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?