Control charts are powerful tools for monitoring and improving quality in manufacturing and service processes. They help detect variations, allowing businesses to maintain consistent output and reduce defects.
For measurable characteristics like length or weight, we use variable control charts. For countable features like defects, we use attribute control charts. Both types help identify out-of-control processes and non-random patterns, guiding quality improvement efforts.
Control Charts for Variables
Control charts: variables vs attributes
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Control charts for variables used when quality characteristics measurable on continuous scale (length, weight, temperature, time)
Control charts for attributes used when quality characteristics categorical or counted (number of defects, proportion of defective items)
Common types of control charts for variables: , , S chart
Common types of control charts for attributes: , , ,
X-bar and R charts
X-bar chart monitors process mean over time
Center line: Xˉˉ=k∑i=1kXˉi, where Xˉi is sample mean and k is number of samples
Upper control limit (UCL): Xˉˉ+A2Rˉ
Lower control limit (LCL): Xˉˉ−A2Rˉ
A2 is constant based on sample size, and Rˉ is average range
R chart monitors process variability over time
Center line: Rˉ=k∑i=1kRi, where Ri is sample range
UCL: D4Rˉ
LCL: D3Rˉ
D3 and D4 are constants based on sample size
Points outside indicate out-of-control process
Non-random patterns (, shifts, cycles) suggest process instability
Control Charts for Attributes
P-charts and c-charts
p-chart monitors proportion of defective items in sample
Center line: pˉ=k∑i=1kpi, where pi is proportion of defective items in sample i
UCL: pˉ+3npˉ(1−pˉ)
LCL: pˉ−3npˉ(1−pˉ), where n is sample size
c-chart monitors number of defects per unit in sample
Center line: cˉ=k∑i=1kci, where ci is number of defects in sample i
UCL: cˉ+3cˉ
LCL: cˉ−3cˉ
Points outside control limits indicate out-of-control process
Non-random patterns suggest process instability
Out-of-control patterns
Out-of-control points are points outside UCL or LCL
Non-random patterns include:
Trends: Continuous increase or decrease in points
Shifts: Abrupt change in level of process
Cycles: Repeating patterns over time
Clustering: Points grouped close to center line or control limits
Mixing: Points alternating between high and low values
Investigating and addressing out-of-control points and patterns crucial for process improvement