Welcome to MM305 Unit 8 Seminar Prof. Dan 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 TQM

Statistical 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 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 Widgets 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?

Space Shuttle Widgets Construct limits for xbar and R charts. SampleWeight 1Weight 2Weight 3Weight 4AverageRange Average From the Control Chart Limits Factors table: A 2 = 0.729; D 4 = 2.282; D 3 = 0 UCL Xbar = *0.037 = = LCL Xbar = – 0.729*0.037 = – = UCL R = 2.282*0.037 = LCL R = 0*0.037 = 0

Space Shuttle Widgets Construct limits for xbar and R charts. SampleWeight 1Weight 2Weight 3Weight 4AverageRange Average UCL Xbar = UCL R = LCL Xbar = LCL R = 0 The smallest sample mean is.97 which is within LCL but the largest sample mean is 1.03 which is above the UCL = so the process is out of control.

QM for Windows – Xbar Charts Please note that this process produced both the Mean (x-bar) and Range (r) chart.

X-Bar Chart

Control 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 charts 1.Charts that measure the percent defective in a sample are called p -charts 2.Charts that count the number of defects in a sample are called c -charts

p-Charts  If the sample size is large enough a normal distribution can be used to calculate the control limits where = mean proportion or fraction defective in the sample z =number of standard deviations =standard deviation of the sampling distribution which is estimated by where n is the size of each sample QM for Windows: Quality Control; p-Charts

p-Charts A manufacturer of USB microphones has learned that you have completed a course in Quantitative Analysis and wants you to help him understand a p-chart. Unfortunately he has lost the chart but has the following information for you. Historically, 4% of microphones have been found to be defective. They have taken a random sample of 100 microphones and found that 8 of them are defective. Without any further data, create a p-chart and determine the UCL and LCL. Based on that information tell the manufacturer whether the process should be considered out of control?

p-Charts A manufacturer of USB microphones has learned that you have completed a course in Quantitative Analysis and wants you to help him understand a p-chart. Unfortunately he has lost the chart but has the following information for you. Historically, 4% of microphones have been found to be defective. They have taken a random sample of 100 microphones and found that 8 of them are defective. Without any further data, create a p-chart and determine the UCL and LCL. Based on that information tell the manufacturer whether the process should be considered out of control? z of 99.7% control limits is z = 3 P =.04 σ p = √P*(1-P)/n = √.04*.96/100 =.0196 UCL p = (.0196) = =.098 LCL p = * = = -.019, which is 0 Since 8% [.08] is in this range, therefore the process is in control.

ARCO p-Chart Example (page 285) Figure 8.3 reproduced with QM for Windows

c-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 QM for Windows: Quality Control; c-Charts

Red Top Cab Example (page 287)

Red Top Cab Company Chart

Questions?