Quality Control  Statistical Process Control (SPC)

Step 5 – Control  Statistical Process Control (SPC)  Use data from the actual process  Estimate distributions  Look at capability - is good quality possible  Statistically monitor the process over time

Quality Two types of variation

Common Cause Variation (low level) Common Cause Variation (high level) Assignable Cause Variation Need to measure and reduce common cause variation Identify assignable cause variation as soon as possible What is common cause variation for one person might be assignable cause to the other Two Types of Variation

Time Process Parameter Upper Control Limit (UCL) Lower Control Limit (LCL) Center Line Track process parameter over time - average weight of 5 bags - control limits - different from specification limits Distinguish between - common cause variation (within control limits) - assignable cause variation (outside control limits) Detect Abnormal Variation in the Process: Identifying Assignable Causes

Statistical Process Control Capability Analysis Conformance Analysis Investigate for Assignable Cause Eliminate Assignable Cause Capability analysis What is the currently "inherent" capability of my process when it is "in control"? Conformance analysis SPC charts identify when control has likely been lost and assignable cause variation has occurred Investigate for assignable cause Find “Root Cause(s)” of Potential Loss of Statistical Control Eliminate or replicate assignable cause Need Corrective Action To Move Forward

 Statistical process control (SPC) involves testing a random sample of output from a process to determine whether the process is producing items within a preselected range.

Statistical Process Control (SPC) Charts UCL LCL Samples over time UCL LCL Samples over time UCL LCL Samples over time Normal Behavior Possible problem, investigate

Control Limits are based on the Normal Curve x z  Standard deviation units or “z” units.

Control Limits Process Average UCL = Process Mean + 3 Standard Deviations LCL = Process Mean – 3 Standard Deviations UCL LCL +3σ - 3σ- 3σ time Forming the Upper control limit (UCL) and the Lower control limit (LCL):

Control Chart Basics Process Mean UCL = Process Mean + 3 Standard Deviations LCL = Process Mean – 3 Standard Deviations UCL LCL +3σ - 3σ- 3σ Common Cause Variation: range of expected variability Special Cause Variation: Range of unexpected variability time

Process Variability Process Mean UCL = Process Mean + 3 Standard Deviations LCL = Process Mean – 3 Standard Deviations UCL LCL ±3σ → 99.7% of process values should be in this range time Special Cause of Variation: A measurement this far from the process average is very unlikely if only expected variation is present

In-control Process  A process is said to be in control when the control chart does not indicate any out-of-control condition  Contains only common causes of variation  If the common causes of variation is small, then control chart can be used to monitor the process  If the common causes of variation is too large, you need to alter the process

Process In Control  Process in control: points are randomly distributed around the center line and all points are within the control limits UCL LCL time Process Mean

Process Not in Control Out of control conditions:  One or more points outside control limits  8 or more points in a row on one side of the center line  8 or more points in a row moving in the same direction

Process Not in Control One or more points outside control limits UCL LCL Eight or more points in a row on one side of the center line UCL LCL Eight or more points in a row moving in the same direction UCL LCL Process Average

Out-of-control Processes  When the control chart indicates an out-of-control condition (a point outside the control limits or exhibiting trend, for example)  Contains both common causes of variation and assignable causes of variation  The assignable causes of variation must be identified  If detrimental to the quality, assignable causes of variation must be removed  If increases quality, assignable causes must be incorporated into the process design

Types of Statistical Sampling  Attribute (Go or no-go information)  Defectives refers to the acceptability of product across a range of characteristics.  Defects refers to the number of defects per unit which may be higher than the number of defectives. (good or bad, function or malfunction, 0 or 1)  p -chart application  Variable (Continuous)  Usually measured by the mean and the standard deviation.  X-bar and R chart applications

Example of Constructing a p -Chart: Required Data Sample No. No. of Samples Number of defects found in each sample

Where is the fraction defective, is the standard deviation, is the sample size, is the number of standard deviations for a specific confidence. Typically, (99.7 percent confidence) or (99 percent confidence) Compute control limits: Statistical Process Control Formulas: Attribute Measurements ( p -Chart) Given:

1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample Example of Constructing a p-chart: Step 1

2. Calculate the average of the sample proportions 3. Calculate the standard deviation of the sample proportion Example of Constructing a p -chart: Steps 2&3

4. Calculate the control limits UCL = LCL = (or 0) Example of Constructing a p -chart: Step 4

Example of Constructing a p -Chart: Step 5 5. Plot the individual sample proportions, the average of the proportions, and the control limits

Some notes for p-charts  The size of the sample must be large enough to allow counting of the attribute. A rule of thumb when setting up a p chart is to make the sample large enough to expect to count the attribute twice in each sample.  The assumption is that the sample size is fixed. If the sample size varies, the standard deviation and upper and lower control limits should be recalculated for each sample.

Some notes for p-charts

Process Control With Variable Measurements: Using X-bar and R Charts  Size of the samples (keep the sample size small, 4-5 is preferred)  the sample needs to be taken within a reasonable length of time  the larger the sample, the more it costs to take.  Number of samples (25 or so samples is suggested to set up the chart)  Frequency of samples  Control limits

Example of x-bar and R Charts: Required Data

Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges.

Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values  E.L.Grant and R.Leavenworth computed a table, where n is the number of observations in subgroup, A2 is the factor for X-bar chart, D3 and D4 are factors for R chart.

Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values UCL LCL Central Line

Example of x-bar and R charts: Steps 5&6. Calculate R-chart and Plot Values UCL LCL

The R Chart  Monitors variability in a process  The characteristic of interest is measured on a numerical scale  Is a variables control chart  Shows the sample range over time  Range = difference between smallest and largest values in the subgroup

The R Chart 1.Find the mean of the subgroup ranges (the center line of the R chart) 2.Compute the upper and lower control limits for the R chart 3.Use lines to show the center and control limits on the R chart 4.Plot the successive subgroup ranges as a line chart

The X Chart  Shows the means of successive subgroups over time  Monitors process average  Must be preceded by examination of the R chart to make sure that the variation in the process is in control

The X Chart  Compute the mean of the subgroup means (the center line of the X chart)  Compute the upper and lower control limits for the X chart  Graph the subgroup means  Add the center line and control limits to the graph