This study aims to investigate the utility and potentialities of statistical process control for monitoring performances of healthcare organizations. We retrospectively applied the statistical process control for monitoring perioperative system performance, represented in this study by the operating room turnaround time. The results showed that the control charts are able to identify the steady-state behavior of the process and to detect improvements or deteriorations in process performance over tim

Apreda, Mariarosaria

Napoli, Nicola

Scagliarini, Michele

Valpiani, Giorgia

Wienand, Ulrich

AMS Acta - Alm@DL - Università di Bologna

 Mod.01P.5.5 
Rev.01 24.5.08 
 
Mariarosaria Apreda, Ulrich Wienand, 
Giorgia Valpiani, Nicola Napoli, 
Michele Scagliarini 
Statistical Process Control for Improving 
Healthcare Processes. A Case Study in an 
Italian Teaching Hospital 
 
 
 
 
Dipartimento di Scienze Statistiche “Paolo Fortunati” 
 
Quaderni di Dipartimento 
 
Serie Ricerche 2015, n.3  
ISSN 1973-9346 
1 
 
Statistical Process Control for Improving Healthcare Processes. A Case 
Study in an Italian Teaching Hospital 
 
 
Mariarosaria Apreda 
Department of Statistical Sciences, University of Bologna; e-mail: marymena9@hotmail.it 
 
Ulrich Wienand 
Head of Research Innovation Quality and Accreditation Office, Ferrara University 
Hospital, Ferrara, Italy; e-mail: wnnlch@unife.it 
 
Giorgia Valpiani 
Research Innovation Quality and Accreditation Office, Ferrara University Hospital, Ferrara 
Italy; e-mail: giorgia.valpiani@ospfe.it 
 
Nicola Napoli 
Performance Analysis and Programming Office, Ferrara University Hospital, Ferrara Italy; 
e-mail: n.napoli@ospfe.it 
 
Michele Scagliarini 
Department of Statistical Sciences, University of Bologna, Bologna Italy; email: 
michele.scagliarini@unibo.it 
 
 
Abstract 
This study aims to investigate the utility and potentialities of statistical process control for 
monitoring performances of healthcare organizations. We retrospectively applied the 
statistical process control for monitoring perioperative system performance, represented in 
this study by the operating room turnaround time. The results showed that the control 
charts are able to identify the steady-state behavior of the process and to detect 
improvements or deteriorations in process performance over time. 
 
Keywords: Operating room turnaround time, Organizational Indicator, Shewhart control 
charts; EWMA control charts;  
2 
 
1. Introduction  
There is growing attention in the use of Statistical Process Control (SPC) in healthcare, [1-
5], to aid in process performance monitoring, to obtain ideas for improvement, to test 
changes to see whether they are improvements, and to see whether improvements are 
maintained. 
However, SPC is relative new to clinicians and healthcare managers and cultural and 
conceptual barriers slow down the spread of SPC within the healthcare framework. 
The Ferrara University Hospital “Sant’Anna” employs 2,628 members of staff, houses 
626 beds for inpatients and 85 for those receiving day-hospital care. In 2013, there were 
22,647 admissions and 9,048 day-hospital patients.  
Since 2001, the hospital developed a web-based performance measurement system, 
comprising a total of 768 internal and 67 external measures, with a view to improving 
service provision, accountability and quality of care, [6]. 
Within this framework, in order to improve understanding of processes and increase the 
quality of performance, hospital management decided to monitor several clinical, 
organizational and economic indicators through a suitable methodology. 
An important organizational indicator is the Operating Room (OR) Turnaround Time 
(TaT). OR TaT is defined as the time between the “incision close” of patient n to the 
“incision open” of patient n+1. It is a key process indicator for hospital business 
management: delays in OR turnaround time lead to a reduced number of surgical 
interventions per day with a consequent increase in costs and decrease in efficiency. 
This study aims to investigate the utility and potentialities of statistical process control 
for monitoring the OR TaT, assessing the steady-state behaviour of the process and 
identifying changes that indicate either improvement or deterioration in quality. With this 
purpose, we applied SPC retrospectively to the data conveniently extracted from the 
hospital information system.  
The results showed that Shewhart and EWMA control charts are able to identify the 
steady-state behaviour of the process and to detect positive or negative changes in process 
performance. 
 
2. The Data  
The Hospital Quality Department decided to focus attention on the five operating room 
suites located in Block 24. For these ORs, we examined the data from January 2013 to 
3 
 
February 2014 considering only the elective surgeries performed on weekdays: in total 
there were 2,469 surgical operations. In particular, we considered the OR 1 in detail, which 
was the most used with 680 (28%) surgical operations. 
Table 1 contains several descriptive statistics and Figure 1 shows the histogram of the 
TaT of operating room 1. 
 
First Quartile 34.75 
Median 50.00 
Third Quartile  70.00 
Mean 57.44 
Standard Deviation 40.68 
Table 1: descriptive statistics for OR1 TaT 
 
 
Figure 1: Histogram of the original data for OR 1 TaT 
 
The data were highly positively skewed as evidenced by the histogram and by the 
estimated moment coefficient of skewness: 1ˆ 2.93  . 
We performed a preliminary application of the SPC on the original data and, as 
expected, we found an unreasonable number of false alarms likely due to the high 
skewness.  
4 
 
In order to reduce the asymmetry, we performed a Box–Cox power transformation [7] 
using the R package “car” [8]. The optimal lambda value has been determined using a 
profile log-likelihood approach (Figure 2) and resulted: 0.0084   . 
 
Figure 2: Profile Log-likelihood for Box-Cox transformations 
 
Although not normally distributed (Shapiro-Wilk normality test: p<0.01), the 
transformed data (Figure 3) exhibited only a slight departure from symmetry: 
1ˆ 0.0019.    
 
 
Figure 3: Histogram of transformed data for OR 1 TaT 
5 
 
Therefore, in the rest of the work we used the transformed data for process performance 
monitoring. 
 
3. Control Charts 
We were interested in monitoring the average ( X -chart) and the standard deviation (S-
chart) of the transformed operating room TaT per week. In the time interval of interest, the 
number of surgical operations per week was variable. On average there were 12.15 surgical 
interventions per week (minimum=3, median=12, maximum=26 and mode=7). 
We considered the week as a suitable “small window of time” representative of a stable 
process subject only to natural variation. Furthermore, due to the non-elevated number of 
surgical interventions per week and to the consideration that in healthcare settings there is 
much less emphasis on sampling only a portion of the output of a process at periodic 
intervals than in the industrial SPC [3], we decided to consider all the surgical 
interventions performed in each week. In such a way, we used control charts with variable 
sample size [9]. 
To estimate process parameters on which to base the control limits, we performed 
“Phase I” using the first m=30 weeks (January 2013-August 2013). 
The X  and S-Shewhart control charts (3-sigma limits) are given by:  
 
ˆ3 iLCL X n   
CL X  
ˆ3 iUCL X n  , 
and 
CL S  
4( )iUCL SB n , 
3( )iLCL SB n  
respectively. 
With 
1 1
m m
i i i
i i
X n x n
 
  , 
   1 4 1 4...ˆ m m
s c n s c n
m

 
  and 
 
1/2
2
1 1
1
m m
i i i
i i
S n s n m
 
  
    
  
  , where in  is the sample size, ix  is the sample mean, is  
6 
 
is the sample standard deviation of the i-th subgroup (week), m is the number of subgroups 
and  3 iB n ,  4 iB n ,  4 ic n  are the values of the factors 3B , 4B  and 4c  for samples of size 
in  [9-10]. 
The control charts, obtained using the R package [11], for the m=30 preliminary 
samples, are shown in the left side (Calibration) of Figures 4 and 5. 
 
 
Figure 4: S-chart for the preliminary samples (Calibration 1÷30) and new observations (31÷56). 
 
 
Figure 5: X  chart for the preliminary samples (Calibration 1÷30) and new observations (31÷56). 
 
Process parameters estimates should be based on a process that is in control. Therefore, 
we investigated the run above CL (weeks: 6÷12) in the calibration data of the X -chart 
(Figure 5) seeking common features that might indicate a non-random cause for their 
7 
 
occurrence. No consistent assignable cause was found for these data points and considering 
that a few “out-of control” points (in our case none, since we observed only a sequence of 
statistics above CL but below UCL) will not distort the control limits significantly [9], we 
chose to retain these data and keep the parameter estimates unchanged. 
Based on these preliminary samples, we obtained: 3.798X  , 0.584S   and 
ˆ 0.591  . These estimates were calculated on the transformed data. However, since it 
was of interest for the Hospital Quality Department to know the “in control” process mean 
and variability of the original data, we also computed the corresponding estimates on the 
untransformed data: the average OR TaT was 55.65 minutes and the standard deviation 
was 41.20 minutes. 
Therefore, once we assessed the stability of the process in the preliminary samples, we 
retrospectively monitored the remaining data (26 weeks). 
On studying the control charts from week 31 it can be noted that: the S-chart showed a 
sequence of points (weeks 32÷38) below the central line (Figure 4); the X -chart showed a 
similar sequence of statistics (weeks 31÷37) below the central line (Figure 5). 
Then, as of week 39, the S-chart did not show any systematic behaviour or out-of 
control points, while very different results were observed in the X -chart.  
Two sequences above the central line were present: the first run involving weeks 38÷44; 
the second sequence from week 46 to 52 (Figure 5). Applying the Western Electric run 
rules [9, 11-12] the presence of such a non-random behaviour is a strong indication that in 
this period the process was affected by assignable causes. 
With the benefit of hindsight in such a retrospective study, we naturally know where to 
look for any anomalies in the control charts. However, it is incontrovertible that as of week 
39 the performance monitored by X -chart degraded slightly: the systematic pattern above 
the central line indicates an increase in the average of the OR TaT.  
On October 1, 2013 (week 39) an important change occurred in the OR organizational 
system. Patient transportation from and to the operating room, carried out until then by 
internal hospital staff, was committed to an external private company. 
Summarising, monitoring the process from August 2013 through February 2014, an 
increment in average OR TaT appeared during the first week of October 2013, coinciding 
with the change in patient transfer service. The increase is significant, from a former 
8 
 
average of 55.65 minutes of non-operative time between operations (for the preliminary 
samples) to 66.13 minutes (for the period October 2013, February 2014). 
In the X -chart, to detect the shift in the process outcomes, we used one of the Western 
Electric rules (seven, or eight, consecutive points on one side of the centre line). Runs rules 
can increase the ability of the chart to detect small process shifts (<1.5) but can also 
increase the number of false alarms. To avoid this problem the combined use of Shewhart 
and exponentially weighted moving average (EWMA) charts is suggested and strongly 
encouraged also in healthcare applications [3,13]. In such a way, the relatively poor 
performance in detecting small process shifts of the Shewhart chart is balanced by the 
ability of EWMA which on the other end may be less sensitive to detect large process 
shifts. Therefore we complete our study using also an EWMA chart for the process mean.  
Each point on the chart indicates the value of the exponentially weighted moving 
average for that subgroup.  
The EWMA statistic for the i-th subgroup iZ  is defined recursively as [9] 
  11i i iZ x Z      
where ix  is the mean of the sample i of size in ,  is a weight parameter ( 0 1  ). 
When the process mean is known 0Z   otherwise 0Z X  where 
1 1
m m
i i i
i i
X n x n
 
   and 
m is the number of preliminary samples.  
 
In the case of variable sample size, the EWMA control limits are [9,10]  
 
 
1 22
0
ˆ 1
i j
i jj
UCL X L n  


    
and  
 
1 22
0
ˆ 1
i j
i jj
LCL X L n  


   , 
where L is the constant for the control limits and as before 
   1 4 1 4...ˆ m m
s c n s c n
m

 
  
 
9 
 
In our case, in order to use an EWMA chart with the same “in-control” performance of 
the X -chart, we chose 0.05   and 2.492L  : in such a way the EWMA control chart 
has an ARL0=370.4 [9]. 
The EWMA control chart for the process mean, obtained using the R package [11], is 
shown in Figure 6. 
 
 
Figure 6: EWMA chart for the process mean: preliminary samples (Calibration 1÷30); new 
observations (31÷56). 
 
There are several features of Figure 6 that are worthy of discussion.  
First, as for the X -chart, the preliminary samples were in statistical control.  
Second, in weeks 35÷37, the EWMA statistic is below the LCL. These out-of-control 
signals confirm the pattern observed in the X -chart where we noted a sequence of points 
(weeks 31÷37) below the central line (Figure 5). A very tentative explanation might be that 
the awareness of future changes in the OR working conditions might have affected the 
internal hospital staff with consequently improved performances.  
Third, the performance deterioration in OR TaT since October 2013 (i.e. coinciding 
with the change in the OR patient transfer staff) is also confirmed by the EWMA chart: 
10 
 
since week 39, the EWMA statistic iZ  is constantly rising with two out-of-control points 
on weeks 50 and 51. 
 
4. Concluding remarks 
In the European Union the cost of each OR wasted minute can easily be greater than 
€30, [14]. Therefore, OR TaT can be extremely expensive and this measure is also a good 
indicator of efficiency.  
Managers of health care organizations need to evaluate and monitor efficiency 
indicators and they also need to find benchmarks to reduce costs and increase efficiency. 
The challenge is thus to select a useful statistical tool for accurately monitoring and 
providing benchmarks for such indicators.  
Statistical process control provides both a method for assessing the undisturbed, or 
steady-state, process behaviour and a method for detecting positive or negative changes in 
performance quickly.  
We have retrospectively used Shewhart and EWMA control charts for monitoring the 
operating room turnaround time.  
Our results showed that control charts are able to detect quality improvements or quality 
deterioration. We have not been able to test SPC as a monitoring tool applied continuously 
in a prospective mode: this will be the next step of our work. 
 
Acknowledgments 
The authors are grateful to the medical and administrative staff of Ferrara University 
Hospital “Sant’Anna” for their useful collaboration and advices. In particular, we would 
like to thank Dr Mirco Santini, Department of Surgery and Dr Rossella Carletti, 
Pharmaceutical Department who were so generous with their time and willingness to share 
information about procedures, strategies, and visions. 
The authors did not receive any fund for writing this manuscript. 
11 
 
References 
[1] Carey RG. Improving healthcare with control charts. Basic and advanced SPC 
methods and case studies. Wisconsin, USA: American Society for Quality, Quality Press, 
2003. 
[2] Benneyan JC, Lloyd RC, Plsek PE. Statistical process control as a tool for research and 
healthcare improvement. Qual Saf Health Care 2003;12:458–64. 
[3] Woodall WH. The use of control charts in health-care and public-health surveillance. 
(with discussion). J Qual Technol 2006;38: 2:89-134. 
[4] Seim A, Andersen B, Sandberg WS. Statistical Process Control as a Tool for 
Monitoring Nonoperative. Time Anesthesiology 2006; 105: 370-380. 
[5] Mohammed MA, Worthington P, Woodall W. Tutorial notes on how to plot some basic 
control charts. Qual Saf Health Care 2008;17:2:137-45. 
[6] Wienand U, Rinaldi G., Gianesini G, Ferrozzi A. Poretti L, Valpiani G, Verzola A. 
Management of Healthcare Processes Based on Measurement and Evaluation: Changing 
the Policy in an Italian Teaching Hospital. International Journal of Reliable and Quality E-
Healthcare (IJRQEH) 2014; 3(2): 15-35. doi:10.4018/ijrqeh.2014040102 
[7] Carroll RJ, Ruppert D. Transformation and Weighting in Regression. New York: 
Chapman and Hall, 1988. 
[8] John Fox and Sanford Weisberg. An R Companion to Applied Regression. Second 
Edition. Thousand Oaks CA: Sage. 2011. 
URL: http://socserv.socsci.mcmaster.ca/jfox/Books/Companion 
[9] Montgomery DC. Introduction to statistical quality control. 7th edn. New York, NY: 
John Wiley & Sons, Inc., 2012. 
[10] SAS Institute Inc. SAS/QC® 13.2 User’s Guide. Cary, NC: SAS Institute Inc. 2014. 
[11] Scrucca L. qcc: an R package for quality control charting and statistical process 
control. R News 2004;4: 11-17. 
[12] Western Electric Company. Statistical quality control handbook. 1st edn. 
Indianapolis, Indiana USA: Western Electric Corporation, 1956. 
[13] Woodall WH, Adams BM, Benneyan JC. The Use of Control Charts in Healthcare. In: 
Statistical Methods in Healthcare, F. Faltin, R. Kenett, F. Ruggeri, eds., New York: Wiley, 
2012: 253-267 
[14] Macario, Editorial: What does one minute of operating room time cost? Journal of 
Clinical Anesthesia 2010, 22:233–236. 


Statistical process control for improving healthcare processes. A case study in an Italian teaching hospital

AMS Acta

 Mod.01P.5.5 Rev.01 24.5.08  Mariarosaria Apreda, Ulrich Wienand, Giorgia Valpiani, Nicola Napoli, Michele Scagliarini Statistical Process Control for Improving Healthcare Processes. A Case Study in an Italian Teaching Hospital     Dipartimento di Scienze Statistiche “Paolo Fortunati”  Quaderni di Dipartimento  Serie Ricerche 2015, n.3  ISSN 1973-9346 1  Statistical Process Control for Improving Healthcare Processes. A Case Study in an Italian Teaching Hospital   Mariarosaria Apreda Department of Statistical Sciences, University of Bologna; e-mail: marymena9@hotmail.it  Ulrich Wienand Head of Research Innovation Quality and Accreditation Office, Ferrara University Hospital, Ferrara, Italy; e-mail: wnnlch@unife.it  Giorgia Valpiani Research Innovation Quality and Accreditation Office, Ferrara University Hospital, Ferrara Italy; e-mail: giorgia.valpiani@ospfe.it  Nicola Napoli Performance Analysis and Programming Office, Ferrara University Hospital, Ferrara Italy; e-mail: n.napoli@ospfe.it  Michele Scagliarini Department of Statistical Sciences, University of Bologna, Bologna Italy; email: michele.scagliarini@unibo.it   Abstract This study aims to investigate the utility and potentialities of statistical process control for monitoring performances of healthcare organizations. We retrospectively applied the statistical process control for monitoring perioperative system performance, represented in this study by the operating room turnaround time. The results showed that the control charts are able to identify the steady-state behavior of the process and to detect improvements or deteriorations in process performance over time.  Keywords: Operating room turnaround time, Organizational Indicator, Shewhart control charts; EWMA control charts;  2  1. Introduction  There is growing attention in the use of Statistical Process Control (SPC) in healthcare, [1-5], to aid in process performance monitoring, to obtain ideas for improvement, to test changes to see whether they are improvements, and to see whether improvements are maintained. However, SPC is relative new to clinicians and healthcare managers and cultural and conceptual barriers slow down the spread of SPC within the healthcare framework. The Ferrara University Hospital “Sant’Anna” employs 2,628 members of staff, houses 626 beds for inpatients and 85 for those receiving day-hospital care. In 2013, there were 22,647 admissions and 9,048 day-hospital patients.  Since 2001, the hospital developed a web-based performance measurement system, comprising a total of 768 internal and 67 external measures, with a view to improving service provision, accountability and quality of care, [6]. Within this framework, in order to improve understanding of processes and increase the quality of performance, hospital management decided to monitor several clinical, organizational and economic indicators through a suitable methodology. An important organizational indicator is the Operating Room (OR) Turnaround Time (TaT). OR TaT is defined as the time between the “incision close” of patient n to the “incision open” of patient n+1. It is a key process indicator for hospital business management: delays in OR turnaround time lead to a reduced number of surgical interventions per day with a consequent increase in costs and decrease in efficiency. This study aims to investigate the utility and potentialities of statistical process control for monitoring the OR TaT, assessing the steady-state behaviour of the process and identifying changes that indicate either improvement or deterioration in quality. With this purpose, we applied SPC retrospectively to the data conveniently extracted from the hospital information system.  The results showed that Shewhart and EWMA control charts are able to identify the steady-state behaviour of the process and to detect positive or negative changes in process performance.  2. The Data  The Hospital Quality Department decided to focus attention on the five operating room suites located in Block 24. For these ORs, we examined the data from January 2013 to 3  February 2014 considering only the elective surgeries performed on weekdays: in total there were 2,469 surgical operations. In particular, we considered the OR 1 in detail, which was the most used with 680 (28%) surgical operations. Table 1 contains several descriptive statistics and Figure 1 shows the histogram of the TaT of operating room 1.  First Quartile 34.75 Median 50.00 Third Quartile  70.00 Mean 57.44 Standard Deviation 40.68 Table 1: descriptive statistics for OR1 TaT   Figure 1: Histogram of the original data for OR 1 TaT  The data were highly positively skewed as evidenced by the histogram and by the estimated moment coefficient of skewness: 1ˆ 2.93  . We performed a preliminary application of the SPC on the original data and, as expected, we found an unreasonable number of false alarms likely due to the high skewness.  4  In order to reduce the asymmetry, we performed a Box–Cox power transformation [7] using the R package “car” [8]. The optimal lambda value has been determined using a profile log-likelihood approach (Figure 2) and resulted: 0.0084   .  Figure 2: Profile Log-likelihood for Box-Cox transformations  Although not normally distributed (Shapiro-Wilk normality test: p<0.01), the transformed data (Figure 3) exhibited only a slight departure from symmetry: 1ˆ 0.0019.      Figure 3: Histogram of transformed data for OR 1 TaT 5  Therefore, in the rest of the work we used the transformed data for process performance monitoring.  3. Control Charts We were interested in monitoring the average ( X -chart) and the standard deviation (S-chart) of the transformed operating room TaT per week. In the time interval of interest, the number of surgical operations per week was variable. On average there were 12.15 surgical interventions per week (minimum=3, median=12, maximum=26 and mode=7). We considered the week as a suitable “small window of time” representative of a stable process subject only to natural variation. Furthermore, due to the non-elevated number of surgical interventions per week and to the consideration that in healthcare settings there is much less emphasis on sampling only a portion of the output of a process at periodic intervals than in the industrial SPC [3], we decided to consider all the surgical interventions performed in each week. In such a way, we used control charts with variable sample size [9]. To estimate process parameters on which to base the control limits, we performed “Phase I” using the first m=30 weeks (January 2013-August 2013). The X  and S-Shewhart control charts (3-sigma limits) are given by:   ˆ3 iLCL X n   CL X  ˆ3 iUCL X n  , and CL S  4( )iUCL SB n , 3( )iLCL SB n  respectively. With 1 1m mi i ii iX n x n   ,    1 4 1 4...ˆ m ms c n s c nm   and  1/221 11m mi i ii iS n s n m           , where in  is the sample size, ix  is the sample mean, is  6  is the sample standard deviation of the i-th subgroup (week), m is the number of subgroups and  3 iB n ,  4 iB n ,  4 ic n  are the values of the factors 3B , 4B  and 4c  for samples of size in  [9-10]. The control charts, obtained using the R package [11], for the m=30 preliminary samples, are shown in the left side (Calibration) of Figures 4 and 5.   Figure 4: S-chart for the preliminary samples (Calibration 1÷30) and new observations (31÷56).   Figure 5: X  chart for the preliminary samples (Calibration 1÷30) and new observations (31÷56).  Process parameters estimates should be based on a process that is in control. Therefore, we investigated the run above CL (weeks: 6÷12) in the calibration data of the X -chart (Figure 5) seeking common features that might indicate a non-random cause for their 7  occurrence. No consistent assignable cause was found for these data points and considering that a few “out-of control” points (in our case none, since we observed only a sequence of statistics above CL but below UCL) will not distort the control limits significantly [9], we chose to retain these data and keep the parameter estimates unchanged. Based on these preliminary samples, we obtained: 3.798X  , 0.584S   and ˆ 0.591  . These estimates were calculated on the transformed data. However, since it was of interest for the Hospital Quality Department to know the “in control” process mean and variability of the original data, we also computed the corresponding estimates on the untransformed data: the average OR TaT was 55.65 minutes and the standard deviation was 41.20 minutes. Therefore, once we assessed the stability of the process in the preliminary samples, we retrospectively monitored the remaining data (26 weeks). On studying the control charts from week 31 it can be noted that: the S-chart showed a sequence of points (weeks 32÷38) below the central line (Figure 4); the X -chart showed a similar sequence of statistics (weeks 31÷37) below the central line (Figure 5). Then, as of week 39, the S-chart did not show any systematic behaviour or out-of control points, while very different results were observed in the X -chart.  Two sequences above the central line were present: the first run involving weeks 38÷44; the second sequence from week 46 to 52 (Figure 5). Applying the Western Electric run rules [9, 11-12] the presence of such a non-random behaviour is a strong indication that in this period the process was affected by assignable causes. With the benefit of hindsight in such a retrospective study, we naturally know where to look for any anomalies in the control charts. However, it is incontrovertible that as of week 39 the performance monitored by X -chart degraded slightly: the systematic pattern above the central line indicates an increase in the average of the OR TaT.  On October 1, 2013 (week 39) an important change occurred in the OR organizational system. Patient transportation from and to the operating room, carried out until then by internal hospital staff, was committed to an external private company. Summarising, monitoring the process from August 2013 through February 2014, an increment in average OR TaT appeared during the first week of October 2013, coinciding with the change in patient transfer service. The increase is significant, from a former 8  average of 55.65 minutes of non-operative time between operations (for the preliminary samples) to 66.13 minutes (for the period October 2013, February 2014). In the X -chart, to detect the shift in the process outcomes, we used one of the Western Electric rules (seven, or eight, consecutive points on one side of the centre line). Runs rules can increase the ability of the chart to detect small process shifts (<1.5) but can also increase the number of false alarms. To avoid this problem the combined use of Shewhart and exponentially weighted moving average (EWMA) charts is suggested and strongly encouraged also in healthcare applications [3,13]. In such a way, the relatively poor performance in detecting small process shifts of the Shewhart chart is balanced by the ability of EWMA which on the other end may be less sensitive to detect large process shifts. Therefore we complete our study using also an EWMA chart for the process mean.  Each point on the chart indicates the value of the exponentially weighted moving average for that subgroup.  The EWMA statistic for the i-th subgroup iZ  is defined recursively as [9]   11i i iZ x Z      where ix  is the mean of the sample i of size in ,  is a weight parameter ( 0 1  ). When the process mean is known 0Z   otherwise 0Z X  where 1 1m mi i ii iX n x n    and m is the number of preliminary samples.   In the case of variable sample size, the EWMA control limits are [9,10]    1 220ˆ 1i ji jjUCL X L n      and   1 220ˆ 1i ji jjLCL X L n     , where L is the constant for the control limits and as before    1 4 1 4...ˆ m ms c n s c nm    9  In our case, in order to use an EWMA chart with the same “in-control” performance of the X -chart, we chose 0.05   and 2.492L  : in such a way the EWMA control chart has an ARL0=370.4 [9]. The EWMA control chart for the process mean, obtained using the R package [11], is shown in Figure 6.   Figure 6: EWMA chart for the process mean: preliminary samples (Calibration 1÷30); new observations (31÷56).  There are several features of Figure 6 that are worthy of discussion.  First, as for the X -chart, the preliminary samples were in statistical control.  Second, in weeks 35÷37, the EWMA statistic is below the LCL. These out-of-control signals confirm the pattern observed in the X -chart where we noted a sequence of points (weeks 31÷37) below the central line (Figure 5). A very tentative explanation might be that the awareness of future changes in the OR working conditions might have affected the internal hospital staff with consequently improved performances.  Third, the performance deterioration in OR TaT since October 2013 (i.e. coinciding with the change in the OR patient transfer staff) is also confirmed by the EWMA chart: 10  since week 39, the EWMA statistic iZ  is constantly rising with two out-of-control points on weeks 50 and 51.  4. Concluding remarks In the European Union the cost of each OR wasted minute can easily be greater than €30, [14]. Therefore, OR TaT can be extremely expensive and this measure is also a good indicator of efficiency.  Managers of health care organizations need to evaluate and monitor efficiency indicators and they also need to find benchmarks to reduce costs and increase efficiency. The challenge is thus to select a useful statistical tool for accurately monitoring and providing benchmarks for such indicators.  Statistical process control provides both a method for assessing the undisturbed, or steady-state, process behaviour and a method for detecting positive or negative changes in performance quickly.  We have retrospectively used Shewhart and EWMA control charts for monitoring the operating room turnaround time.  Our results showed that control charts are able to detect quality improvements or quality deterioration. We have not been able to test SPC as a monitoring tool applied continuously in a prospective mode: this will be the next step of our work.  Acknowledgments The authors are grateful to the medical and administrative staff of Ferrara University Hospital “Sant’Anna” for their useful collaboration and advices. In particular, we would like to thank Dr Mirco Santini, Department of Surgery and Dr Rossella Carletti, Pharmaceutical Department who were so generous with their time and willingness to share information about procedures, strategies, and visions. The authors did not receive any fund for writing this manuscript. 11  References [1] Carey RG. Improving healthcare with control charts. Basic and advanced SPC methods and case studies. Wisconsin, USA: American Society for Quality, Quality Press, 2003. [2] Benneyan JC, Lloyd RC, Plsek PE. Statistical process control as a tool for research and healthcare improvement. Qual Saf Health Care 2003;12:458–64. [3] Woodall WH. The use of control charts in health-care and public-health surveillance. (with discussion). J Qual Technol 2006;38: 2:89-134. [4] Seim A, Andersen B, Sandberg WS. Statistical Process Control as a Tool for Monitoring Nonoperative. Time Anesthesiology 2006; 105: 370-380. [5] Mohammed MA, Worthington P, Woodall W. Tutorial notes on how to plot some basic control charts. Qual Saf Health Care 2008;17:2:137-45. [6] Wienand U, Rinaldi G., Gianesini G, Ferrozzi A. Poretti L, Valpiani G, Verzola A. Management of Healthcare Processes Based on Measurement and Evaluation: Changing the Policy in an Italian Teaching Hospital. International Journal of Reliable and Quality E-Healthcare (IJRQEH) 2014; 3(2): 15-35. doi:10.4018/ijrqeh.2014040102 [7] Carroll RJ, Ruppert D. Transformation and Weighting in Regression. New York: Chapman and Hall, 1988. [8] John Fox and Sanford Weisberg. An R Companion to Applied Regression. Second Edition. Thousand Oaks CA: Sage. 2011. URL: http://socserv.socsci.mcmaster.ca/jfox/Books/Companion [9] Montgomery DC. Introduction to statistical quality control. 7th edn. New York, NY: John Wiley & Sons, Inc., 2012. [10] SAS Institute Inc. SAS/QC® 13.2 User’s Guide. Cary, NC: SAS Institute Inc. 2014. [11] Scrucca L. qcc: an R package for quality control charting and statistical process control. R News 2004;4: 11-17. [12] Western Electric Company. Statistical quality control handbook. 1st edn. Indianapolis, Indiana USA: Western Electric Corporation, 1956. [13] Woodall WH, Adams BM, Benneyan JC. The Use of Control Charts in Healthcare. In: Statistical Methods in Healthcare, F. Faltin, R. Kenett, F. Ruggeri, eds., New York: Wiley, 2012: 253-267 [14] Macario, Editorial: What does one minute of operating room time cost? Journal of Clinical Anesthesia 2010, 22:233–236. 

This study aims to investigate the utility and potentialities of statistical process control for
monitoring performances of healthcare organizations. We retrospectively applied the
statistical process control for monitoring perioperative system performance, represented in
this study by the operating room turnaround time. The results showed that the control
charts are able to identify the steady-state behavior of the process and to detect
improvements or deteriorations in process performance over time

Apreda, M.

Wienand, U.

Napoli, N.

SCAGLIARINI, MICHELE

VALPIANI, GIORGIA

Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna

English

Statistical Process Control for Improving Healthcare Processes. A Case Study in an Italian Teaching Hospital

 
Mod.01P.5.5 
Rev.01 24.5.08 
 
Mariarosaria Apreda, Ulrich Wienand, 
Giorgia Valpiani, Nicola Napoli, 
Michele Scagliarini 
Statistical Process Control for Improving 
Healthcare Processes. A Case Study in an 
Italian Teaching Hospital 
 
 
 
 
Dipartimento di Scienze Statistiche “Paolo Fortunati” 
 
Quaderni di Dipartimento 
 
Serie Ricerche 2015, n.3  
ISSN 1973-9346 
1 
 
Statistical Process Control for Improving Healthcare Processes. A Case 
Study in an Italian Teaching Hospital 
 
 
Mariarosaria Apreda 
Department of Statistical Sciences, University of Bologna; e-mail: marymena9@hotmail.it 
 
Ulrich Wienand 
Head of Research Innovation Quality and Accreditation Office, Ferrara University 
Hospital, Ferrara, Italy; e-mail: wnnlch@unife.it 
 
Giorgia Valpiani 
Research Innovation Quality and Accreditation Office, Ferrara University Hospital, Ferrara 
Italy; e-mail: giorgia.valpiani@ospfe.it 
 
Nicola Napoli 
Performance Analysis and Programming Office, Ferrara University Hospital, Ferrara Italy; 
e-mail: n.napoli@ospfe.it 
 
Michele Scagliarini 
Department of Statistical Sciences, University of Bologna, Bologna Italy; email: 
michele.scagliarini@unibo.it 
 
 
Abstract 
This study aims to investigate the utility and potentialities of statistical process control for 
monitoring performances of healthcare organizations. We retrospectively applied the 
statistical process control for monitoring perioperative system performance, represented in 
this study by the operating room turnaround time. The results showed that the control 
charts are able to identify the steady-state behavior of the process and to detect 
improvements or deteriorations in process performance over time. 
 
Keywords: Operating room turnaround time, Organizational Indicator, Shewhart control 
charts; EWMA control charts;  
2 
 
1. Introduction  
There is growing attention in the use of Statistical Process Control (SPC) in healthcare, [1-
5], to aid in process performance monitoring, to obtain ideas for improvement, to test 
changes to see whether they are improvements, and to see whether improvements are 
maintained. 
However, SPC is relative new to clinicians and healthcare managers and cultural and 
conceptual barriers slow down the spread of SPC within the healthcare framework. 
The Ferrara University Hospital “Sant’Anna” employs 2,628 members of staff, houses 
626 beds for inpatients and 85 for those receiving day-hospital care. In 2013, there were 
22,647 admissions and 9,048 day-hospital patients.  
Since 2001, the hospital developed a web-based performance measurement system, 
comprising a total of 768 internal and 67 external measures, with a view to improving 
service provision, accountability and quality of care, [6]. 
Within this framework, in order to improve understanding of processes and increase the 
quality of performance, hospital management decided to monitor several clinical, 
organizational and economic indicators through a suitable methodology. 
An important organizational indicator is the Operating Room (OR) Turnaround Time 
(TaT). OR TaT is defined as the time between the “incision close” of patient n to the 
“incision open” of patient n+1. It is a key process indicator for hospital business 
management: delays in OR turnaround time lead to a reduced number of surgical 
interventions per day with a consequent increase in costs and decrease in efficiency. 
This study aims to investigate the utility and potentialities of statistical process control 
for monitoring the OR TaT, assessing the steady-state behaviour of the process and 
identifying changes that indicate either improvement or deterioration in quality. With this 
purpose, we applied SPC retrospectively to the data conveniently extracted from the 
hospital information system.  
The results showed that Shewhart and EWMA control charts are able to identify the 
steady-state behaviour of the process and to detect positive or negative changes in process 
performance. 
 
2. The Data  
The Hospital Quality Department decided to focus attention on the five operating room 
suites located in Block 24. For these ORs, we examined the data from January 2013 to 
3 
 
February 2014 considering only the elective surgeries performed on weekdays: in total 
there were 2,469 surgical operations. In particular, we considered the OR 1 in detail, which 
was the most used with 680 (28%) surgical operations. 
Table 1 contains several descriptive statistics and Figure 1 shows the histogram of the 
TaT of operating room 1. 
 
First Quartile 34.75 
Median 50.00 
Third Quartile  70.00 
Mean 57.44 
Standard Deviation 40.68 
Table 1: descriptive statistics for OR1 TaT 
 
 
Figure 1: Histogram of the original data for OR 1 TaT 
 
The data were highly positively skewed as evidenced by the histogram and by the 
estimated moment coefficient of skewness: 1̂ 2.93  . 
We performed a preliminary application of the SPC on the original data and, as 
expected, we found an unreasonable number of false alarms likely due to the high 
skewness.  
4 
 
In order to reduce the asymmetry, we performed a Box–Cox power transformation [7] 
using the R package “car” [8]. The optimal lambda value has been determined using a 
profile log-likelihood approach (Figure 2) and resulted: 0.0084   . 
 
Figure 2: Profile Log-likelihood for Box-Cox transformations 
 
Although not normally distributed (Shapiro-Wilk normality test: p<0.01), the 
transformed data (Figure 3) exhibited only a slight departure from symmetry: 
1̂ 0.0019.    
 
 
Figure 3: Histogram of transformed data for OR 1 TaT 
5 
 
Therefore, in the rest of the work we used the transformed data for process performance 
monitoring. 
 
3. Control Charts 
We were interested in monitoring the average ( X -chart) and the standard deviation (S-
chart) of the transformed operating room TaT per week. In the time interval of interest, the 
number of surgical operations per week was variable. On average there were 12.15 surgical 
interventions per week (minimum=3, median=12, maximum=26 and mode=7). 
We considered the week as a suitable “small window of time” representative of a stable 
process subject only to natural variation. Furthermore, due to the non-elevated number of 
surgical interventions per week and to the consideration that in healthcare settings there is 
much less emphasis on sampling only a portion of the output of a process at periodic 
intervals than in the industrial SPC [3], we decided to consider all the surgical 
interventions performed in each week. In such a way, we used control charts with variable 
sample size [9]. 
To estimate process parameters on which to base the control limits, we performed 
“Phase I” using the first m=30 weeks (January 2013-August 2013). 
The X  and S-Shewhart control charts (3-sigma limits) are given by:  
 
ˆ3 iLCL X n   
CL X  
ˆ3 iUCL X n  , 
and 
CL S  
4( )iUCL SB n , 
3( )iLCL SB n  
respectively. 
With 
1 1
m m
i i i
i i
X n x n
 
  , 
   1 4 1 4...ˆ m m
s c n s c n
m

 
  and 
 
1/2
2
1 1
1
m m
i i i
i i
S n s n m
 
  
    
  
  , where in  is the sample size, ix  is the sample mean, is  
6 
 
is the sample standard deviation of the i-th subgroup (week), m is the number of subgroups 
and  3 iB n ,  4 iB n ,  4 ic n  are the values of the factors 3B , 4B  and 4c  for samples of size 
in  [9-10]. 
The control charts, obtained using the R package [11], for the m=30 preliminary 
samples, are shown in the left side (Calibration) of Figures 4 and 5. 
 
 
Figure 4: S-chart for the preliminary samples (Calibration 1÷30) and new observations (31÷56). 
 
 
Figure 5: X  chart for the preliminary samples (Calibration 1÷30) and new observations (31÷56). 
 
Process parameters estimates should be based on a process that is in control. Therefore, 
we investigated the run above CL (weeks: 6÷12) in the calibration data of the X -chart 
(Figure 5) seeking common features that might indicate a non-random cause for their 
7 
 
occurrence. No consistent assignable cause was found for these data points and considering 
that a few “out-of control” points (in our case none, since we observed only a sequence of 
statistics above CL but below UCL) will not distort the control limits significantly [9], we 
chose to retain these data and keep the parameter estimates unchanged. 
Based on these preliminary samples, we obtained: 3.798X  , 0.584S   and 
ˆ 0.591  . These estimates were calculated on the transformed data. However, since it 
was of interest for the Hospital Quality Department to know the “in control” process mean 
and variability of the original data, we also computed the corresponding estimates on the 
untransformed data: the average OR TaT was 55.65 minutes and the standard deviation 
was 41.20 minutes. 
Therefore, once we assessed the stability of the process in the preliminary samples, we 
retrospectively monitored the remaining data (26 weeks). 
On studying the control charts from week 31 it can be noted that: the S-chart showed a 
sequence of points (weeks 32÷38) below the central line (Figure 4); the X -chart showed a 
similar sequence of statistics (weeks 31÷37) below the central line (Figure 5). 
Then, as of week 39, the S-chart did not show any systematic behaviour or out-of 
control points, while very different results were observed in the X -chart.  
Two sequences above the central line were present: the first run involving weeks 38÷44; 
the second sequence from week 46 to 52 (Figure 5). Applying the Western Electric run 
rules [9, 11-12] the presence of such a non-random behaviour is a strong indication that in 
this period the process was affected by assignable causes. 
With the benefit of hindsight in such a retrospective study, we naturally know where to 
look for any anomalies in the control charts. However, it is incontrovertible that as of week 
39 the performance monitored by X -chart degraded slightly: the systematic pattern above 
the central line indicates an increase in the average of the OR TaT.  
On October 1, 2013 (week 39) an important change occurred in the OR organizational 
system. Patient transportation from and to the operating room, carried out until then by 
internal hospital staff, was committed to an external private company. 
Summarising, monitoring the process from August 2013 through February 2014, an 
increment in average OR TaT appeared during the first week of October 2013, coinciding 
with the change in patient transfer service. The increase is significant, from a former 
8 
 
average of 55.65 minutes of non-operative time between operations (for the preliminary 
samples) to 66.13 minutes (for the period October 2013, February 2014). 
In the X -chart, to detect the shift in the process outcomes, we used one of the Western 
Electric rules (seven, or eight, consecutive points on one side of the centre line). Runs rules 
can increase the ability of the chart to detect small process shifts (<1.5) but can also 
increase the number of false alarms. To avoid this problem the combined use of Shewhart 
and exponentially weighted moving average (EWMA) charts is suggested and strongly 
encouraged also in healthcare applications [3,13]. In such a way, the relatively poor 
performance in detecting small process shifts of the Shewhart chart is balanced by the 
ability of EWMA which on the other end may be less sensitive to detect large process 
shifts. Therefore we complete our study using also an EWMA chart for the process mean.  
Each point on the chart indicates the value of the exponentially weighted moving 
average for that subgroup.  
The EWMA statistic for the i-th subgroup iZ  is defined recursively as [9] 
  11i i iZ x Z      
where ix  is the mean of the sample i of size in ,  is a weight parameter ( 0 1  ). 
When the process mean is known 0Z   otherwise 0Z X  where 
1 1
m m
i i i
i i
X n x n
 
   and 
m is the number of preliminary samples.  
 
In the case of variable sample size, the EWMA control limits are [9,10]  
 
 
1 22
0
ˆ 1
i j
i jj
UCL X L n  


    
and  
 
1 22
0
ˆ 1
i j
i jj
LCL X L n  


   , 
where L is the constant for the control limits and as before 
   1 4 1 4...ˆ m m
s c n s c n
m

 
  
 
9 
 
In our case, in order to use an EWMA chart with the same “in-control” performance of 
the X -chart, we chose 0.05   and 2.492L  : in such a way the EWMA control chart 
has an ARL0=370.4 [9]. 
The EWMA control chart for the process mean, obtained using the R package [11], is 
shown in Figure 6. 
 
 
Figure 6: EWMA chart for the process mean: preliminary samples (Calibration 1÷30); new 
observations (31÷56). 
 
There are several features of Figure 6 that are worthy of discussion.  
First, as for the X -chart, the preliminary samples were in statistical control.  
Second, in weeks 35÷37, the EWMA statistic is below the LCL. These out-of-control 
signals confirm the pattern observed in the X -chart where we noted a sequence of points 
(weeks 31÷37) below the central line (Figure 5). A very tentative explanation might be that 
the awareness of future changes in the OR working conditions might have affected the 
internal hospital staff with consequently improved performances.  
Third, the performance deterioration in OR TaT since October 2013 (i.e. coinciding 
with the change in the OR patient transfer staff) is also confirmed by the EWMA chart: 
10 
 
since week 39, the EWMA statistic iZ  is constantly rising with two out-of-control points 
on weeks 50 and 51. 
 
4. Concluding remarks 
In the European Union the cost of each OR wasted minute can easily be greater than 
€30, [14]. Therefore, OR TaT can be extremely expensive and this measure is also a good 
indicator of efficiency.  
Managers of health care organizations need to evaluate and monitor efficiency 
indicators and they also need to find benchmarks to reduce costs and increase efficiency. 
The challenge is thus to select a useful statistical tool for accurately monitoring and 
providing benchmarks for such indicators.  
Statistical process control provides both a method for assessing the undisturbed, or 
steady-state, process behaviour and a method for detecting positive or negative changes in 
performance quickly.  
We have retrospectively used Shewhart and EWMA control charts for monitoring the 
operating room turnaround time.  
Our results showed that control charts are able to detect quality improvements or quality 
deterioration. We have not been able to test SPC as a monitoring tool applied continuously 
in a prospective mode: this will be the next step of our work. 
 
Acknowledgments 
The authors are grateful to the medical and administrative staff of Ferrara University 
Hospital “Sant’Anna” for their useful collaboration and advices. In particular, we would 
like to thank Dr Mirco Santini, Department of Surgery and Dr Rossella Carletti, 
Pharmaceutical Department who were so generous with their time and willingness to share 
information about procedures, strategies, and visions. 
The authors did not receive any fund for writing this manuscript. 
11 
 
References 
[1] Carey RG. Improving healthcare with control charts. Basic and advanced SPC 
methods and case studies. Wisconsin, USA: American Society for Quality, Quality Press, 
2003. 
[2] Benneyan JC, Lloyd RC, Plsek PE. Statistical process control as a tool for research and 
healthcare improvement. Qual Saf Health Care 2003;12:458–64. 
[3] Woodall WH. The use of control charts in health-care and public-health surveillance. 
(with discussion). J Qual Technol 2006;38: 2:89-134. 
[4] Seim A, Andersen B, Sandberg WS. Statistical Process Control as a Tool for 
Monitoring Nonoperative. Time Anesthesiology 2006; 105: 370-380. 
[5] Mohammed MA, Worthington P, Woodall W. Tutorial notes on how to plot some basic 
control charts. Qual Saf Health Care 2008;17:2:137-45. 
[6] Wienand U, Rinaldi G., Gianesini G, Ferrozzi A. Poretti L, Valpiani G, Verzola A. 
Management of Healthcare Processes Based on Measurement and Evaluation: Changing 
the Policy in an Italian Teaching Hospital. International Journal of Reliable and Quality E-
Healthcare (IJRQEH) 2014; 3(2): 15-35. doi:10.4018/ijrqeh.2014040102 
[7] Carroll RJ, Ruppert D. Transformation and Weighting in Regression. New York: 
Chapman and Hall, 1988. 
[8] John Fox and Sanford Weisberg. An R Companion to Applied Regression. Second 
Edition. Thousand Oaks CA: Sage. 2011. 
URL: http://socserv.socsci.mcmaster.ca/jfox/Books/Companion 
[9] Montgomery DC. Introduction to statistical quality control. 7th edn. New York, NY: 
John Wiley & Sons, Inc., 2012. 
[10] SAS Institute Inc. SAS/QC® 13.2 User’s Guide. Cary, NC: SAS Institute Inc. 2014. 
[11] Scrucca L. qcc: an R package for quality control charting and statistical process 
control. R News 2004;4: 11-17. 
[12] Western Electric Company. Statistical quality control handbook. 1st edn. 
Indianapolis, Indiana USA: Western Electric Corporation, 1956. 
[13] Woodall WH, Adams BM, Benneyan JC. The Use of Control Charts in Healthcare. In: 
Statistical Methods in Healthcare, F. Faltin, R. Kenett, F. Ruggeri, eds., New York: Wiley, 
2012: 253-267 
[14] Macario, Editorial: What does one minute of operating room time cost? Journal of 
Clinical Anesthesia 2010, 22:233–236. 


http://amsacta.unibo.it/4354/1/Quaderni_2015_3_ApredaWienandValpianiNapoliScagliarini_Statistical.pdf

Statistical process control for improving healthcare processes. A case study in an Italian teaching hospital

Abstract

Similar works

Full text

Available Versions

AMS Acta - Alm@DL - Università di Bologna

AMS Acta

Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna

AMS Acta