Time-between Charts

Introduction

93 people have rated this page an average of 4.1 out of 5 stars. See their suggestions and questions. Rate this page.

	Lecture on Time-between chart for exercise (See related slides)
	Lecture on Time-between chart for asthma (see related slides)
	Time between chart for exercise Video► SWF► Excel 2003►
	Time-between chart for asthma attacks using Excel (no pause option)

Introduction
Why construct a chart
What is a control chart
Which chart is right?
How to read a control chart
Minimum number of observations
Calculating limits
Conclusions
Chart for asthma care
Chart for courts
Chart for diet & exercise
Presentations
Analyze data
FAQ
More
Minute evaluation

Recently asked: Should R ALWAYS be <1? If the number of occurrences of missed and kept days is equal, then R will be 1. What should be done in this situation? See answer to this and other questions.

In this section, you will learn about constructing Time-between charts and interpreting the findings. We focus on constructing a control chart for your diet and exercise patterns, though other applications are also possible and you will see examples of application of control charts to family drug court data or asthma care at end of this section. An important application of Time-between charts is time to dissatisfied customer, that is also presented at end of this section.

In constructing control chart for diet or exercise, we assume that you have made a change in your life style (daily processes and routines) and have collected data and are wondering if the change has led to improvement. Since your weight and exercise time vary for many reasons, the key question is whether current weight and exercise time is better than historical patterns.

This section assumes that you can plot data, take a square root and calculate means. These are relatively simple tasks but some people may have little experience with any data manipulation. Tutorials on how to do these tasks are also available at end of this section.

Why Construct a Control Chart

A control chart is constructed to help guide our intuitions. Most people read too much into their success and attribute their failures to external events. Control charts can help discipline intuitions about success and failure. For example, in weight loss there are considerable variations depending on timing of weight measurement, instruments used to measure the weight, clothes on the person while weight is measured, recent food intake, whether, and many other sources. These variations lead to unreliability in the measure of weight. It would be a fallacy to see these variations as weight loss or gain. Control charts can help remove the guess work. These charts establish if new values are different from historical values. Control charts can help answer whether your new weight and exercise patterns indicate a departure from their historical levels.

What is a Control Chart?

In a control chart, you monitor your progress over time. You create a plot, where the X-axis is days since start and the Y-axis is the outcome you are monitoring. To decide if your outcomes are different from historical patterns, the upper (UCL) and lower control limits (LCL) are calculated. These limits are organized in such a way as to make sure that if your historical pattern has continued then 99% of time data will fall within these limits. The upper and lower control limits are calculated using mathematical formulas that are specific to the type of outcome you are monitoring. This section shows you how to calculate these limits depending on whether you are monitoring your weight, your exercise time, days diet missed, days exercise missed, or other similar outcomes.

Figure 1 shows the structure of a typical control chart. In this figure, all points, except for one, fall within the control limits.

Figure 1 shows the structure of a typical control chart.

How to Read a Control Chart?

A control chart is useful in many different ways. Points outside the limits are unusual and mark departure from historical patterns. You have lost weight if your new measure is below the lower control limit. Two points in Figure 1 fall below the LCL and therefore mark a weight loss. All other points do not indicate any real weight loss, even though there are lots of them showing a decrease in weight. These small fluctuations are random and not different from your historical changes rise and falls in your weight.

In Figure 1, none of the points fall above the upper control limits; therefore the person has not gained weight.

You can also use the control chart to see if you are maintaining your gains in a previous time periods. If your data falls within the control limits, despite day to day variations, there has not been any change in your weight and exercise. If you are at ideal weight and exercise, then you want your data to fall within the limits.

Minimum Number of Observations

The more data you have, the more precision you have in constructing the upper and lower control limits. Not all of the data are used for calculation of control limits. Often, the limits are based on pre-intervention period. Then subsequent post-intervention observations are compared to the pre-intervention limits. At a minimum, you need at least 7 data points in the pre-intervention period to start most charts. When you make a change, you want to see if your weight and exercise have been affected by the change. In these circumstances, you set the limits based on the pre-intervention data. You compare post-intervention findings to these limits. If any points fall outside the limits, you can then conclude that the intervention has changed your weight or exercise patterns. See Figure 2 for an example of limits set based on pre-intervention periods.

Figure 2: An example of limits set based on pre-intervention periods

Compare the chart in Figure 2 with the chart in Figure 1. Both are based on the same data, but in Figure 2 the limits are based on the first 7 days, before the intervention. Figure 2 shows that post intervention data are lower than LCL and therefore a significant change has occurred. When Figure 2 is compared to Figure 1, we see that more points are out of the limits in Figure 2. By setting the limits to pre-intervention patterns, we were able to detect more accurately the improvements since the intervention.

The length of data used in construction of control limit depends on the timing of the intervention and changes in the underlying process. Use about 15 data points before the start of the intervention to set the control limit. You can of course use more data points to get a more stable picture of the process but keep in mind that as you use more data points you are going back further in time. The more distant the data the less relevant it is to the current situation. There is a practical limit of how far back can you go to collect the data you need. Taking data from months ago may make your analysis less accurate if the process has changed since then.

Assumptions of Time-between Charts

Figure 3: Time-between chart is best when there are single observations per
period, outcomes are dichotomous (not interval scale) and the event of interest is rare

Time-between charts is one method of constructing control charts, there are many more ways to construct a control chart. Time between charts are best best suited when four assumptions are met: (1) Data should have been collected over time with one observation per time period. (2) The chart should be drawn for dichotomous, discrete rare event. For example, Time-between charts can be constructed for days diet-missed, days exercise-missed, days without coffee, days without junk food, time to unsatisfied customer, time to next adverse event, time to suicide, days to wrong side surgery, smoke free days, etc. (3) Observations over time should be independent of each other. Knowing the value of observation at one time period should not change the probability of observation at next time period. (4) The time to the event should have a Geometric distribution, in which longer time to the event is increasingly more rare.

There are many other methods of control chart that are also available (see Figure 3 for examples). You could use a P-chart, designed specifically to track mortality or adverse health events over time. A P-chart is reasonably only if the event of interest is not rare. You could use an X-bar chart designed for tracking health status and satisfaction surveys of a group of patients over time. You could use a moving average chart to help you construct control chart for an individual patient's data over time. This section helps you decide which of these various charts are appropriate for your application. If you do not have a specific application in mind or if you wish to learn more about each of the various different charts, skip this section. In the following, we ask you 4-7 questions and based on your answers advise you which chart is right for the application that you have in mind.

Have you collected observations over different time periods?

Yes

No

Calculating Limits for Time-between Charts

The steps in constructing control limits for time in between charts are:

Verify that days missed are fewer than days in which you kept up with the plan. Control limits must be derived on rare events. If day missed is more common, it is important to plot days the person kept up with the plan. If days the person kept up with the plan, it is important to chart days missed.
Calculate consecutive time between events. Consecutive days between events are calculated based on what happened in the previous day and today. Table 1 shows how these values are calculated for length of missed days and length of days habit kept. The analysis either plots consecutive missed-days or consecutive days habit kept based on which one happens less often. If missed days are less often, the chart is constructed by plotting length of missed-days on the Y-axis and time since start on the X-axis. If otherwise, the control chart is constructed by calculating the consecutive days in which the habit was kept.

Yesterday	Today	Length of missed-days	Length of days habit kept
No data	Missed day	1 day	0 day
No data	Habit kept	0 day	1 day
Habit kept	Habit kept	0 day	1 + yesterday's length of days habit kept
Missed day	Habit kept	0 day	1 day
Habit kept	Missed day	1 day	0 day
Missed day	Missed day	1 + yesterday’s length of Missed day	0 day
Table 1: Rules for Calculating length of time between missed-days

Calculate R, the ratio of days missed to days keeping up with plan:

The value of R muse always be less than one. If the data distinguish between pre- and post-intervention periods, then the value of R is calculated either based on pre- or post-intervention data. The period used for calculation of R is selected so that it would minimize the value of R. If the pre-intervention period has little variation in the duration of the event being tracked, then R is calculated from the pre-intervention period. Otherwise, it is calculated from the post intervention period. Then, comparing the observed data to the control limits allows us to examine the impact of the intervention.

Calculate UCL as R plus 3 times the square root of R times one plus R.

There is no Lower Control Limit (LCL) for Time-between Charts. As the event plotted is rare, the LCL will always be a negative number. Since time cannot be negative, the LCL does not make sense in the context of Time-between Charts.
Plot either duration of days missed or days kept up with the plan against time. Check to see if the duration exceeds UCL.

Please note that time between charts are about the a series of consecutive events and not about a specific point in the series. When you look at a chart for failure, for example, and see a string of consecutive failures, and one point of this string is above the upper control limit, the interpretation is that the entire series is unusual and not just the point that is above the control limit. Strictly speaking, time in between charts for failures should be drawn as sum of continuous days of failure. This means that the chart would be on 0 for days of success and when a string of failures start, would have no value until the end of the string, at which point it will the value will be at the sum of days in the string. This produces a chart with lots of discontinuous events. To make the interpretation of the chart easier we draw the days of failure from the start of the string till its end. So we draw the first day, the second day until the last day in the string of failures. This gives a more continuous feeling to the chart. Even though we have changed how the chart looks, the statistical tests are still done as before on the end point of the series.

An Example

Table 2 shows data collected over 18 days by a 35 year old female trying to exercise more. She decided to take morning showers at the gym and thus combine her exercise and shower routines. The first 10 days show the data before the intervention. The remaining days show the data after the intervention. The question was whether this new habit has led to increased use of the gym.

Day	Missed?	Duration of missed-days
1	No	0
2	Yes	1
3	Yes	2
4	Yes	3
5	No	0
6	Yes	1
7	Yes	2
8	No	0
9	No	0
10	No	0
11	No	0
12	No	0
13	No	0
14	No	0
15	No	0
16	Yes	1
17	No	0
18	No	0
R =0.13
Table 2: Missed-days of exercise

To construct the control chart, we first need to use the rules in Table 1 to calculate the duration of missed-days in Table 2. Note that missed-days grow in length until she goes to the gym, at which point they are re-set to zero. The last column in Table 2 shows the calculated length of missed-days. The control limit can be calculated from either the pre- or the post-intervention data, which ever leads to a lower upper control limit. In this case the control limit is calculated form the post intervention data, the data for days 8 through 18, because it has the least variability. There is 1 missed day and 8 days she has kept up with plans. Therefore, R is calculated as 1/8 = 0.13. The UCL is then calculated as:

Figure 5 shows the resulting chart and control limit.

Figure 4: Analysis of Data in Table 2

Interpretation of Time-between Control Chart

If the observations in the control chart exceed the Upper Control Limit, then these observations are unlikely to occur by chance. They signify a change in the underlying frequency of the event being tracked. If the control limits were based on pre- or post-intervention periods, observations above control limit indicate the impact of the intervention. Of course, it is possible that the change in probability of the event might be due to another event not tracked in the control chart. Therefore, attribution of change in the probability of the event to the intervention should be made with caution.

The chart in Figure 5 shows that in the pre-intervention period the patient had two strings of missed-days. In the first string, she did not go to the gym for 4 days. In the second string, she did not go for 2 consecutive days. Both strings exceed the UCL. Compared to post intervention period, these two strings of missed-days are long enough to constitute a real change in the process. Based on these findings, we conclude that the intervention was working and the rate of missed-days has dropped. It is however possible that the rate of missed-days dropped for another reason besides taking showers at the gym.

Conclusion

The point of any control chart is to help you improve. The effort we put into measurement and analysis is wasted if it does not help us improve. Constructing a control chart is time consuming and for some difficult. But what is the alternative. Many err in detecting real changes in their weight and exercise times. They mistake random fluctuations for real progress. Control charts help discipline our intuitions to see beyond the rise and fall of weight and exercise patterns.

Analyze Data

Advanced learners like you, often need different ways of understanding a topic. Reading is just one way of understanding. Another way is through doing and practicing the concepts learned in this section. The enclosed date are designed to get you to think more about the concepts taught in this session.

Analyze if the person described below has changed his/her pattern of exercising? Please note that there are no pre- and post intervention periods and therefore control limits must be calculated from the entire period.

Day	Exercise?
1	Yes
2	Yes
3	Yes
4	Yes
5	Yes
6	No
7	Yes
8	Yes
9	Yes
10	No
11	Yes
12	Yes
13	Yes
14	Yes
15	No
16	No
17	No
18	Yes
19	Yes
20	Yes

Produce a control chart. Make sure that your control chart does not have any of the following typical errors:

The chart includes un-named labels such as "Series 1" and "Series 2."

The markers in the control line were not removed.

The X-axis does not have a title

The Y-axis does not have a title

Colors used in the chart and in the cell values, do not help in understanding of the work.

Except for the data, all cell values should be calculated as a formula. If this is not the case, it is very important that you point this out. You should be able to change a data value and all calculations should change automatically.

When you are done, please answer the following questions within your email:

What value did you calculate for the R constant?

What is the value for Upper Control Limit?

Has the patient's exercise patterns changed?

Email your instructor. Send an email with your Excel file attached. In the subject line include the course number and your name. For example, subject line could be: "Joe Smith from HAP 586 analysis of data in lecture on Time Between control chart" Email►

Presentations

There are six sets of presentations for this lecture:

Time-between charts for missed exercise Slides► Listen► Video► SWF►
Introduction to Control Chart Slides► Listen►
How to plot a control chart Slides► Listen►
Learn more about Excel. More►
Time-between charts in asthma care. The narrated slides include formulas used in Excel to calculate control charts. These formulas are not as easy to see in the Video. Slides► Listen► Video► SWF►
See video on calculation of UCL based on post intervention period for Time-between chart in Excel. Note that in this video the formula for Countif function in Excel differs from previous videos. Both set are correct but calculated in different ways. Video►

Listening to narrated slides and videos may require Flash►

Frequently Asked Questions

Ask a question and we will answer it within the next 48 hours. If you have no questions, please review the answer to the questions asked by others:

Question: Should R ALWAYS be <1? If the number of occurrences of missed and kept days is equal, then R will be 1. What should be done in this situation? Answer: Yes R should always be less than one. This is accomplished by making sure that the event being tracked is rare. This question was asked on 4/27/2008 3:48:48 PM and answered on 4/28/2008 6:47:02 AM.

Question: "Strictly speaking, time in between charts for failures should be drawn as sum of continuous days of failure. This means that the chart would be on 0 for days of success and when a string of failures start, would have no value until the end of the string, at which point it will the value will be at the sum of days in the string. This produces a chart with lots of discontinuous events. To make the interpretation of the chart easier we draw the days of failure from the start of the string till its end. So we draw the first day, the second day until the last day in the string of failures. This gives a more continuous feeling to the chart. Even though we have changed how the chart looks, the statistical tests are still done as before on the end point of the series." I am not sure I really understand this. Can you please explain? Answer: I am glad you asked this question. The point of this note is the chart is drawn in a way that strictly speaking is wrong but helps visual interpretation. Since the statistical test is not changed, this modification in visual display does not affect the conclusion one arrives at but gives us a better sense of the changes that are occurring in the data. This question was asked on 4/19/2008 8:42:38 PM and answered on 4/19/2008 8:52:30 PM.

Question: I did the homework for the time between control charts and I wanted to know how you get the "yes" and "no" not to appear on the X-axis on top of the day numbers? Answer: Select the chart, a menu option appears in the tool bar, select from it the source data and change the X-axis information This question was asked on 2/18/2008 8:16:12 PM and answered on 2/19/2008 8:05:10 AM.

Question: Is it possible for your lecture examples to be in both Microsoft Excel 2003 and 2007? I am asking because of the major functionality changes that have occured between the 2 programs. Answer: We are in the process of preparing Microsoft 2007 version of the course. It takes considerable amount of time and I do not think we can get it to you in time. This question was asked on 2/18/2008 10:16:29 AM and answered on 2/18/2008 10:18:29 AM.

Question: For the lecture example of Missed-days of exercise, why is the ratio of days days missed to days exercised (post intervention) 1:8 and not 1:10?? Answer: Good point, I have corrected the example so it is clear that the pre-intervention period are days 1 through 10 and the post intervention period are remaining days. One in eight post intervention period had missed days. Thanks for noticing this inconsistency. This question was asked on 2/18/2008 12:35:40 AM and answered on 2/18/2008 10:00:50 AM.

Question: I did the assignment for the chart assuming we were to assume there was pre/post intervention since the tutorial instructed such. After reading the FAQs I noticed you said this was not the case. So I re-calculated without using it as pre and post data and submitted a second spreadsheet and the answers that applied to the second spreadsheet. Just want to make sure I received credit for the second one. It might be better to use tutorials that are appicable to the particular assignments. Just a thought. Thank you. Answer: The assignments are graded by Ms. Jackson, please send her an email asking her to ignore your first submission and grade the second one. This question was asked on 2/17/2008 9:55:07 PM and answered on 2/17/2008 11:10:51 PM.

Question: For the Rubric exercise are we to comment on another's paper as a group or individually? Answer: You are to make the comments individually. This question was asked on 2/17/2008 9:08:27 PM and answered on 2/17/2008 11:09:38 PM.

Question: In trying to calculate the UCL for the exercise data, the only value I am getting in the cell is the #VALUE. My R value is .3 Not sure what I am doing wrong. Answer: This occurs when the wrong type of argument or operand is used. Click the cell that displays the error, click the button that appears, and then click Trace Error if it appears. Review the possible causes and solutions. Or alternatively provide me with the formula for the cell and I can tell you what is the cause of the error. This question was asked on 2/17/2008 5:14:02 PM and answered on 2/17/2008 5:48:05 PM.

Question: When calculating the R value, and you use the =COUNTIF(C2:C19,0... method, I was not getting the same answer as when I used the other method where you denote the number of days missed and days kept and divide. I tried the COUNTIF method with a number 2 (instead of 1) as the variable, and got a different answer. When using this method, do you have to somehow note that the numbers could be 1-n? Answer: Yes, please note that if you are counting days that are 0, the countif will work but if you are using duration of missed days or some other measure in which the count increases, counting the number of days with 1 will miss the days with 2 and 3. The countif function will work if you count the number of days missed, i.e. "Yes", and number of days not missed, i.e. "No." The point is to use column of data with only two values. This question was asked on 2/17/2008 2:44:58 AM and answered on 2/17/2008 8:21:50 AM.

Question: for calculations of duration of exercise should we use the same formula as is used in exercise (video demonstration) =if(b2="no",0,1)or we change the formula .Same for R value ,do we use this formula which is R=countif(c2:c21,1)/countif(c2:c21,0) and my value of R=0.8 and value of UCL=4.4. I just want to make sure Answer: You can use count or countif statements to accomplish the same task. You need to make sure that the formula makes sense. Try and see if the output is what you expect. This question was asked on 2/14/2008 8:16:02 PM and answered on 2/14/2008 9:51:10 PM.

Suggestions

Add your own suggestions or read below suggestions made by others regarding how to improve this session:

Suggestion: Great lecture! This comment was left on 4/22/2008 8:08:58 PM.

Suggestion: The feedback on what our chart should have looked like was very helpful, as was the reminder that all calculated values should change if any data elements changed. In my current work environment, I do not always need to use calculated values, so I had done the manual calculations versus include the formulas. This comment was left on 2/26/2008 3:14:23 PM.

Suggestion: The lecture was clear, except I could not understand why we need to calculate R from the duration column. This comment was left on 2/19/2008 3:19:43 PM.

Suggestion: The lecture materials were easy to follow through..thank you.. This comment was left on 2/18/2008 11:02:03 PM.

Suggestion: The example provided on the webpages helps a little with the HW assignment, but there is still room for error. However, overall very good examples and information. This comment was left on 2/18/2008 10:07:04 AM.

Suggestion: The powerpoint lecture for Time-between chart for exercise was very helpful in completing the homework. More hands on exercises would make usage of excel easier. Thanks for the challenge. This comment was left on 2/18/2008 12:41:26 AM.

Suggestion: Lecture was very easy to understand! I enjoyed it a lot. (Last time, I wrote a question by mistake...oops!) This comment was left on 2/17/2008 2:46:21 AM.

Suggestion: When calculating the R value, and you use the =COUNTIF(C2:C19,0... method, I was not getting the same answer as when I used the other method where you denote the number of days missed and days kept and divide. I tried the COUNTIF method with a number 2 (instead of 1) as the variable, and got a different answer. When using this method, do you have to somehow note that the numbers could be 1-n? This comment was left on 2/17/2008 2:43:46 AM.

Suggestion: The concept of counting days missed could be a little challenge, as it seems counter-intuitive. But once that's understood things the rest isn't too bad. This comment was left on 2/16/2008 8:55:46 PM.

Suggestion: Lecture and examples were easy to follow online. This comment was left on 2/15/2008 9:29:39 PM.

Time-between chart for Asthma Care: Alemi and colleagues provide an example of how patients can use Time-between charts to analyze diaries of asthmatic patients. Also see annotated bibliography for using control charts in management of asthma. See also use of statistical process control tools in asthma care.
Time-between Chart for Relapse to drug use in a Drug Court: Alemi and colleagues describe how judges in Family Drug Court can use Time-between charts to help them decide if patients' relapse is a return to old patterns. See chart for family drug courts. Also see annotated bibliography for what is relapse. More on impact of family drug courts.
Benneyan JC. Number-between g-type statistical quality control charts for monitoring adverse events. Health Care Management Science. 2001 Dec; 4(4): 305-18.
Benneyan JC. Performance of number-between g-type statistical control charts for monitoring adverse events. Health Care Management Science. 2001 Dec; 4(4): 319-36.
List of online sites for construction of g-charts

This page is copyright protected by Farrokh Alemi, Ph.D.. This page is part of the course on quality / process improvement, lecture on Time-between charts. This page was first made on Wednesday, November 06, 2002 and most recent revision was on 1/1/2006