I touched on statistical process control (SPC) by using a simple run chart. The run chart is one of my favorites, because it’s easy to use and gives good results. There are also several other type charts that give better results with certain types of data. Interpreting chart results and even which chart is best used is a field unto itself and out of the scope of casual discussion. The enclosed reading list offers far more information.
The uses of charts to help management are almost endless. This example shows a few twist not covered in the last. Every business that works by appointment has folks that sometimes do not show up for their appointments. Naturally the less it happens the better for the business, Company X decided to track the occurrences and try to improve.
First, whenever things are counted, an operational definition (OD) must be established. For instance what is a missed appointment, what will be counted. Change the OD and the count changes. This is important if we wish to compare historical data, what is being counted must be the same.
For instance, will a person that shows up one hour late for an appointment be counted as missing the appointment? How about two hour, four and so on? If a person calls to cancel and appointment after it has occurred, did they miss the appointment? How about a person that shows up the following day? The OD is not as important as consistency. If the results are to be trusted, there cannot be variation in the counts.
Next company X tracked the number of no shows per week, for 27 weeks.
The mean of the data is 2. Calculation shows the square of the mean to be about 1.4. Three [standard deviation] times 1.4 equals 4.2. Adding 4.2 to the mean gives an upper control limit of 6.2 or six as we can’t have .2 no shows. Subtracting the standard deviation from the mean gives a negative 2.2. Clearly we cannot have a negative no show, so the lower limit is zero.
All points fall around the mean, with none outside of the limits and no runs or trends. This means we are dealing with a stable system, that is in statistical control [no special causes likely exist.] This might be expected as the reasons for missing an appointment could be almost endless. Over sleeping, forgetting, another commitment, change of plans, another problem took precedence and on and on. It also means unless we make a change we can expect between zero and six no shows a week, from now on.
This brings us to another tool for improving common cause issues, which is called the PDSA cycle. PDSA stands for Plan, Do, Study, Act and is a great way to gain knowledge, while minimizing risk. This is basically how it is employed.
First a plan is formulated. This should be a plan on a limited scale to reduce risk. One factor that seems pertinent is chosen. A theory was formed to call clients the day before their appointment to remind them.
Next the plan is implemented, this is the Do stage and results in data which we Study in the next stage. Finally, based on the study we Act. We may accept and expand the plan or we may find the evidence does not support the plan. In this case it can be revised or discarded and a new plan formed.
Imperative is to act only on the evidence and not what we thought might happen or wished would happen. This is why SPC was introduced before mentioning PDSA. Each is an asset to the other.
Here’s how it worked. For ten-weeks the plan was implemented and the data recorded. Plotted on the chart results appear like this.
Question, can we say the plan accomplished its objective?
Joined: 19 May 2007 Posts: 206 Location: Camp Verde, AZ
Posted: Thu May 31, 2007 2:59 pm Post subject:
Louis,
Depends on what the plan wanted to accomplish. If the plan was just to reduce the amount of missed appointments, the goal was accomplished. If the plan wanted to reduce missed appointments by a certain amount, who knows, we need that amount.
If my math is correct, the first 27 weeks had an average of 1.1 missed appointments per week. The next 10 weeks had an average of .7 missed appointments.
Interestingly, when I looked at the graph, I was not positive if there was a reduction, but when the numbers were ran, there was definitely a reduction.
Joined: 15 May 2007 Posts: 146 Location: Garden City, KS
Posted: Fri Jun 01, 2007 3:11 pm Post subject:
Perhaps that with the data supporting the plan, it could be decided to run the Do the Plan another 10 weeks. If the data again supports the Plan, it could be acted upon and then expanded on to further reduce. Maybe casually inquiring as to why the appointment was missed? Is that too intrusive? Then it could be assertained as to whether the shop/business can offer something to help that person not miss the appointment. Perhaps offering Loaner vehicles, or rides? Thanks for another great post, Louis. Later, Matt.
Joined: 15 May 2007 Posts: 146 Location: Garden City, KS
Posted: Fri Jun 01, 2007 4:05 pm Post subject:
Hmm. That didn't make a whole lot of sense. I meant, that perhaps with the data coming off as not completely conclusive, one may decide to enact the plan another 10 weeks to see if the results remain consistent or go back to previous trials. Sorry about the typo. Later, Matt.
Joined: 15 May 2007 Posts: 774 Location: Baton Rouge, LA
Posted: Sat Jun 02, 2007 7:42 am Post subject:
Hi Dave,
Dave wrote:
Louis,
Depends on what the plan wanted to accomplish. If the plan was just to reduce the amount of missed appointments, the goal was accomplished. If the plan wanted to reduce missed appointments by a certain amount, who knows, we need that amount.
If my math is correct, the first 27 weeks had an average of 1.1 missed appointments per week. The next 10 weeks had an average of .7 missed appointments.
Interestingly, when I looked at the graph, I was not positive if there was a reduction, but when the numbers were ran, there was definitely a reduction.
Thanks,
Dave
I apologize for being misleading with this post, but I did it to make a point concerning the use of statistics. The question was a bit unfair to pose because I had only briefly mentioned the rules that govern control chart use. Please see the second post for a more in-depth explanation.
Joined: 15 May 2007 Posts: 774 Location: Baton Rouge, LA
Posted: Sat Jun 02, 2007 7:56 am Post subject:
Hi Matt,
MattFMN wrote:
Hmm. That didn't make a whole lot of sense. I meant, that perhaps with the data coming off as not completely conclusive, one may decide to enact the plan another 10 weeks to see if the results remain consistent or go back to previous trials. Sorry about the typo. Later, Matt.
You definitely have the concept down. This would represent the Study phase of PDSA. Statistical process control (SPC) is a tool to aid in this phase. The Act must depend on the results.
We could revise the theory or reject it and form another, if it does not show results. All too often people get too fond of a theory. When this happens, it is easy to try to ignore contrary facts and look only for those that support the belief. This can be disastrous to the attempt to solve the problem. Thanks Matt, I appreciate your input.
Joined: 19 May 2007 Posts: 206 Location: Camp Verde, AZ
Posted: Sun Jun 03, 2007 1:39 pm Post subject:
louis wrote:
Hi Dave,
I apologize for being misleading with this post, but I did it to make a point concerning the use of statistics. The question was a bit unfair to pose because I had only briefly mentioned the rules that govern control chart use. Please see the second post for a more in-depth explanation.
Joined: 15 May 2007 Posts: 774 Location: Baton Rouge, LA
Posted: Sun Jun 03, 2007 3:34 pm Post subject:
Dave wrote:
Thank you for the opportunity to show my ignorance, .
I know you well enough from posts on iATN to know that it was a trick question, just could not figure out the trick.
Will read on and learn more,
Dave
Hi Dave
(laughing out loud) I once had a teacher that started every class with a puzzler, man I hated those. It takes a good deal of courage to speak up in those situations and a eagerness to find answers.
Joined: 15 May 2007 Posts: 146 Location: Garden City, KS
Posted: Tue Jun 05, 2007 2:20 pm Post subject:
One question on the calculations. I don't understand "square of the mean". I understand what the mean is and how to find it, but if square of the mean is the square root...wouldn't that be 1? 1.4 was the calculation. What is used to make that calculation? Thanks, Matt.
Joined: 15 May 2007 Posts: 774 Location: Baton Rouge, LA
Posted: Tue Jun 05, 2007 4:22 pm Post subject:
Hi Matt,
MattFMN wrote:
One question on the calculations. I don't understand "square of the mean". I understand what the mean is and how to find it, but if square of the mean is the square root...wouldn't that be 1? 1.4 was the calculation. What is used to make that calculation? Thanks, Matt.
Great observation! The mean of the first data chart was 2 so the square root would be 1.4. With the additional data in the second chart the mean is recalculated and comes to 1, with a square root of one, as you observed.
For any that may not know, the mean is calculated by first rank ordering all of the data, from least to greatest. The mean is the value of the number that falls equal distant from either end. For example:
5
4
3 <--
2
1
In the numbers above, the mean would be three. This is more indicative, in many cases than the average. For instance salaries at company A may be
$250,000
42,000
40,000
35,000
30,000
The average salary $79,400 is not as indicative of the salaries in general as the mean which is $40,000. Thanks Matt, I appreciate you bringing this up.
Joined: 19 May 2007 Posts: 206 Location: Camp Verde, AZ
Posted: Tue Jun 05, 2007 9:23 pm Post subject:
louis wrote:
For any that may not know, the mean is calculated by first rank ordering all of the data, from least to greatest. The mean is the value of the number that falls equal distant from either end.
What do we do when some of the numbers are the same?
Is it
4
3,3
2
1
0,0,0,0
where the mean would be 2.
Or, is it
4
3
3
2
1
0
0
0
0
where the mean would be 1?
Joined: 15 May 2007 Posts: 774 Location: Baton Rouge, LA
Posted: Tue Jun 05, 2007 9:31 pm Post subject:
Dave wrote:
louis wrote:
For any that may not know, the mean is calculated by first rank ordering all of the data, from least to greatest. The mean is the value of the number that falls equal distant from either end.
What do we do when some of the numbers are the same?
Is it
4
3,3
2
1
0,0,0,0
where the mean would be 2.
Or, is it
4
3
3
2
1
0
0
0
0
where the mean would be 1?
Thanks,
Grasshopper
Hi Grasshopper, Laughing out loud
The second method is the correct one. There is also a procedure when the number of data are even, but it is a bit wordy to explain. Any of the books in the suggested reading list will give a better explanation than I might. Thanks Dave, I appreciate your interest.
Joined: 15 May 2007 Posts: 774 Location: Baton Rouge, LA
Posted: Wed Apr 16, 2008 2:01 pm Post subject:
Dave wrote:
When using a control chart are there a certain number of points that should be used to establish the mean?
Hi Dave,
Technically, any number above thee could work, but it has to be a number that represents the sample. For instance the more variation in the numbers, the more numbers necessary to get a representative sample.
As an example, if we wished to know the mean income of people in a company. The rank and file all make close to the same amount, so if we took five samples and calculated the mean, it would be pretty representative of that group.
Now suppose we wanted to know the mean of the entire company, including executives and delivery people. We would need more samples to get a more indicative figure.
There is a chart called an x-bar R chart that takes this into account, but it is a lot more difficult to use and possibly not necessary for our applications. As Bud stated, seven to ten numbers should be good for most applications. Just watch the variation between figures as a guide.
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I meant, that perhaps with the data coming off as not completely conclusive, one may decide to enact the plan another 10 weeks to see if the results remain consistent or go back to previous trials. Sorry about the typo. Later, Matt.
.
(laughing out loud) I once had a teacher that started every class with a puzzler, man I hated those. It takes a good deal of courage to speak up in those situations and a eagerness to find answers.
What do we do when some of the numbers are the same?
