What type of control chart would be used to monitor the number of defectives in the output of a process for making iron castings?

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Variable Control Charts:
X bar control chart.
Range “R” control chart.
Standard Deviation “S” control chart.
Attribute Control Charts:
“u” and “c” control charts.
“p” and “np” control charts.
Pre-control Charts.
Selection of Control chart
Why and When do you use a c Chart?
Assumptions of Attribute charts: c chart
c chart formulas
How do you Create a c Chart
Example of using a c Chart in a Six Sigma project
C Chart Excel Template
Videos of c Charts
Additional Helpful Links

The Information you need, provided in an easy to understand visual format.

There are various types of control charts which are broadly similar and have been developed to suit particular characteristics of the quality attribute being analyzed. Two broad categories of chart exist, which are based on if the data being monitored is “variable” or “attribute” in nature.

Variable Control Charts:

X bar control chart.

This type of chart graphs the means (or averages) of a set of samples, plotted in order to monitor the mean of a variable, for example the length of steel rods, the weight of bags of compound, the intensity of laser beams, etc.. In constructing this chart, samples of process outputs are taken at regular intervals, the means of each set of samples are calculated and graphed onto the X bar control chart. This chart can then be utilized to determine the actual process mean, versus a nominal process mean and will demonstrate if the mean output of the process is changing over time.

Range “R” control chart.

This type of chart demonstrates the variability within a process. It is suited to processes where the sample sizes are relatively small, for example <10. Sets of sample data are recorded from a process for the particular quality characteristic being monitored. For each set of date the difference between the smallest and largest readings are recorded. This is the range “R” of the set of data. The ranges are now recorded onto a control chart. The center line is the averages of all the ranges.

Standard Deviation “S” control chart.

The “S” chart can be applied when monitoring variable data. It is suited to situations where there are large numbers of samples being recorded. The “S” relates to the standard deviation within the sample sets and is a better indication of variation within a large set versus the range calculation. An advantage of using the standard deviation is that all data within a set are utilized to determine the variation, rather than just the minimum and maximum values.

Develop your understanding of Control Charts, Process Capability, Process Improvement, etc. …

Attribute Control Charts:

Attribute control charts are utilized when monitoring count data. There are two categories of count data, namely data which arises from “pass/fail” type measurements, and data which arises where a count in the form of 1,2,3,4,…. arises. Depending on which form of data is being recorded, differing forms of control charts should be applied.

“u” and “c” control charts.

The “u” and “c” control charts are applied when monitoring and controlling count data in the form of 1,2,3, …. i.e. specific numbers. An example of such data is the number of defects in a batch of raw material, or the number of defects identified within a finished product. The c chart is used where there can be a number of defects per sample unit and the number of samples per sampling period remains constant. In the u chart, again similar to the c chart, the number of defects per sample unit can be recorded, however, with the u chart, the number of samples per sampling period may vary.

“p” and “np” control charts.

P charts are utilized where there is a pass / fail determination on a unit inspected. The p chart will show if the proportion defective within a process changes over the sampling period (the p indicates the portion of successes). In the p chart the sample size can vary over time. A similar chart to the p chart is the np chart. However, with the np chart the sample size needs to stay constant over the sampling period. An advantage of the np chart is that the number non-conforming is recorded onto the control rather than the fraction non conforming. Some process operators are more comfortable plotting the number rather than the fraction of non-conformances.

Pre-control Charts.

Where a process is confirmed as being within statistical control, a pre-control chart can be utilized to check individual measurements against allowable specifications. Pre-control charts are simpler to use than standard control charts, are more visual and provide immediate “call to actions” for process operators. If however a process is not statistically “capable” i.e. having a Cpk of at least 1, pre-control can result in excessive process stoppages.

Develop your understanding of Control Charts, Process Capability, Process Improvement, etc. …

Attribute chart: c chart is also known as the control chart for defects (counting of the number of defects). It is generally used to monitor the number of defects in constant size units. There may be a single type of defect or several different types, but the c chart tracks the total number of defects in each unit and it assumes the underlying data approximate the Poisson distribution. The unit may be a single item or a specified section of items—for example, scratches on plated metal, number of insufficient soldering in a printed circuit board.

c chart takes into account the number of defects in each defective unit or in a given sample. While p chart analyzes the proportions of non-conforming or defective items in a process.

c chart, the number of defects is plotting on the y-axis and the number of units on the x-axis. The centerline of the c chart (c̅) is the total number of defects divided by the number of samples.

Selection of Control chart

The control chart is a graph used to study how process changes over time. A control chart always has a central line for average, an upper line for upper control limit, and lower line for the lower control limit. The control limits are ±3σ from the centerline.

Selection of appropriate control chart is very important in control charts mapping, otherwise ended up with inaccurate control limits for the data.

X̅ and R chart are used for measurable quantities such as length, weight height. Attribute control charts are used for attribute data. In other words, the data that counts the number of defective items or the number of defects per unit. For example number of tubes failed on a shop floor. Unlike variable charts, only one chart is plotted for attributes.

Why and When do you use a c Chart?

c chart is one of the quality control charts used to track the number of defects in a product of constant size, while u chart is used for a varying size.

c-chart is used to determine if the process is stable and predictable and also to monitor the effects of before and after process improvements. c chart is especially used when there are high opportunities for defects in the subgroup, but the actual number of defects is less.

c chart requires that each subgroup’s sample size be the same and compute control limits based on the Poisson distribution.

Four types of control charts exist for attribute data. p chart plots the proportion of defective items, and np chart is for the number of defectives. u chart is for the average number of defects per unit and c chart is for the number of defects.

Assumptions of Attribute charts: c chart

The probability of defect is the same for each item
Each unit is independent of the other
The testing procedure should be the same for each lot

c chart formulas

Where c = number of defects
k= number of samples

How do you Create a c Chart

Determine the subgroup size. The subgroup size must be large enough for the c chart; otherwise, control limits may not be accurate when estimated from the data.
Count the number of defects in each sample
Compute centreline c̅ = total number of defects / number of samples =Σc/k
Calculate upper control limit (UCL) and low control limit (LCL). If LCL is negative, then consider it as 0.
Plot the graph with number of defects on the y-axis, lots on the x-axis: Draw centerline, UCL and LCL. Use these limits to monitor the number of defects going forward.
Finally, interpret the data to determine whether the process is in control.

Example of using a c Chart in a Six Sigma project

Example: Mobile charger supplier drawn randomly constant sample size of 500 chargers every day for quality control test. Defects in each charger are recorded during testing. Based on the given data, draw the appropriate control chart and comment on the state of control.

no of lots k = 20
Σc = 326

Compute c̅ = total number of defects / total number of lots =Σc/k =326/20= 16.3

Then calculate upper control limit (UCL) and low control limit (LCL)

Plot the graph with number of defects on the y-axis, lots on the x-axis and also draw center line (c̅), UCL and LCL.

Interpret the chart: If any of the points in the chart is outside of ± 3σ limit, then consider the process is out of control. In the above example, the average number of defects per lot is 16.3. Sample 9 is outside of the control limit. Hence the process is out of control. Thus team needs to identify the root cause for the special cause variation.