IENG 484 Quality Engineering LAB 3 Statistical Quality Control (SPSS) Research Assistant Kehinde Adewale Adesina

Statistical Quality Control This is the use of statistical methods and techniques to evaluate the quality of products and processes in order to monitor and where necessary improve their quality. Products which are checked for defectives to determine whether or not the process is in control. The method uses control charts to measure and analyze variation in processes.

Statistical Quality Control A control chart graphically represents statistics of repeated samples of a production process in time. If fact, a control chart is a time series plot of a statistic. It consists of points representing a statistic, a center line, and upper and lower control limits. It may consists of the mean of this statistic, the standard error of the statistic, upper and lower warning limits, and so on.

Statistical Quality Control Variation in production is a key aspect of quality control. Control charts is used to study how a process changes over time It is assumed to arise from two different main sources: - Common causes (un-controllable factors). -Assignable causes (operator fatigue, tools wearing out, incorrect machine settings).

A control chart always has a central line, upper control limit and the lower control limit.

By comparing current data to these lines, conclusion about whether the process variation is consistent (in control) or is unpredictable (out of control due to special causes of variation). A process is considered in control, when there are no assignable causes. If the outcome of a statistic is outside the control limits, then the process is considered out of control. Control charts are of two types (i) Variable Control Charts (ii) Attribute Control Charts

If the outcome of a statistic is outside the control limits, then the process is considered out of control. Process may be considered out of control when the control charts reveals a systematic pattern Control charts are of two types (i) Variable Control Charts (ii) Attribute Control Charts

When can a Control Chart be employed  controlling ongoing processes by finding and correcting problems as they occur.  predicting the expected range of outcomes from a process.  determining whether a process is stable (in statistical control).  analyzing patterns of process variation from special causes (non-routine events) or common causes (built into the process).  determining whether your quality improvement project should aim to prevent specific problems or to make fundamental changes to the process.

Control Chart Procedure Choose the appropriate control chart for your data. Determine the appropriate time period for collecting and plotting data. Collect data, construct your chart and analyze the data. Look for “out-of-control signals” on the control chart. When one is identified, mark it on the chart and investigate the cause. Document how you investigated, what you learned, the cause and how it was corrected. 

Out-of-control signals A single point outside the control limits like point 16. Two out of three successive points are on the same side of the centerline and farther than 2 σ from it. Like point 4. Four out of five successive points are on the same side of the centerline and farther than 1 σ from it. Point 11. A run of eight in a row are on the same side of the centerline. Or 10 out of 11, 12 out of 14 or 16 out of 20. Point 21 is eighth in a row above the centerline. Obvious consistent or persistent patterns that suggest something unusual about the process.

Variable Control Charts Data are used in pairs viz the top X-bar chart and the bottom range R chart. The X-bar monitors the average or the centering of the distribution of the data (variation) from the process. The R chart monitors the range or the width of the distribution. For example:

Example: Variable Control Charts Consider a process by which coils are manufactured. Samples size 5 are randomly selected from the process and the resistance values of the coils are measured. Please, download the excel files from the FTP and import it into SPSS ftp.ie.emu.edu.tr (username: iedept, password: cdwriter) Click on File/Select “Read Text data”/ Lookin “select source of the data”/ Text of type “Excel txt” /Click the file/Open/Woeksheet select the sheet/Ok

Remedial actions needed Delete samples 3, 22, 23 and revised the control limits.

Remedial actions needed Notice that sample 15 falls slightly above the upper control limits so delete sample 15 and revised the control limits.

X-S Chart

Control Charts for Attributes An attribute is a quality characteristic for which a numerical value is not specified. It is measured on a nominal scale; For example taste of a certain dish is labeled as acceptable or unacceptable. A quality characteristic that does not meet certain prescribed standards is said to be a nonconformity (or defect). For example if the length of steel bars is expected to be 50 ± 1.0 cm, a length of 51.5 cm is not acceptable. A product with one or more nonconformities, such as it is unable to function as required, is a nonconforming item (or defective)

They are grouped into 3 categories; 1st category includes control charts that focus on proportion. p – Chart : The proportion of nonconforming items (equal sample size and unequal sample size) (2) np- Chart: Number of Nonconforming items 2nd category deals with three charts that focuses on the nonconformity itself. (1) c-Chart: Chart for total number of nonconformities. (2) u-Chart: Chart for nonconformities per unit. (3) U-Chart: Deals with combining nonconformities on a weighted basis.

THANKS For further information : kehinde.adesina@cc.emu.edu.tr