Assignment 1-SPC

 Read the attached article then answer the following questions- (APA Style) 

What observations about statistical process control can you make after reading the article?

1. How important is implementing corrective action techniques in maintaining an efficient SPC system?
2. One of the significant difficulties in advancing healthcare quality is the lack of specificity in defining healthcare processes, establishing performance standards, and measuring compliance with standards after they are defined. Explain how the use of SPC can help solve these issues.

Q Manage Health Care
Vol. 15, No. 4, pp.

221

–236
c© 2006 Lippincott Williams & Wilkins, Inc.

A Statistical Process Control Case Study
Thomas K. Ross, PhD

Statistical process control (SPC) charts
can be applied to a wide number of health
care applications, yet widespread use has not
occurred. The greatest obstacle preventing
wider use is the lack of quality management
training that health care workers receive. The
technical nature of the SPC guarantees that
without explicit instruction this technique
will not come into widespread use. Reviews
of health care quality management texts
inform the reader that SPC charts should be
used to improve delivery processes and
outcomes often without discussing how they
are created. Conversely, medical research
frequently reports the improved outcomes
achieved after analyzing SPC charts. This
article is targeted between these 2 positions:
it reviews the SPC technique and presents a
tool and data so readers can construct SPC
charts. After tackling the case, it is hoped
that the readers will collect their own data
and apply the same technique to improve
processes in their own organization.

Key words: case study, control charts, quality
management, SPC, statistical process control

O ne of Edward Deming’s quality princi-
ples is to make quality everyone’s job.1

Health care organizations have always as-
sumed that quality is everyone’s job and

everyone knows the difference between quality care
and substandard care. Yet health care by relying on
individualistic definitions of quality without perfor-
mance evaluation systems has never made quality
everyone’s job. Consequently, quality management
is left to quality improvement director, department,
and/or committee, fails to achieve widespread sup-
port in the organization, and produces few tangible
improvements in processes or outcomes.

Implementing Deming’s principle requires em-
ployees to understand what quality is, be capable of
identifying substandard performance, and have the
authority to make changes that will improve perfor-
mance. According to Deming, it is the responsibility
of management to suffuse this quality focus into their
organizations. Of course, this is the problem in health
care; other industries have developed rigorous sys-
tems to monitor quality and modify processes when
output does not meet expectations. Berwick bluntly
addressed this problem; doctors, nurses, reception-
ists, and other health care workers are not trained in
or capable of changing how they work.2

Health care has been implementing quality im-
provement programs for decades but efforts to cross
into the fertile fields of quality management always
seem to flounder. The inability to apply the quality
management techniques of other industries is due to
the more complex nature of health care but part of
the problem is the way health care has approached
quality management. Berwick recognizes that health

From the Department of Health Services and Informa-
tion Management, School of Allied Health Sciences, East
Carolina University, Greenville, NC.

Corresponding author: Thomas K. Ross, PhD, Department
of Health Services and Information Management, School of
Allied Health Sciences, East Carolina University, 600 Moye
Blvd, Greenville, NC 27858 (e-mail: rossth@ecu.edu).

221

222 QUALITY MANAGEMENT IN HEALTH CARE/VOLUME 15, ISSUE 4, OCTOBER–DECEMBER 2006

care workers have not been given the tools to sys-
tematically incorporate quality measurement in their
work.

The following case was developed to demonstrate
how statistical process control (SPC) can be applied
to health care processes. The SPC is a tool that de-
fines what quality is, how performance is measured,
and when investigation and possibly correction must
occur. The SPC, once understood, empowers the doc-
tor, nurse, department manager, and other health
care workers to enter into the quality management
process on a more equal basis with those trained
in quality management techniques. The initial audi-
ence for this article is health care managers, but as
Deming and Berwick note, improvement occurs only
when all employees understand and embrace these
quality improvement techniques. Getting managers
and opinion leaders on board is only the first step
to institutionalizing quality practices throughout the
organization.

This article does not assume that the reader is
versed in statistics or quality management tech-
niques, it does however assume familiarity with
spreadsheet software. The goal is to demonstrate that
quality improvement techniques can be used produc-
tively by all health care workers. At the end of this
case it is hoped that the reader will be able to identify
a use for the SPC in their area of responsibility, create
SPC charts using Excel, and interpret these charts to
improve outcomes.

QUALITY IMPROVEMENT IN
HEALTH CARE

One of the greatest obstacles to quality improve-
ment in health care is the belief of providers that
quality management tools developed in other indus-
tries are not relevant to health care services. Not only
are the initiatives of other industries deemed irrele-
vant to health care, many providers hold that quality
improvement mechanisms developed in other health
care organizations are not applicable to the institu-
tion they work in. This belief is the direct result of the
second factor, and health care providers are not famil-
iar with the purpose, operation, and interpretation

of quality management tools. Without understand-
ing quality management techniques and the ends to
which they can be applied, it is understandable that
health care providers would think these tools have
little to offer them.

Health care quality management texts inform the
reader that SPC charts should be used to improve
delivery processes and outcomes often without dis-
cussing how they are created. Conversely, medical
research frequently reports the improved outcomes
achieved after analyzing SPC charts. This article is
targeted between these 2 positions: it reviews the SPC
technique and presents a tool and an application so
readers can learn how to construct SPC charts and
offers suggestions as to when they can be used to im-
prove health care delivery processes.

A case study is developed and followed to con-
clusion to demonstrate one potential application of
the SPC to health care. The intent is to provide the
readers with a basic understanding of how to build
SPC charts and encourage them to access and analyze
the case data using Excel to evaluate performance on
their own. The case question is: are medicines de-
livered in a timely manner to maximize medical ef-
fectiveness and patient comfort? The control charts
developed are used to draw conclusions regarding
the operation of the system, explore potential rea-
sons for the performance observed, and speculate
on system changes that could improve the timeli-
ness of medicine delivery. After working through the
case, it is hoped that the reader will be motivated
to apply the principles and techniques to their own
work.

One of the major difficulties in advancing health
care quality is the lack of specificity in defining health
care processes, establishing performance standards,
and measuring compliance with standards after they
are defined. Attempts to improve operations and out-
comes are difficult if not impossible when standards
and measures are ill-defined or absent. Efforts to de-
fine medical processes continue to be hotly debated,
and opponents argue that there is too much variation
in medical practice to establish one way of treating
patients and dictating to physicians will not improve
patient care and may hurt patients.3

A Statistical Process Control Case Study 223

On the other hand, countless research has been
done to define proper medical practice; much of this
work is amendable to and should be tracked by the
SPC to improve health care outcomes for patients.
McGlynn et al found that patients received 54.9% of
recommended care, more important than their con-
clusion was their technical supplement that provided
the indicators of what should occur and when it
should occur for 30 conditions.4

Other industries recognize that poor performance
is the result of variation, that is, deviations from how
things should be done that adversely impact out-
comes. Controlling variation is the key to process
improvement. Health care providers are arguably
saddled with more sources of variation than pro-
ducers of other goods and services but the issue re-
mains; is there too much variation in treatment and
will a more systematic approach to health care de-
livery processes improve outcomes? The SPC is a
tool health care workers can use to determine when
variation is a routine part of patient care, neces-
sary and beneficial for patients and the health care
system, and when variation is excessive and poten-
tially harmful. Armed with this information, it is the
duty of health care providers to reduce inappropriate
variation.

IMPROVING HEALTH CARE

Root cause analysis or routine monitoring?

Current quality control efforts revolve around root
cause analysis, that is, a comprehensive examina-
tion of an adverse event with the goal of reducing
harm to patients by preventing the reoccurrence of
the event. JCAHO-accredited health care organiza-
tions must conduct a root cause analysis focusing
on systems and processes when a sentinel event oc-
curs. Root cause analysis is limited by its initiating
cause; it is undertaken after an adverse event has oc-
curred and examines only those processes that were
part of the care episode. In arguing for a broader ap-
proach it has been noted “when multiple sources of
variation are present, isolated observations provide
insufficient information on which to base objective
decision making.”5

The SPC is a broader approach that continuously
examines processes to identify undesirable trends in
performance and institute corrective action before
harm arises. Fasting and Gisvold used the SPC in
anesthesia to study a range of adverse events that are
less severe and more frequent than sentinel events
that contained the potential for harm. As a result
of their study, they were able to reduce anesthesia
accidents.6 The SPC complements root cause analysis
and extends process improvement efforts by adding
ongoing monitoring of a broad range of events to qual-
ity management. JCAHO (LD.5.2) notes that sentinel
event analysis is reactive and does not meet the intent
of the JCAHO patient safety standard.7 The SPC is not
concerned with particular cases but rather with the
ongoing function of systems and thus is a proactive
approach to operations that monitors performance to
detect changes in system performance before prob-
lems arise.

The 6 steps of SPC

The goal of the SPC as envisioned by Walter
Shewhart is to determine when a system is out of con-
trol and requires adjustment to improve its output.
An in-control system simply indicates that it is oper-
ating close to its historical performance; this perfor-
mance, however, may fail to meet generally accepted
standards or customer expectations. A system that
is out of control indicates performance that is sig-
nificantly different from historical performance. The
goals of the SPC are to identify when performance
deviates sufficiently to endanger quality and improve
in-control performance to improve outcomes.

Shewhart’s second goal was to devise a quality
monitoring and improvement system that could be
operated effectively by workers whose expertise lies
in areas other than statistics.8 Such a system required
clear signals to indicate when system performance
fluctuates too much and be easy to use. Shewhart cre-
ated his system in a manufacturing environment for
those trained in engineering and, as will be demon-
strated, it is as applicable for service industries and
those trained in medical sciences. The SPC is de-
signed for ease of use; the technique can be described
and completed in 6 steps.

224 QUALITY MANAGEMENT IN HEALTH CARE/VOLUME 15, ISSUE 4, OCTOBER–DECEMBER 2006

The SPC can be used to monitor the behavior of
any system that produces outputs that can be mea-
sured numerically. The SPC can monitor the percent-
age of defects in a sample (P charts), the number of de-
fects in a sample (c charts), or output characteristics
(average and variance, X̄ and R charts) among other
things. These applications require employees to rou-
tinely collect simple performance measures to moni-
tor quality: percent defective, number of defects, the
average weight or length of a product, time required
to deliver a product or service, and the variance in
these characteristics. The case uses X̄ and R charts
since the concern is the interval between prescribed
medication time and the actual delivery of medicines
to patients. An earlier article in this journal provides
a concise explanation of when the different control
charts should be used.9

Step 1: Data collection

Data collection is the most time consuming part of
the SPC process. A manager wanting to assess per-
formance using the SPC must determine the desired
sample size, how often samples are to be drawn,
procedures to ensure that the samples are random,
and who is responsible for data collection. Managers
must realize that they face a trade-off between the
cost of collecting data (sample size and sampling fre-
quency) and the accuracy of information obtained
from the collected data. Larger samples typically pro-
duce more accurate information but are more costly
and time consuming to collect. The events sampled
must be randomly drawn to ensure that the sample
is not biased; that is, the information gained from
the sample must be representative of the larger pop-
ulation for it to accurately assess the performance of
the nonsampled phenomena. The procedures and re-
sponsibility for data collection should ensure that the
data collector has no incentive to collect either favor-
able or nonfavorable performance. After the data are
collected, it should be recorded in a spreadsheet.

Step 2: Calculation of descriptive statistics

After the data are recorded, descriptive statistics
must be calculated. Descriptive statistics provide the
information necessary to understand how the sys-

tem is operating, the first statistic is the mean. The
mean is the measure of central tendency and re-
ports “average” performance. The mean is used to
determine whether performance meets the desired
standard. The mean for a sample is calculated as
follows: X̄ = ∑

xi/n, the sum of the sampled ob-
servations divided by the sample size. If Excel is
used to record data, the mean is calculated as fol-
lows: =AVERAGE(range of observations). In medica-
tion management the mean can be used to determine
whether patients received the specified dose—larger
or smaller dosage is a problem. Likewise, science and
common sense dictate that the most effective inter-
ventions are delivered proximate to a medical event;
the case seeks to determine whether medicine is de-
livered to patients within (plus or minus) 2 hours of
the prescribed time.

The second statistic, range (R), provides a mea-
sure of the variance in the sample. Range is the high-
est value in the sample minus the lowest value and
is used to assess the variability in performance. Ex-
cel can be directed to scan a series of numbers and
identify the maximum and minimum values and per-
form the subtraction by the command: =MAX(range
of observations)-MIN(range of observations).

The need for both statistics is demonstrated by
assuming that the average turnaround time for a labo-
ratory test is 60 minutes. Those awaiting results pre-
fer a process in which 50% of tests are available
in 65 minutes and the remaining 50% in 55 min-
utes to a process where one half of results are avail-
able in 10 minutes and the other half take 110 min-
utes. Average turnaround time, X̄ , for each process is
60 minutes but the first process has a 10-minute range
(65–55 minutes) while the second has a 100-minute
range (110–10 minutes). Lack of predictability in the
second process is a problem. The person awaiting re-
sults from the second process does not know whether
he or she will receive them quickly or have to wait
almost 2 hours. Processes with the narrowest range
are generally superior; the process with a 10-minute
range provides users with a clear idea of when re-
sults will be available and allows them to schedule
work accordingly. The variance in the second process
can lead to inefficiency if delays in the availability of

A Statistical Process Control Case Study 225

Figure 1. The 6 steps of statistical process control.

information impacts the effectiveness of treatment
or providers must repeatedly check for results
because they do not know when they will be
available.

Differences in system performance are the result
of variance, and all systems are affected by variance.
Variance is categorized as natural or special cause;
natural variation is inherent to a process and is the
result of noncontrollable forces such as the capabil-
ities of labor and equipment, the impossibility of
100% accurate measurements, and/or environmen-
tal factors (ie, the weather). Special cause variation
can be traced to a controllable cause(s) that should
not be present in a properly operating system. Spe-
cial cause variation may arise from system design, in-
puts used, fatigue, wear and tear, lack of equipment
maintenance, lack of training, etc. Any of these causes
could reduce performance below desired or achiev-
able levels.10 When assignable variation arises, it is
the responsibility of managers to identify its cause
and control it to improve outcomes.

Process improvement is built on meeting a desired
standard and reducing the variance in performance.
Managers must monitor performance on an ongoing
basis, using the mean and range to ensure that perfor-
mance targets are met. The X̄ chart monitors how ac-
tual performance varies from historical performance
while the R chart monitors uniformity—the differ-
ence between the best and worst performance in a
sample. Both charts seek to identify when perfor-
mance should be investigated, that is, when observed
performance deviates significantly (is too high or too
low) from historical performance.

Step 3: Calculation of control limits

The calculation of control limits requires 4 formu-
las and provides a quantitative answer to how much
variance will be accepted before a process is investi-
gated. The formulas for the upper control limit (UCL)
and lower control limit (LCL) of the X̄ chart are as
follows:

UCL : ¯̄X + (A ∗ R̄)

LCL : ¯̄X − (A ∗ R̄)

The new terms in these formulas are ¯̄X , aver-
age performance across the samples collected ( ¯̄X =
∑

X̄ i/number of samples); this is an average of aver-
ages, R̄, the average range across the samples (R̄ =
∑

Ri/number of samples), and A, the control chart
factor. ¯̄X and R̄ establish the historical performance
against which individual samples will be judged. ¯̄X
specifies what average performance has been over
a large number of samples or extended time period
and R̄ defines how performance has varied across the
samples or time period. The control chart factor is
multiplied by the average range to determine the ac-
ceptable range of performance.

The magnitude of the control chart factor (A) is de-
termined by sample size that is the number of items
(n) in a sample. A larger sample size generally pro-
duces more accurate statistics, and consequently the
control chart factor is reduced producing tighter lim-
its (see Fig 2). When selecting a control chart factor,
it is a common mistake for students of the SPC to
confuse the number of samples taken with the sam-
ple size—control chart factors are determined by the

Figure 2. Control chart factors.11 LCL indicates lower control
limit; UCL, upper control limit.

226 QUALITY MANAGEMENT IN HEALTH CARE/VOLUME 15, ISSUE 4, OCTOBER–DECEMBER 2006

sample size (the number of observations in the sam-
ple) rather than by the number of samples drawn.

The product of the control chart factor and the aver-
age range is added (or subtracted) from the historical
performance (the average of the averages) to deter-
mine the upper (or lower) control limit. For example,
when samples of 25 are drawn, the average output of
a process is expected to routinely fluctuate around
its historical performance by ±15.3% of its average
range (±0.153 ∗ R̄). Investigation is required when-
ever the average for a sample varies by more than
15.3% of the average range.

The upper and lower limits for the R chart also
require 2 formulas:

UCL :D2 ∗ R̄

LCL :D1 ∗ R̄

D1 and D2 are control chart factors and, similar to A,
these factors produce tighter control limits as sam-
ple size increases. When samples of 10 are drawn,
a sample range could be up to 77.7% above or be-
low the average range (1.000 ± 0.541 ∗ R̄) before in-
vestigation is warranted. Using a larger sample of 25,
acceptable variation is reduced to 54.1% above or be-
low the average range (1.000 ± 0.541 ∗ R̄). It is only
when a sample range exceeds the control chart limits
that investigation and potential corrective action are
required.

Step 4: Graphing performance

Steps 2 and 3 provide all the necessary informa-
tion to graph actual performance, the average, and
the range between the highest and lowest values,
against historical and expected performance. Sam-
ple averages (or ranges) are graphed as XY charts
with the x-axis defining when the sample was col-
lected (reported in a chronological order) and the
y-axis recording the value of the sample average or
range. The centerline (CL), ¯̄X or R̄, and the upper
and lower control limits are also graphed to provide
the baselines against which actual performance is
measured. Routine monitoring of performance, after
the control limits are established, requires the rela-
tively simple task of collecting data, calculating the

mean and range, and charting the values for new
samples.

Step 5: Interpreting performance

Step 5 is the examination of actual and expected
performance to determine whether the process is in
control or out of control. An in-control or stable pro-
cess is one where actual performance, X̄ or R, falls
within the control limits with data points lying on
either side of the centerline, without exhibiting a pat-
tern. Figure 3 presents 6 configurations to look for
when examining control charts. Chart 1 shows an in-
control process in which data points do not breach
the upper or lower control limits and are randomly
distributed around the centerline. Chart 2 presents
the classic out-of-control process where multiple
sample values (samples 2, 5, and 8) breach the es-
tablished control limits. Charts 3–6 show no samples
breaching the control limits but all have recogniz-
able patterns that indicate instability in the process
or a systemic change. Sample values fall only on one
side of the centerline in chart 3, an upward trend be-
ginning in period 5 is evident on chart 4, a cyclical
pattern occurs on chart 5, and the lack of variance
starting in period 6 on chart 6 suggests that none of
these systems are operating as they have in the past.

Charts 2–6 suggest that the process has changed;
it is the manager’s job to identify if and why perfor-
mance has changed and the impact of this change
on patients. SPC charts may record positive or nega-
tive changes to system performance. Once the change
and its impact are understood, managers need to in-
stitutionalize those changes that improve outcomes
or initiate corrective action for those that reduce the
effectiveness of the health care process.

Step 6: Investigation

Steps 1 through 5 are necessary to identify when a
process should be reviewed, control charts clearly in-
dicate when a limit is exceeded or the starting point
of a trend but they do not identify what has changed
or the impact of the change on patients. Step 6 is the
most challenging part of the process; does breach-
ing a control limit or an identifiable pattern indi-
cate that the process is out of control and requires

A Statistical Process Control Case Study 227

Figure 3. Control chart examples. UCL indicates upper control limit; CL, centerline; and LCL, lower control limit.

correction (or does it signal improved performance)?
Correspondingly, in the absence of limit breaches or
trend, is a process performing at a high enough level?
The answers are not straightforward, and the nature
of sampling ensures that occasionally nonrepresen-

tative samples are drawn. A particular sample may
include a disproportionate number of high (or low)
values and breach an upper (or lower) control limit,
indicating a process change when no change has oc-
curred. The first task of an employee, after a control

228 QUALITY MANAGEMENT IN HEALTH CARE/VOLUME 15, ISSUE 4, OCTOBER–DECEMBER 2006

limit is exceeded, is to determine whether the system
is truly out of control or whether a nonrepresentative
sample has been drawn.

When a sample exceeds a control limit (Fig 3,
chart 2), the first step in the investigation is to in-
crease the sample size to determine whether the out-
of-range result holds as more observations are exam-
ined. If the expanded sample produces a mean or
range that falls within the control limits, the man-
ager can assume that the process is in control, re-
sume monitoring, and avoid tinkering with a stable
system. One of the primary goals of the SPC is to fo-
cus employee effort on areas that require correction
by eliminating processes that do not need attention.

If the out-of-range results persist after the sample
size is increased, the employee can assume that non-
representative sampling did not produce the control
limit breach and the harder task of determining why
performance has changed arises. Breaches of con-
trol limits are designed to be rarely occurring events
so employees will not spend significant amounts of
time or efforts investigating trivial variation in per-
formance. The SPC can maximize the effectiveness
of improvement efforts by concentrating employee
efforts toward assignable variation and controllable
causes and away from stable processes.

Given the rarity of breaches of limits or patterns
demonstrated on charts 3–6 in Figure 3 that indi-
cate processes are not functioning as they have in
the past, the manager’s and employees’ job is to pin-
point the cause(s) of change and enact corrective ac-
tion if the change has impaired outcomes. The SPC
enhances employees’ ability to pinpoint causes by
providing an early detection system to identify per-
formance that is inconsistent with historical perfor-
mance. Prompt identification of change may enhance
employees’ ability to pinpoint the cause of change
while the causes of change are still fresh in their
mind.

The uses to which the SPC can be applied in health
care are numerous: are generally accepted standards
of care being followed, is health care provided dif-
ferently to different populations, are waiting times
appropriate, and does performance vary with the per-
sonnel delivering care, the location of service, or the

time or day of service?12 The next section applies the
6-step process to a set of hypothetical data to illus-
trate the SPC technique. The readers are encouraged
to calculate the descriptive statistics and control lim-
its and create the control charts for themselves.

A MEDICATION MANAGEMENT CASE

Effective and high-quality medical care requires
that medicines be administered on a timely basis,
and the performance standard expected in this case
is that medicines should be administered within
2 hours of the prescribed time. Rather than exam-
ining every dose delivered, the SPC allows the use of
a sample of a small number of drug administrations
to determine whether the system is in control, is it
meeting the 2-hour window, or is it out of compli-
ance? A 100% sample may not be particularly infor-
mative as it is unlikely if 100% of drugs are delivered
within 2 hours since natural variation is at work, that
is, patients have the right to refuse medication and do
so, the patient may be receiving other treatments and
be unavailable for medication, etc. A 100% sample
would also be arduous, if not impossible, to collect
given that a 500-bed hospital may dispense 160,000
medications in a month. The 6-step SPC technique
described above is followed to analyze medication
management.

Step 1: Collect data

A random sample of 50 medications was drawn
for the day, evening, and night shifts every day for
a month; a total of 4650 observations (50 medica-
tions × 3 shifts per day × 31 days) and recorded in
a spreadsheet. The sample size of 50 was arbitrarily
determined; it is hoped that a sample size of this mag-
nitude would persuade skeptical employees that the
data were valid. As the validity of the SPC process
is demonstrated, the sample size could and should
be reduced. Technical note: with a sample size of
50, an X̄ and SD (standard deviation) chart is recom-
mended but this case will use the more understand-
able R chart.9 A copy of this data can be obtained at
http://personal.ecu.edu/rossth/QMHCv15i4.xls and
pasted into Excel.

A Statistical Process Control Case Study 229

Step 2: Calculate descriptive statistics

The first sample (Day 1, Day Shift, Monday) pro-
duced an average delivery time of 111.38 minutes,
=AVERAGE(B5:B54). The difference between actual
and prescribed administration time was recorded as
absolute values so medicines administered prior to
and after the prescribed time are both recorded as
positive values. Once the Excel formula is entered,
it can be copied to the remaining columns (through
column CP) to calculate average administration time
for each shift each day. The performance of the first
sample can be contrasted against the most timely av-
erage delivery time of 100.12 minutes (#52), and the
least timely, 134.44 minutes (#71). The average time
between the prescribed medication time and the ac-
tual administration of medicines for all 93 samples
(3 shifts per day × 31 days), ¯̄X , is 115 minutes. The
Excel formula is =AVERAGE(B56:CP56). The center-
line is thus established at 115 minutes on the basis
of historical performance, as stated earlier an indus-
try average or patient expectation, if known, could be
used to establish expected performance.

Sample #1 has a range of 98 minutes between
the most on-time delivery of medicine and the least
timely delivery, =MAX(B5:B54)-MIN(B5:B54). This
formula must again be copied across to column CP
to calculate the range for each shift each day. Sample
#1’s range of 98 minutes can be contrasted with the
low of 33 minutes (#41) and the high of 100 (#10). The
average time between the most on-time and the least
on-time administration for the 93 samples is 65 min-
utes. The average and the range indicate that average
medication administration time is 115 ± 65 minutes
or actual administration of medicine ranges from 82.5
to 147.5 minutes (115 ± 65/2) before or after the pre-
scribed time.

A cursory review of performance, based on the de-
scriptive statistics, provides a manager with a good
idea of where she or he should devote her or his at-
tention. For example, the highest mean delivery time
occurs on the Monday through Friday evening shifts
and the greatest variance occurs on the day shifts dur-
ing the week. Is this performance acceptable? Should
the manager devote his or her time and energy to

investigating the delivery processes on these shifts?
The SPC will answer these questions; at this point
the high mean and wide range suggest that desired
performance is not being achieved.

Step 3: Calculate control limits

X̄ UCL: 115 + ((0.75 × 1/
√

50) × 65) = 121.9 minutes

Centerline (the mean) = 115.0 minutes

X̄ LCL: 115 − ((0.75 × 1/
√

50) × 65) = 108.1 minutes

R UCL: (1.55 − (0.0015 × 50)) × 65 = 95.9 minutes

Centerline(therange) = 65.0 minutes

R LCL: (0.45 + (0.001 × 50)) × 65 = 32.5 minutes

Enter the X̄ control limits and centerline directly be-
low the calculation of the average medication time in
the spreadsheet and copy across all columns. Simi-
larly, the R chart limits and centerline should be en-
tered and copied below the range for each sample.

The control limits indicate whether the medication
process is stable and subject to only natural varia-
tion, and average medication time for a sample of 50
should fluctuate between 108 and 122 minutes. Sim-
ilarly, the range between the most and least on-time
delivery should vary from 33 to 96 minutes. If these
thresholds are exceeded, the SPC indicates an unsta-
ble process or a potential change in performance that
requires investigation. Breaches of the upper limit in
this case indicate deterioration in performance (less
timely administration of medicines) while down-
ward breaches may indicate positive changes in the
process and improved performance.

Step 4: Graph actual and expected performance

Once the averages and ranges for each sample have
been calculated and the upper and lower control
limits and centerlines are entered, Excel can create
control charts through the INSERT function. After
INSERT is selected, the user selects CHART and LINE
(type of chart) and enters the desired data range for
the X̄ chart, the data range entered must include the
mean for an X̄ chart (or the range for the R chart), the
upper and lower control limits, and the centerline.
In Figure 4, the x-axis reports the sample number,
1 though 93.

230 QUALITY MANAGEMENT IN HEALTH CARE/VOLUME 15, ISSUE 4, OCTOBER–DECEMBER 2006

Figure 4. X̄ and R charts. UCL indicates upper control limit;
LCL, lower control limit.

Step 5: Interpret graphs

The X̄ chart demonstrates that medication is rou-
tinely delivered outside the desired 2-hour window.
The sample means reveal that average performance
ranges from 100 to 134 minutes. The R chart demon-
strates that there is only a 33-minute difference
between the most on-time and the least on-time de-
livery of medicine on the most uniform shift (#41), on
the other hand shift sample #10 shows a 100-minute
difference in performance.

Given average performance of 115 minutes and the
average range of 65 minutes, patients are receiving
their medication on average a minimum of 50 min-
utes before or after their prescribed time (115–65) or
up to 170 minutes before or after their prescribed
time. At this point the reader should see we have
a potent tool to evaluate how a process has and is op-
erating. Is the process operated acceptably? In spite
of the fact that the LCL is set at 108 minutes, the orga-
nization in this case should be striving to reduce its

average medication time below the current 115 min-
utes. In addition, the control charts provide an early
detection device for changes in system functioning
over time, more (or less) on-time delivery of medica-
tion or more (or less) consistent delivery of medicines
should be reflected in the sample average and range
allowing a manager to recognize positive or negative
changes in their operations.

In this case, we can clearly see that performance
is unacceptable, and the X̄ chart shows numerous
breaches of the UCL and increasing delivery times
on the last 3 days of the sampling period (samples
#84–93). The manager should explore both of these
issues.

The sample ranges on the R chart generally lie
within their control limits but there are many samples
located around the upper and lower control limits.
There are no data points substantially above or below
the calculated control limits yet the multiple samples
at or slightly beyond the UCL and the multiple con-
secutive samples clustering around 40 minutes sug-
gest the need for investigation. Further investigation
will reveal that there are systematic differences in
average performance and the range between the most
on-time and the least on-time administration times
on various shifts.

Similar to the finding of the X̄ chart, the range on
the last 3 days of the month is significantly different
from performance throughout the month. Contrary to
the X̄ chart, which showed an upward trend signal-
ing a divergence between actual delivery time and
the prescribed time, the R chart shows a downward
trend, that is, a reduction in the difference between
the most on-time and least on-time delivery of med-
ication. Simple calculations reveal that the average
medication time and range were 114.3 and 69.4 min-
utes during the first 10 days of the month, during the
last 10 days it was 117.2 ± 60.5 minutes. The con-
clusion is that medications at the end of the month
were less likely to be delivered at the prescribed time
but when they would be delivered they became more
predictable.

The control charts demonstrate a wide fluctuation
in performance across shifts and days, indicating
an unstable medication management process. These

A Statistical Process Control Case Study 231

differences provide valuable information to under-
stand system performance; which shifts provide the
most on-time delivery of medicines, are there differ-
ences in performance related to the day of the week,
and why is end-of-month performance different from
that in the rest of the month?

Step 6: Investigate when indicated and fix as
appropriate

Control charts do not judge performance, in this
case, both charts indicate that investigation is re-
quired and suggest that the medication management
system is out of control. The UCL on the X̄ chart
shows that medicines are routinely not administered
within the desired 2-hour window. Having received
this signal, it is the responsibility of managers and
employees to determine whether the system requires
fixing. The first question that should be asked is:
what factor(s) prevents the timely administration of
medicines? This is an open-ended question but the
SPC can make identifying the cause(s) easier by exam-
ining performance on different days or shifts. Diag-
nosing and improving a system are easier when sub-
standard performance can be isolated to a particular
shift, day, or unit; that is, can differences be detected
between shifts, days, or units with high performance
and those with low performance?

DIAGNOSING THE PROBLEM

Given that medication times are failing to meet the
desired standard, what is wrong? Are there unique
factors occurring on different shifts or days that pre-
vent prompt administration of medicines? At this
point the manager could decide to draw a larger sam-
ple to see whether the results persist, but we will
assume that they are valid and proceed to diagnosing
the problem.

Sorting the data allows the performance of indi-
vidual shifts or days to be graphed against the estab-
lished control limits. If the data are sorted by shifts
(use the Excel SORT function: select DATA, SORT,
OPTIONS, ORIENTATION, LEFT TO RIGHT, row 4,
day, evening, and night shifts), the charts in Figure 5
can be created. The x-axis now reports the day of the

month, 1 though 31, rather than the sample number
since only 1 shift per day is graphed.

Day shift

Medications are routinely delivered in less than
115 minutes on the day shift, and there are only 5
(out of 31) samples in which the medication time
is above the centerline, that is, the historical aver-
age. Performance according to the X̄ chart meets the
established standard yet the R chart raises concern.
Although average administration time is within the
established control limits, the variability in perfor-
mance is troubling. The upper limit is 95.9 minutes;
12 samples breached this limit, suggesting a unifor-
mity problem. The large range indicates that indi-
vidual patients routinely receive their medications
beyond the desired 2-hour window, thus violating
the established standard. The greatest variation oc-
curs Monday through Friday while performance on
Saturday and Sunday is more uniform (the 2 data
points clustering around 40 on the 6th, 7th, 13th,
14th . . . days of the month). What factors are differ-
ent between weekdays and weekends, which could
account for this difference in performance?

This finding demonstrates the need for both con-
trol charts; the X̄ chart may show performance within
control limits but performance may be unacceptable
if the range is large. Assuming that one half of pa-
tients received their medication within 1 hour and
the other half in 3 hours of the prescribed time, the X̄
chart would report an acceptable average of 2 hours
but the average of 2 hours with a 2-hour range clearly
indicates that medications are not delivered within
the 2-hour goal.

Evening shift

Analysis of the X̄ chart for the evening shift shows
that the Monday through Friday shifts routinely pro-
duce samples above the UCL. Obviously, this should
be the chief concern of employees, and graphing
the performance of the second shift against histori-
cal performance reveals no samples falling under the
mean performance time of 115 minutes and 23 sam-
ples breaking the UCL. The R chart reinforces the
concern as it shows a difference between the most

232 QUALITY MANAGEMENT IN HEALTH CARE/VOLUME 15, ISSUE 4, OCTOBER–DECEMBER 2006

Figure 5. Performance by shift. UCL indicates upper control limit; LCL, lower control limit.

A Statistical Process Control Case Study 233

on-time and least timely delivery of medicines is
80 minutes. Twenty observations are above the cen-
terline and these are in consecutive runs of 5, again
emphasizing that employees working the evening
shift Monday through Friday are less likely to de-
liver medications at the prescribed time and are less
uniform in the delivery of medication than employ-
ees working on the weekend. As asked in the anal-
ysis of the day shift, what factors are at work that
account for the different performance of the evening
shift between weekdays and the weekend? After iso-
lating evening shift performance, it is clear that per-
formance on this shift is failing to achieve the stan-
dards set and further investigation is needed.

Night shift

The night shift has the promptest medication times
with the majority of samples falling below the LCL
and only 3 samples produce an average above the
centerline. Breaking the lower limit may indicate su-
perior performance but it could also reflect a bro-
ken reporting system—data may not be recorded or
recorded properly.13 The 3 samples above the center-
line were also above the UCL and occurred on the
last 3 days of the month. This may be the result of a
system change that requires rectification or perhaps
it was due to an unplanned absence and performance
will return to its previous level with the return of the
absent employee. The R chart shows very consistent
performance on the night shift, its range falls below
the centerline indicating superior performance com-
pared with the day and evening shifts. Once again,
the pattern reflects strings of 5 and 2 showing that the
weekend shifts are more consistent in their delivery
times than those of the Monday through Friday shifts.
It is interesting to note that the end-of-month change
that indicated a movement away from the prescribed
time reduced the variation in performance.

While on-time delivery of medication is the goal of
the organization, the lack of consistency between the
shifts indicates process instability. Unstable in this
case means an inability to predict outcomes; the orga-
nization cannot predict when medications will be de-
livered given the differing performance across shifts.
The manager should explore the reason(s) for inabil-

ity of the evening weekday shift to deliver medicines
within 2 hours of their prescribed time and the vary-
ing performance of the day shift. There appears to be
at least 1 factor that accounts for the lack of on-time
administration of the evening shift and wide range in
delivery times on the day shift during the week, given
the performance demonstrated on Saturday and
Sunday. The difference between weekday and week-
end performance may be due to patient volume,
staffing, or the assignment of duties.

Comparing performance across shifts

The discussion above was based on analyzing per-
formance on a shift; analyzing performance across
shifts indicates that there are 1 or more factors that
explain the different performance of the day, evening,
and night shifts. Average medication time clusters
around 110 minutes on the day shift, 125 minutes
on the evening shift, and 105 minutes on the night
shift. The night shift provides medicines 20 minutes
closer to their prescribed times than the evening shift
and 5 minutes closer than the day shift. Similarly,
there are pronounced differences in the range be-
tween the shortest and longest administration times,
100 minutes on days, 80 minutes on evenings, and
60 minutes on nights. The night shift demonstrates
consistently superior performance as in more timely
delivery of medicines and more uniform delivery
times than the other 2 shifts. Obviously the reasons
for the differences in performance across shifts must
be understood, whether it is wholly or partially due
to the distribution of nursing and pharmacy duties
between shifts, to improve performance.

The stratification of the control charts by shift
makes it apparent that performance improvement ef-
forts should begin on the evening shift. Managers and
employees should embrace process improvement as
an ongoing process (ie, continuous quality improve-
ment [CQI]); hence, over time the goal should be ad-
ministration of medicines at or at least closer to the
prescribed across all shifts and days but the first step
begins by analyzing the process on the shift with the
widest gap between desired and actual performance.

The CQI is an ongoing process of striving for bet-
ter performance; once an organization improves its

234 QUALITY MANAGEMENT IN HEALTH CARE/VOLUME 15, ISSUE 4, OCTOBER–DECEMBER 2006

Figure 6. Cause and effect diagram.

performance and SPC indicates these improvements
are stable, it should attempt to reduce its control
limits and institute tighter control over processes to
produce even better patient outcomes. An institu-
tion that successfully implements the SPC can ex-
pect better patient outcomes, higher patient and em-
ployee satisfaction that accompany better outcomes,
and more effective use of resources.

Identifying the major causes of a problem

The first task in improving outcomes is to iden-
tify an area for improvement; in this case, the SPC
was used to recognize the untimely delivery of med-
ications on the evening shift on weekdays. The next
task is to explore and ultimately identify the poten-
tial causes of substandard performance. Why is per-
formance failing to meet expectations? Fishbone or
cause and effect charts are often employed to explore
the potential causes of performance problems. Fish-
bone charts begin the exploration process by identify-
ing the major reasons why unacceptable performance
could occur and then exploring each reason to iden-
tify the specific organization practices that could con-
tribute to the problem. Off-schedule medication may
be the result of 4 or more major causes, for brevity 4
causes; staffing, caseload, process design, and phar-
macy, are identified in Figure 6.

After the major causes are identified, employees
should explore the issues within each major cause
to identify if, why, and how it impacts the deliv-
ery of medicines. For example, examining staffing
as a major potential cause affecting the timeliness
of medication may lead the QI team to investigate
staffing levels, employee qualifications and training,
productivity of personnel, or any numbers of staffing
issues. Examining caseload may lead the team to in-
vestigate whether the number of patients and/or the
intensity of care required affects the timeliness of
drug delivery. Similarly, questions of process design
may explore job assignments and scheduling (ad-
missions, surgeries, ancillary tests, discharges, and
housekeeping duties), while pharmacy issues may
include the delivery of medications from the phar-
macy, medication errors (dosage and/or type), illeg-
ibility of orders, and adverse drug reactions and/or
contraindications.

In this case the reasons for off-schedule medication
may arise from too few employees and too many pa-
tients, communication problems, poor oversight, or
any other factor suggested on the fishbone diagram.
Any or all of these issues (plus others not identified)
could impact the timeliness of the medication man-
agement process.

The role of manager, quality or process improve-
ment director, and other members of the health

A Statistical Process Control Case Study 235

care delivery process is to evaluate and eliminate
the causes identified on the fishbone diagram until
the most probable factor(s) is identified and correc-
tive action taken. The identification process may in-
volve reaching consensus among the involved parties
or running investigations and tests.

After the most likely cause is identified and correc-
tive action taken, the team should determine whether
the action produced the intended effect, and were
medications delivered more timely? If timeliness
does not improve, then further review is required.
If corrective action is successful in improving perfor-
mance, outcomes must continue to be monitored to
ensure that the improvement is not lost over time and
as a baseline for further improvement thus initiating
a CQI cycle.

The SPC improves management by setting clear
performance standards for employees, establishing
a consistent evaluation standard for managers and
employees to use, and providing a tool to moni-
tor processes when managers are absent; that is, the
head nurse has the ability to monitor evening and
night processes in spite of the fact that she or he
may generally work in the day shift (or weekend
performance when she or he works Monday through
Friday).

CONCLUSION

Improving patient care is a formidable task, which
should not be hampered by a lack of or misunder-
standing of quality management techniques. This ar-
ticle reviewed the SPC technique, demonstrated how
a widely available spreadsheet package can be used
to record and analyze data, and analyzed an SPC case.
Readers were encouraged to access the case data, per-
form their own calculations, create their own graphs
to complete the case, and consider how a comparable
process could be used to monitor and improve care
in their organization. This case demonstrates that the
SPC can be used anytime timeliness is a factor af-
fecting medical outcomes and/or patient satisfaction
such as the timeliness of discharge, procedure time,
test turnaround time, registration time, waiting time,
and etcetera.

The SPC compliments and extends current health
care efforts to improve health care processes and out-
comes. Analysis of the case demonstrates that the SPC
can provide a wealth of information to understand
how current processes are performing and a basis to
institute improvement. More important than the in-
formation generated however is how instilling this
way of thinking into employees will change how they
approach their work. The discussion shows that there
can be multiple causes for substandard performance,
these causes are not revealed by the SPC but rather
provide employees with a starting point to apply
their analytical and problem-solving skills. Employ-
ees will determine how successful the quality im-
provement process is and they must see themselves
as stakeholders in the process. We know that health
care workers are committed to improving the health
of their patients; the SPC is simply a tool to assist
them in these efforts by quantifying performance and
signaling when a process has changed sufficiently to
impact outcomes.

The SPC is a tool specifically designed for those
not trained in management science or statistics to
improve the quality of their work and remains un-
derutilized in the health care field. Quality improve-
ment in health care is not going to be the result of
a top-down approach but will become only an inte-
gral part of the health care delivery system when all
employees embrace quality improvement tools. The
first step is to convince health care workers that qual-
ity improvement tools are relevant to their work and
that they can measure performance themselves. It is
only when employees begin to measure and analyze
their performance that we can expect to see ongoing
and widespread improvement in health care delivery
processes and outcomes.

REFERENCES

1. Lighter DE, Fair DC. Quality Management in Health Care. 2nd
ed. Sudbury, Mass: Jones and Bartlett Publishers; 2004.

2. Galvin R. Deficiency of will and ambition: a conversation with
Donald Berwick. Health Affairs. 2005;24(Web Exclusive):W5-
1–W5-9.

3. Timmermans S, Maulk A. The promises and pitfalls of evidence
based medicine; non-adherence to practice guidelines remains

236 QUALITY MANAGEMENT IN HEALTH CARE/VOLUME 15, ISSUE 4, OCTOBER–DECEMBER 2006

the major barrier to the successful practice of evidence-based
medicine. Health Aff. 2005;24:18–28.

4. McGlynn EA, Asch SM, Adams J, et al. The quality of health
care delivered to adults in the United States. N Engl J Med.
2003;348(26):2635–2645.

5. Laffel G, Blumenthal D. The case for using industrial qual-
ity management science in health care organizations. JAMA.
1989;262(20):2869–2873.

6. Fasting S, Gisvold S. Statistical process control methods allow
the analysis and improvement of anesthesia care. Can J Anesth.
2003;50:767–774.

7. 2001 JCAHO Standards in Support of Patient Safety and Med-
ical/Health Care Error Reduction. Available at: http://www.
dcha.org/JCAHORevision.htm. Accessed April 10, 2006.

8. Humble C. Caveats regarding the use of control charts. Infect
Control Hosp Epidemiol. 1998;19(11):865–868.

9. Amin S. Control charts 101: a guide to health care applications.
Qual Manag Health Care. 2001;9(3):1–27.

10. Shewhart W. Economic Control of Quality of Manufactured
Product. New York, NY: D Van Nostrand; 1931.

11. Gaither N, Frazier G. Operations Management. Mason, Ohio:
Southwestern Thomson Learning; 2002.

12. Benneyan J. Statistical quality control methods in infection
control and hospital epidemiology, part 1: introduction and
basic theory. Infect Control Hosp Epidemiol. 1998;19(3):194–
214.

13. Finison LJ, Finison KS, Bliersbach CM. The use of control charts
to improve healthcare quality. J Health Qual. 1993;15(1):9–23.