THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 1 Chapter 12 Statistical Process Control

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 2 Statistical Process Control (SPC) A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate SPC relies on control charts

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 3 Process Variation Variation exists in all processes Process variation can be separated into two sources –common causes or natural variation –special causes or assignable causes of variation process operator material environment

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 4 Only Common Causes Present Special Causes Present

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 5 Capability Versus Control Control Capability Capable Not Capable In Control Out of Control IDEAL

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 6 Statistical Process Control (SPC) (1 of 2) The purpose of SPC is to monitor a process to identify when it is believed that some special causes of variation is active This signals the need to investigate the process and take corrective action when appropriate SPC relies on control charts to perform this purpose

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 7 Statistical Process Control (SPC) (2 of 2) SPC tests the hypothesis: H 0 : the process is in control, i.e., there is only natural variation in the output H 1 : the process is out of control, i.e, there is an assignable cause active

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 8 Overview of the Statistical Quality Control (QC) Process Population Sample of size n Inspect Each Item in the Sample Sample Information Compare Decision Criteria IN CONTROL OUT OF CONTROL

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 9 Procedure (1 of 2) A sample is taken from the output of the process and each unit in the sample is inspected The data from the sample is used to calculated a statistic The statistic is plotted on the control chart

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 10 Procedure (2 of 2) If the sample statistic falls on or between the control limits, the quality of the population (process output) is considered to be in control; otherwise quality is judged to be out of control and corrective action should be considered

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 11 Decisions and Risks in Process Control

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 12 Control Charts The vertical axis provides the scale for the sample information that is plotted on the chart The horizontal axis is time The decision criteria consists of two horizontal lines –Upper control limit –Lower control limit

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 13 Histograms do not take into account changes over time. Control charts can tell us when a process changes

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 14 Control Chart Applications Establish state of statistical control Monitor a process and signal when it goes out of control Determine process capability

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 15 Commonly Used Control Charts Variables data –x-bar and R-charts –x-bar and s-charts –Charts for individuals (x-charts) Attribute data –For “defectives” (p-chart, np-chart) –For “defects” (c-chart, u-chart)

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 16 Developing Control Charts 1.Prepare –Choose measurement –Determine how to collect data, sample size, and frequency of sampling –Set up an initial control chart 2.Collect Data –Record data –Calculate appropriate statistics –Plot statistics on chart

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THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 18 Next Steps 3.Determine trial control limits –Center line (process average) –Compute UCL, LCL 4.Analyze and interpret results –Determine if in control –Eliminate out-of-control points –Recompute control limits as necessary

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 19 Inspection of the units in the sample is performed on an variables basis The statistics provided from inspecting a sample of size n is the sample mean, x (the sum of measurement of each unit in the sample divided by n) and the range, R, of measurements within the sample (the highest measurement in the sample minus the lowest measurement in the sample) Control Charts for Variables (1 of 2)

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 20 In this case two separate control charts are used to monitor two different aspects of the process output –Central tendency –Variability The central tendency of the output is monitored using the x-chart The variability of the output is monitored using the R-chart Variables (2 of 2)

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 21 The central line is x, the sum of a number of sample means collected while the process was considered to be “in control” divided by the number of samples The 3 lower control limit is x - A 2 R The 3 upper control limit is x + A 2 R Factor A 2 is based on sample size x-Chart

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 22 The 3 lower control limit is D 3 R The 3 upper control limit is D 4 R Factors D 3 and D 4 are based on sample size R (range)-Chart

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THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 27 Typical Out-of-Control Patterns Point outside control limits Sudden shift in process average Cycles Trends Hugging the center line Hugging the control limits Instability

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 28 Shift in Process Average

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 29 Identifying Potential Shifts

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 30 Cycles

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 31 Trend

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 32 Final Steps 5.Use as a problem-solving tool –Continue to collect and plot data –Take corrective action when necessary 6.Compute process capability

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 33 Process Capability Calculations

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 34 Excel Template

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THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 36 Special Variables Control Charts x-bar and s charts x-chart for individuals

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THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 41 Charts for Attributes Fraction nonconforming (p-chart) –Fixed sample size –Variable sample size np-chart for number nonconforming Charts for defects –c-chart –u-chart

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 42 Estimating Process Capability Collect sample data while the process is considered to be “in control” Under the normality assumption, the standard deviation can be estimated using

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 43 Control Charts for Attributes (1 of 3) Inspection of the units in the sample is performed on an attributes basis The statistic provided from inspecting a sample of size n is the percent defective in a sample, p (the number of units found to be defective in that sample divided by n)

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 44 Attributes (2 of 3) Although the distribution of sample statistic follows a binomial distribution, that distribution can be approximated by a normal distribution with a mean of and a standard deviation of

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 45 Attributes (3 of 3) The 3 lower control limit is The 3 upper control limit is

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THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 56 Control Chart Selection Quality Characteristic variableattribute n>1? n>=10 or computer? x and MR no yes x and s x and R no yes defectivedefect constant sample size? p-chart with variable sample size no p or np yes constant sampling unit? c u yesno

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 57 Control Chart Design Issues Basis for sampling Sample size Frequency of sampling Location of control limits

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THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 59 Pre-Control nominal value Green Zone Yellow Zones Red Zone Red Zone LTLUTL

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 60 SPC Implementation Requirements Top management commitment Project champion Initial workable project Employee education and training Accurate measurement system