Ch. 9 Statistical Process Control (SPC)

Assignable cause variation is due to a change in inputs or the environment? A.True B.False

A.True

key concepts

All measures of product and process performance display variability. Natural variation occurs in a process as result of pure randomness. Assignable cause variation occurs because of a specific change in input or in environmental variables. Control charts help us tell if changes have occurred in our processes.

X and R Charts

Based on a series of samples from process, each of size n Compute the mean and range for each sample Calculate upper and lower control limits for X-bar and R charts -Standard is 3s control limits -This means that 99.7% of samples will have mean/ranges which will fall within the control limits when the process is in control. Plot means (X) on X-bar chart over time Plot ranges (R) on R charts over time Look for trends, jumps above or below control limits.

control charts (general)

Control charts tell you when a process measure is exhibiting abnormal behavior. -upper control limit (UCL) -central line -lower control limit (LCL)

control chart formulas for r charts

Ri is the range of sample i R-bar is the mean of the ranges from k samples LCL is the lower control limit UCL is the upper control limit D3 and D4 are constants based on the sample size, n.

control charts (control band)

To quantify what we mean by the normal amount of variation, we establish a control band. -If variability within this band, it is considered normal. -Any variability beyond this band is considered abnormal.

the statistical process control framework (natural variation, assignable cause variation, root cause)

Variation exists everywhere. Defects are driven by variability. *Natural variation* Occurs in a process as result of pure randomness (also called common cause variation) *Assignable cause variation* Occurs because of a specific change in input or in environmental variables. *Root cause* A root cause for a defect is a change in an input or an environmental variable that initiated a defect

control chart formulas for x-bar charts

x-bar is the sample mean x-barbar is the mean of k sample means and is the center line for the chart LCL is the lower control limit UCL is the upper control limit

interpreting control charts

*A process is out of control when sample means or ranges appear outside of control lines* This signals the need to stop the process and identify the underlying problem that caused the change The following also may warrant intervention: -*Trends* - a trend up or down indicates change -*Runs* - the pattern should be random so a run of lines above or below the center line should cause attention *Key idea:* effective quality control is data-driven

design specifications and process capability

*Key concept:* a process that is "in control" may still fail to deliver the quality demanded by the customer or a downstream operation. Control limits describe how the process has been performing (i.e. whether the process has changed or not). Control limits are not the same thing as design specifications. We use the upper (USL) and lower design specifications (LSL) to compute the capability of the process

variability in statistical process control

*Key concept:* all measures of product and process performance display variability. -No two cars or shirts are exactly identical. -Two customers will probably be served at different times in a fast food restaurant. We must understand different types of variability -Some variability is normal while abnormal variability reflects a change. -We can use SPC tools to help identify when abnormal variability is occurring.

the statistical process control framework (robust, statistical process control SPC, abnormal)

*Robust* The ability of a process to tolerate changes in input and environmental variables without causing the outcomes to be defective. *Statistical process control (SPC)* A framework in operations management built around empirical measurement, statistical analysis of output, and outcome variables. *Abnormal* A variation is abnormal if is not behaving in line with past data: -this allows us to conclude that we are dealing with an assignable cause variation and are not just facing randomness in the form of common cause variation.

control chart types

*for continuous numerical data* Variable charts -R chart -X bar chart *for categorical or discrete numerical data* Attribute charts -P chart -C chart

control charts (sigma)

*in between UCL and LCL* 99% *from centerline to UCL* 3 sigma (half of 99%) *from centerline to LCL* 3 sigma (half of 99%) *outside of UCL and LCL* unexpected zones

monitoring

Once new policies are tested and implemented to reduce quality problems, we want to monitor the process to make sure a new problem has not occurred or that current policies have not been ignored, replaced, etc. We do this with control charts. Control charts monitor a metric over time to make sure it remains stable. The terms statistical process control and control charts are used interchangeably.

challenges with statistical process control (SPC)

One of the challenges of using control charts is deciding what metric to make a control chart -You want to choose metrics that have variability (why?) -These metrics should have a big impact on quality or customer's perception of quality

control charts (data)

There are many kinds of control charts: -*Variable data* (weight, length, time) -*Attribute data* (pass/fail, good/bad) For variable data, X-bar and R charts are used* -*X-bar:* y-axis is the mean of each sample -*R:* y-axis is the range of each sample -Why do we need both charts for variables?