  method? Most of what I have read cautions about doing transformations to Normal on true non-normal data.  Also, can any software do this combination calulations or must this be done via Excel or manually?
    Any guidance would be appreciated.
    Thanks,  Doug
     
     
     
       

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    #60276

    Edwards
    Participant

    Doug, Minitab 14 will do this analysis for you. You would have to calculate the capability of each of your two processes separately but you could combine the two defect rates. Make sure that the processes are both stable over time before you do this or the result will be meaningless. I don’t have any link with Minitab other than being an enthusiastic user. You can download a trail version from their website http://www.minitab.com
    Hope this helps!

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    #60279

    Atul Bhatt
    Participant

    It sounds like there is a more fundamental question to be asked here. The question is “What is the output variable as seen by the customer?”. If the customer sees the total wait time, you really want to treat the 2 components you have as Vital Xs. This treatment will simplify your choice of what parameters you will use to calculate process sigma, capability, etc. to the output variable as seen by the customer.
    Another thing. Now you can easily to correlation on the 2 Xs to determine which one drives the variability in the overall wait time
    Hope this helps ….Atul

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    #60281

    OLD
    Participant

    Doug:
     
    I would like to ask a very simple question: “What does your project charter indicate as the scope of the project?” I would ask you to look at both processes to determine if it makes sense to revise your original charter –OR- does it make more sense to have two projects? We’ve all seen projects with “scope creep” that are continuously revised to include more and we’ve all seen projects that were too narrowly defined and should be expanded.
     
    The reason why I ask the question (from an outsider’s viewpoint), it seems that: “total wait time” is influenced by scheduling parameters, nurse & doctor availability, policies, volume, etc.  “Patient work-up wait time” is influenced by: administration, system aplications, volume, other????
     
    Two very different processes and possibly two, very different solutions? Best handled by one or two projects???? You make the call……
    GOOD LUCK!  OLD

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    #60277

    Dillon
    Participant

    Thank you for your response David.  Could you elaborate on how to calculate the capability for the portion of the process that is Exponentially distributed?  I understand how to do this on a Normal distribution, however I am not clear on how to do this when the mean and sigma are equal (Exponential/Non-Normal), and the percent of data is not a 50/50 split above and below the mean. This is a situation in which I have not encontered before. 
    This may be rudementary for many, but everyone had to learn it the first time. 
    Thank you for your help.   Doug
     

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    #60278

    Atul Bhatt
    Participant

    Box-Cox transformation is one way to translate the non-normal distribution to normal distribution. Johnson’s curve fitting also may be applied. The article at http://www.pyzdek.com/non-normal.htm gives more insight. But there is caution that needs to be exercised as you start using the capability data. While the transformations help in calculating process capability, they do not alter the fact that the process data is non-normally distributed.

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    #60280

    Dillon
    Participant

    Thank you Atul.  The output variable that the customer ultimately sees/feels is how long it takes them to get through the initial wait plus the work up process combined. I have done a correlation analysis on a number of items against this total wait time and the only two items which emerged were 1. number of patients that are in the waiting room at any given time (or what could be called backlog), and 2. (the type of client service needed. I may not have mentiond that this is a facility that takes both appointments and walk-ins, so at, present neither of these variables are controllable.  In addition, I have actually broken the data down to look at patient arrival quantities by hour and day. 
    Based on the above, my approach has been to focus on the variables that can be controlled (patient work up cycle) and evaluate the feasibility of adding an additional person from the existing staff to help during peak hours (typically a.m.), to help reduce the up front wait time to begin the work up process. 
    Any other thoughts?
    Thanks,   Doug 

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    #60282

    Dillon
    Participant

    Old:  Great and appropriate question.  One that I has been going around in my head for the last couple of weeks.  
    Couple of points of clarification.  The total patinet wait cycle (as I have defined it), is from the time they sign in at the window to the time the work up process is completed.  At this point, the patient is now “available” to be seen by the Dr. or RN.  
    On average, the total time to complete the above is around 30 minutes, of which 57% is the up front wait mentioned and 43% is work up process itself.  Variation in the up front wait portion is 3X what the  work up cycle is.
    You are right that this is a scope change from the original, but I keep looking at the majority of the total customer wait cycle being driven by the “waiting to start the process” and felt I could not ignore this area of opportunity to improve the customer expeience.  Maybe I am to new to this and trying to do too much in one project as you suggested. 
    In light of what I shared here, let me know if you have any different thoughts. 
    Thanks,  Doug 

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    #60283

    OLD
    Participant

    Doug:
     
    It is great to read your posts as you include information/data that proves you are utilizing the SS approach! EXCELLENT!
     
    There is no right/wrong answer as to whether your project should be one or two projects. It sounds as if your research/preliminary findings of “upfront” = 57% and “work-up” = 43% has revealed a greater opportunity than the original scope. That is good discovery….
     
    It has been our experience that as a project’s charter changed, the original team may not include the appropriate people to handle the direction of the new scope. We had to assess the team make-up to determine if new expertise should be added to compliment the scope change. If possible, you may want to go through this exercise to ensure your team is well represented. You may want to supplement the make-up of your team with the appropriate SME’s that can handle the likely solutions/improvements associated to “upfront” and “work-up”.
     
    As I read your early posts I was thinking that might be the case for you….GOOD LUCK!  OLD

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    #60284

    lin
    Participant

    Maybe you should try simulation since waiting time and service time are two different animals.  I don’t think it is unusual to find exponential arrival times.  Perhaps you should look into arrival patterns by hour, shift, day of week, etc. to see if there are times when the arrival times are more intense.  It then becomes a problem of matching staffing to those intense periods of arrivals to the extent this is possible.Service times are more process related and can be flow charted and studied with the intent of eliminating non-value added parts.Just throwing in my two cents.

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    #60294

    Don Bass
    Participant

    In support of what Bill says…before I became involved in SS, I was an Industrial Engineer (in the 80s).  I routinely used Queuing Theory to augment Cycle Time where “Service” times were impacted by “Waiting” times to start service.  While this was applied to mostly to a single person working in multi-machine environments, it seems applicable here…especially if you first use Simulation as suggested by Bill.  Once average times for Wait and Service are derived, you can use Queuing Theory to develop an “Interference” value that is factored onto the Service time as a coefficient.

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    #60316

    Maria Madrigal
    Participant

    Doug:
    I’ve read through your original post as well as all of the replies thus far.  I think that I might have two cents to add in here, as I actually just got done working a similar project in healthcare to yours.  Our project objective was to “reduce the overall cycle time for patients seen through the Emergency Department”.  The scope was from the time they walked in and signed in at the triage window until the time they were discharged or admitted to the hospital.
    First, I definitely agree that you should review the team that you have put together to make sure that proper representation is made.  In my case, I went so far as so have 10+ team members, and as we narrowed down to the process areas that contained the largest amt. of variation, we made certain team members “2nd tier” members where they only needed to attend a meeting if asked beforehand.
    Sounds like you know the actual area where the problem is; the time that the patient is waiting before the “work up” begins.  We also found that the largest amt. of waste and variation was around the time before they even where placed in an ED bed.  I would dig further into the process by actually asking the patients themselves to capture data for you by asking them to keep a “tally sheet” on their experience (if you would be allowed to do this).  Everryone hates waiting (they are taking time off work, etc.) and the patients should give you very accurate data.  Then you can further pinpoint where the problems are coming from.  I have several other ideas but don’t want this to turn into some rather lengthy message.  I see that you have already done some statistical analysis, however I am part of the school that says, “stay as high as you can for as long as you can” and only  use stats when you are able to pinpoint exactly where the problems are occuring.  So, this might sound really simplistic, but when I mentor belts I tend to keep it as practical for as long as possible.  Seems like you’re on the right track, just thought I would share this with you from my own experience. 

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    #60317

    Dillon
    Participant

    Maria, thank you for your feedeback and advice.  All good points which I will take to heart as I move forward.  It really helps having someome provide the insight from experience. 
    Thank you.   Doug
     

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    #60425

    Keith M. Bower
    Participant

    Hello David,
    FYI, I submitted a paper yesterday called “Some Comments on Capability Analysis and Non-Normal Data”. Hopefully it’ll be up on my website in a month or so. I’ll be adding an appendix to the reproduced copy on my site to show exactly how I came up with the results (step by step in mtb). I’ll respond to this message again when it’s up, or you can check for yourself via my home page at http://www.keithbower.com.
    Best wishes,
    -Keith

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