Introduction Subgroups of data collected “qcc” library in RStudio in the design of piston rings (pistonsrings) and the data taken from the process are to be analyzed as a proactive measure to ensure that process is in control. It is essential to determine that performance is on the right path with minimal to no defects. The cost of quality is reduced, as well as satisfying customers’ needs when a defect is detected and rectified before the end product reaches the customer. Statistical Process Control (SPC) is a procedure for monitoring business or process performance.SPC is essential for the detection of stability, consistency, and defect. A stable process follows a consistent pattern, and process control is to detect any deviation from the regular pattern. In production lifecycles, the number of substandard or defective items per million produced will likely vary with each production run. In customer service, the number of complaints (customer attrition, churn, turnover, defection) may fluctuate monthly. High school or SAT exam records may vary between schools. For example, samples are collected from measuring units such as plates, rods, or any form or numeric units representing product quality or accuracy. The collected data point graphed against defined metrics, which include the sample mean, the upper and lower limits, or the points cut; the criteria of the limits (center, lower and upper) to establish a graph help to determine the process performance and identify the kinds of error which occurred. The process will be rectified with the proper diagnosis in identifying the common cause or special cause. Dr. Walter Shewhart, quality control guru of Bell Telephone Laboratories, developed a new faculty for managing variation. The effort of this faculty was to identify two causes of variation, as shown in (Figure 1): 1. Common cause variation, alias noise variation, is inherent in a process over time; this cause affects every outcome of the process and the operators working in the process. Managing noise variation causes variation and thus requires improvements to the process. 2. A common cause may be an inherent or apparent weakness in the process or raw material. 3. Special cause variation (assignable cause), also known as signal cause variation, arises because of unusual or unexpected random circumstances and is not due to an inherent part of a process. Controlling such kind of random variation involves locating and removing the unusual cause. Figure 1. Managing variation

Shewhart further identified two types of mistakes possible in managing variation: treating a common cause as special and a special cause as a common cause.

Later, W. Edwards Deming estimated that a lack of an understanding of variation resulted in situations where 95% of management actions result in no improvement. Referred to as “tampering,” action taken to compensate for variation within the control limits of a stable system increases, rather than decreases, variation.

A control chart is the visual representation of the SPC and is allot with; the Upper control limit (UCL), the lower control limit (LCL) the ideal target, which is the central measure or limits of the measurement. Data points of the process are ideally supposed to constrain mean and within the boundaries of the UCL and The LCL to meet acceptance criteria.

Every deviation from the central limit is added or subtracted from the standard error from the mean, bringing the result closer to UCL or LCL.

For simplicity, the control chart provides 3* standard error (SE) towards the UCL or LCL based on the confidence level of the sample distribution. The Confidence interval determines the level of risk to which we want to accept errors.

Figure 2

Explanation of the SPC patterns

“It is imperative to note that; the standard error (SE) is to the distribution of many samples means as the standard deviation (sd) is to a distribution of scores in one sample. The SE calculates a confidence interval around a particular sample means. This confidence interval tells us how confident we are that the true population mean ( µ ) falls within a given range. For example, if the results of a survey on general radio listening show average daily listening of “37 minutes, plus-or-minus 4.5 minutes at the 95% confidence level,” we would say that we are 95% certain that the true population means ( µ ) is between 32.5 and 41.5 minutes.”

Figure 3.

Confidence interval associated with standard error

Wikipedia contributors. (2022, August 20). 68–95–99.7 rule. In Wikipedia, the Free Encyclopedia.

Installing the “qcc” library

#install the “qcc” package

Install.packages(‘’qcc’’)

# Upload the “qcc” package

Library (‘’qcc’’)

# using the available in the “qcc” package data called pistonrings

Figure 4.

Pistonrings datasets.

Figure 5.

Calculating the average diameter of a sample of each subgroup

Figure 6.

Transformed the tables in “qcc” friendly format in terms of the diameter of each subgroup

Figure 7.

Code for Xbar S chart and diagnostic output

Figure 8.

The Xbar s chart

Figure 8B.

Using code “qcc (diameter, type=” S”): The given code is used to check the control status of figure 8, and it shows that the process is in control. From the graph, it can be identified that the outlier is due to a random (sporadic) cause, or the error is not common or inherent to the process. This error due is a special cause, as explained in figure 2.

Figure 9.

Code for Xbar R chart and diagnostic output

Figure 10.

Xbar R chart

Figure 10B.

Similarly, using code “qcc (diameter, type=”R”): the process is in control using the R chart; the cause of the error is not inherent but a common cause.

Miscellaneous insight

Figure 11 shows how the data is distributed and can easily show where the anomaly occurred. Figure 12A, 12B, and 12C also show outliers, the minimum the maximum values recorded.

Figure 11.

Data distribution

Figure 12A.

Summary statistics

Figure 12B.

Minimum and maximum

Figure 12C.

Boxplot of subgroup

Conclusion

The cause of the outliers is due to a special cause, and no major modification of the process is required. However, it requires an investigation so that a cause is assigned to the source of the cause.