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Welcome to MM305 Unit 8 Seminar Prof Greg Statistical Quality Control.
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Transcript of Welcome to MM305 Unit 8 Seminar Prof Greg Statistical Quality Control.
Welcome to MM305
Unit 8 Seminar
Prof Greg
Statistical Quality Control
• “Even though quality cannot be defined, you know what it is.” R.M. Pirsig
• Total quality management (TQM) refers to a quality emphasis that encompasses the entire organization from supplier to customer
• Meeting the customer’s expectations requires an emphasis on TQM if the firm is to complete as a leader in world markets
Defining Quality and TQMDefining Quality and TQM
Statistical Process ControlStatistical Process Control
• Statistical process control involves establishing and monitoring standards, making measurements, and taking corrective action as a product or service is being produced
• Samples of process output are examined. If they fall outside certain specific ranges, the process is stopped and the assignable cause is located and removed
• A control chart is a graphical presentation of data over time and shows upper and lower limits of the process we want to control.
Control Charts for VariablesControl Charts for Variables
The x-chart (mean) and R-chart (range) are the control charts used for processes that are measured in continuous units
The x-chart tells us when changes have occurred in the central tendency of the process
The R-chart tells us when there has been a change in the uniformity of the process
Both charts must be used when monitoring variables
QM for Windows: Quality Control—x-bar and R charts
Space Shuttle WidgetsSpace Shuttle Widgets
Sample Widget 1 Widget 2 Widget 3 Widget 4 1 .98 .99 1.03 .97 2 1.01 1.0 .99 1.0 3 .99 1.02 1.01 .99 4 1.02 1.02 .98 1.01
Let's assume that we are manufacturing widgets and our widgets are used in precision engineered parts for the space shuttle. Each of our widgets is required to be 1 inch in diameter. Each hour, random samples of 4 widgets are measured to check the process control. Four hourly observations are recorded below.
Is our process in control?
QM for Windows – Xbar ChartsQM for Windows – Xbar Charts
Please note that this process produced both the Mean (x-bar) and Range (r) chart.
X-Bar ChartX-Bar Chart
Control Charts for AttributesControl Charts for Attributes
• We need a different type of chart to measure attributes
• These attributes are often classified as defective or non-defective
• There are two kinds of attribute control charts1. Charts that measure the percent defective
in a sample are called p-charts2. Charts that count the number of defects
in a sample are called c-charts
p-Chartsp-Charts If the sample size is large enough a normal
distribution can be used to calculate the control limits
pp zpUCL
pp zpLCL
where= mean proportion or fraction defective in the samplez= number of standard deviations= standard deviation of the sampling distribution which is estimated by
where n is the size of each sample
p
p
n
ppp
)1(ˆ
QM for Windows: Quality Control; p-Charts
ARCO p-Chart Example (page 285)
Figure 8.3 reproduced with QM for Windows
ARCO p-Chart Example (page 285)
Figure 8.3 reproduced with QM for Windows
c-Chartsc-Charts We use c-charts to control the number of
defects per unit of output c-charts are based on the Poisson
distribution which has its variance equal to its mean
The mean is and the standard deviation is equal to
To compute the control limits we use
cc
cc 3
QM for Windows: Quality Control; c-Charts
Red Top Cab Example (page 287)Red Top Cab Example (page 287)
Red Top Cab Company ChartRed Top Cab Company Chart
Lettuce 1 2 3 4
Day 1.2 1.3 0.9 1.3
Swing 0.6 1.0 1.1 0.9
Night 1.3 0.8 1.2 1.4
QM for Windows : Xbar and R Charts
Data
iPod manufacturer:
Usually we get 2% defective units
Took random sample of 50, found 3 defective.
Create p-chart to find UCL and LCL
Out of Control??
QM for Windows : p Chart
Here is where you take the defectives from the sample – 3 of 50 or 6% or 0,06 and see if it falls between UCL and LCL. If it is, then the process is in control, otherwise it is not. The UCL is 0.08 and the LCL is 0, therefore 0.06 is between them and the process is in control.
Excel QM : Xbar/R Chart; Set Sample #/SizeExcel QM : Xbar/R Chart; Set Sample #/Size
Excel QM : Xbar/R Chart; Set Mean/RangeExcel QM : Xbar/R Chart; Set Mean/Range
Excel QM : p Chart; Set Sample #Excel QM : p Chart; Set Sample #
Excel QM : p Chart; Set Sample Size / %Excel QM : p Chart; Set Sample Size / %
Excel QM : c Chart; Set Sample #Excel QM : c Chart; Set Sample #
Excel QM : c Chart; Set # Defects / z valueExcel QM : c Chart; Set # Defects / z value
Questions?