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American Journal of  Applied 
Statistics and Economics (AJASE)

Enhancing Business Performance Using Statistical Quality Control Techniques
Reuben Cheruiyot Lang’at1*

Volume 4 Issue 1, Year 2025
ISSN: 2992-927X (Online)

DOI: https://doi.org/10.54536/ajase.v4i1.6372
https://journals.e-palli.com/home/index.php/ajase

Article Information ABSTRACT

Received: October 16, 2025

Accepted: November 20, 2025

Published: December 05, 2025

Quality control (QC) is central to ensuring that business processes produce goods and 
services that meet customer requirements and regulatory standards. Statistical methods 
underpin modern QC by enabling measurement, monitoring, and improvement of  processes. 
This paper reviews the theoretical foundations of  statistical quality control (SQC), describes 
key statistical tools such as control charts, process capability indices, and links them to 
business applications. It explores how statistics help identify variation (common-cause or 
special-cause), support decision‐making, and drive continuous improvement (e.g., Six Sigma). 
Practical implications, challenges (data quality, assumptions, culture), and future directions 
(big data, multivariate control) are discussed. The aim is to provide business managers and 
researchers with a comprehensive overview of  how statistics can contribute to effective 
quality control in business operations. 

Keywords

Business Performance, Control 
Charts, Process Capability, Quality 
Control 

1 University of  Kabianga P.O. Box 2030-20200 Kericho, Kenya
* Corresponding author’s e-mail: rlangat@kabianga.ac.ke

INTRODUCTION
In a competitive global business environment, maintaining 
product or service quality is essential for customer 
satisfaction, brand reputation, and profitability (Zacharias, 
2022). Quality control (QC) involves the operational 
techniques and activities used to ensure that product 
characteristics meet established requirements. Statistics 
plays a pivotal role in QC by providing objective methods 
to measure process performance, identify variation, 
evaluate conformity, and guide improvement. This paper 
explores how statistical tools support QC in businesses. 
It reviews the major methods, discusses their applications 
and limitations, and outlines future directions.

LITERATURE REVIEW
The discipline of  statistical quality control (SQC) emerged 
in the early twentieth century, primarily through the work 
of  Walter A. Shewhart at Bell Labs, who introduced 
control charts to monitor process variation. Shewhart 
defined the central idea of  distinguishing common‑cause 
variation (inherent in the process) from special-cause 
variation 
(assignable factors) thus enabling process monitoring 
and control. Over time, SQC has been integrated into 
broader framework such as Six Sigma and total quality 
management (TQM). Among the approaches that 
stand out in SQC is the Six Sigma methodology, which 
when applied, can only allow a defect rate of  not more 
than 3.4 per million opportunities. In such a process 
high‑quality output is definitely assured. This approach 
emphasizes continuous improvement and data-driven 
decision-making (Connaughton, 2021). More recently, 
reviews have analysed the evolution of  SQC tools and 
their research tradition  (Nagar & Gahlot, 2022). In 
parallel, business-oriented research has explored how QC 

practices impact reputation, market share and operational 
performance (Zacharias, 2022).
Statistical Quality Control techniques add value in 
multiple ways in business. Through real-time monitoring, 
businesses can detect drift or abnormal variation early, 
reducing waste and defects. Statistical tools enable 
managers to distinguish between common and special 
causes of  variation, allowing targeted corrective actions. 
Sampling plans save costs compared to 100% inspection. 
Moreover, statistical summaries such as process capability 
or defect rates guide data-driven decision making. In 
framework such as Six Sigma, statistical measurement 
and analysis underpin the Define Measure Analyze 
Improve Control (DMAIC) process, ensuring systematic 
quality improvement (Connaughton, 2021). Strategically, 
effective QC enhances customer trust, reputation, and 
compelling competitiveness (Zacharias, 2022).

Theoretical Foundations: Variation, Capability, 
Control
All processes exhibit variation. The key theoretical insight 
from Shewhart is that if  only common-cause variation 
is present, the process is “in statistical control”; if  
special-cause variation occurs, the process may produce 
unpredictable outcomes or defects. Control charts help 
visualize and distinguish these phenomena. Once a 
process is stable (in control), businesses can evaluate how 
well it meets specification limits using capability indices 
such as Process Potential Capability (Cp) or Process 
Centering Capability Index (Cpk), which rely on statistical 
measures of  process mean and standard deviation. The 
objective is to keep the process within control limits so 
that only natural variation remains, facilitating predictable 
performance and enabling improvement initiatives. These 
indices are given by:



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Am. J. Appl. Stat. Econ. 4(1) 150-153, 2025

Cp= (USL‑LSL)/6σ             ....(1)
Where

USL is the upper specification limit
LSL is the lower specification limit
σ  is the process standard deviation

It should be noted from equation (1), that a Cp value 
greater than 1.0 indicates the process has the potential to 
meet specifications. Though so, it doesn’t consider if  the 
process is actually centered. In other words it shows that 
the process could actually work if  it is centered.

               ....(2)

control (SPC). For example, while X̅ and R (or s) charts 
are for variable data, p-charts, np-charts, and c-charts  are 
for attribute data. Control chart rules help detect signals 
that may indicate special-cause also called assignable 
variation. Acceptance sampling, on the other hand, allows 
businesses to inspect samples rather than entire lots, 
reducing costs while maintaining confidence in product 
quality. Descriptive statistical tools such as histograms, Pareto 
charts, and scatter plots assist in diagnosing process issues, 
identifying major defect causes, and exploring relationships 
among variables. Inferential methods like regression analysis 
and Design of  Experiments (DOE) support root cause 
analysis and optimization of  process inputs. 

RESULTS AND DISCUSSION
To illustrate the use of  the control charts the real inbuilt 
dataset on piston rings in R has been used. This statistical 
process control charts were generated using R (R Core 
Team, 2024) with the qcc (Scrucca, 2004) and SixSigma 
(Panwar, 2023) packages. Figure 1 shows the X̅- chart 
for the dataset while Figure 2 shows the corresponding 
R-chart.

where
μ  is the process mean
A   value shows how well the process is centered between 
the upper and lower specification. From equation (2), if    
Cpk > Cp, then there is a high possibility that the process 
is not centered and may have a higher rate of  defects. 
Further a Cpk value of  1.33 or more is considered good 
because it implies that less than 0.01% of  the products 
will be scraped. 
Control charts are the hallmark of  statistical process 

Figure 1: X-bar chart for piston ring diameters

In Figure 1 it is clear that 2 points are outside the upper 
control limit signifying that the process is out of  control. 
In addition there was one (violating run) sequence of  
2 points that violated the statistical rule. The process 
therefore needs to be stopped and action taken to correct.  
The R- chart is hereby presented in Figure 2.

According to Figure 2 the process is in control since all 
the points are within the lower and upper limits. Were 
it not for the X̅- chart, it would have been concluded 
that the process is statistically under control. In general 
therefore the process is not in control.



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Am. J. Appl. Stat. Econ. 4(1) 150-153, 2025

To facilitate the illustration of  the analysis of  the 
attributes, the dataset of  orange juice from qcc was 
used. The dataset has the number of  defectives or 

nonconforming cans in each the sample of  50 drawn. It 
is particularly useful in monitoring the defect rate. The 
output is as given in Figure 3. 

Figure 2: R chart for piston ring diameters

Figure 3: p- chart for defective orange juice bottles

In Figure 3 quite a number of  points lie outside the 
limits. Specifically, 5 points are beyond the upper limits. 
Additionally, there are 17 violating runs portraying 
extreme case of  pattern which is unacceptable even if  
all the points were within the limits. Clearly the chart in 
Figure 3 indicates an out of  control process.
This study picks two commonly used indices (Cp and 
Cpk) as evaluated in Figure 4 which indicate the process 
capability of  meeting the specification and the centralizing 

factor. Cp = 0.33<1 implying the process does not meet 
the specification. The index that show the centeredness of  
the process is Cpk  = 0.212 < 1.33. This value is far from 2 
the index that corresponds to the high quality Six Sigma 
level of  performance. It can therefore be concluded that 
the process is not capable of  consistently meeting the 
specifications.  With this outcome, action should be taken 
to reverse the situation. The process should be stopped 
and action taken to look for the cause of  the problem. 



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Replacement of  worn out parts or scraping of  some parts 
equipment in use may be done to enhance the quality of  
the products.
This analysis of  the dataset illustrates how statistical 
monitoring, detection of  special-cause variation, 
corrective action, and capability analysis all combine to 
deliver business benefit

Challenges and Limitations
Although the statistical QC toolkit is powerful, there 
are several challenges. Data quality and measurement 
system error can mislead analysis. Many tools assume 
independent and normally distributed data; violations of  
these assumptions can invalidate conclusions. Cultural and 
organizational barriers can limit the effectiveness of  QC 
if  management fails to act on findings. The cost‑benefit 
balance must also be considered, as overly complex 
statistical methods may not yield a return on investment. 
Finally, modern processes often involve multivariate 
and dynamic data that require more advanced statistical 
approaches beyond traditional charts.

Future Directions
The future of  statistics in quality control lies in big data 
and real-time analytics. With the advent of  sensors and 
Internet of  Things (IoT), companies can collect massive 
amounts of  data and apply machine learning to detect 
subtle patterns. Multivariate SPC methods will become 
essential as processes grow more complex. Moreover, 
statistical QC is expanding to service sectors 
like healthcare and finance, and integrating with 
sustainability metrics such as waste reduction and energy 
efficiency. These innovations will continue to redefine 
how businesses monitor and manage quality.

CONCLUSION
Statistics underlies effective quality control in business 
performance by providing tools to measure, monitor, 
analyze, and improve processes. From control charts 
to capability indices, from sampling plans to regression 
analysis, statistical methods give managers objective 
insight into variation and process performance. When 
appropriately applied and combined with organizational 
commitment, Statistical Quality Control can transform 
business performance from inspection to process 
management, yielding improved quality, reduced 
costs, higher customer satisfaction, and competitive 
advantage. Organisations should therefore invest in data 
quality, personnel training, and a culture of  continuous 
improvement. Future advances in big data and multivariate 
analysis promise to broaden the scope and impact of  
statistical quality control even further.

REFERENCES
Connaughton, S. (2021). Statistical quality control in 

manufacturing. Retrieved November 16, 2025, from 
https://www.ebsco.com

Nagar, H., & Gahlot, A. (2022). A Review on Statistical 
Quality Control. NeuroQuantology, 20(9), 637-642.

Panwar, A. (2023). SixSigma: Six Sigma tools for quality 
control and improvement. CRAN.

R Core Team. (2024, ). R: A language and environment for 
statistical computing. R Foundation for for Statistical 
Computing.

Scrucca, L. (2004). qcc: An R package for quality control 
charting and statistical process control. R News, 4(1), 
11-17.

Zacharias, M. V. (2022). The Importance of  Quality 
Control for The Success of  A Company. Asian Journal 
of  Logistics Management, 1(2), 99-106.

Figure 4: Process capability Analysis for diameter of  the piston rings


