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Administrative Information

Title: Statistical Process Control

Author: William Guarin

Class: IE 673

eLearning Pack Serial Number: IE673_Spring2006_217

Date: April 23, 2006

Authorship Statement I pledge that I completed this assignment by myself with no aid from anyone in the class

Statistical Process Control

Introduction

One of the most important actions that can help maintain the quality of any good or service is to collect relevant data consistently over time, plot it, and examine the plots carefully. In all production processes, we need to monitor the extent to which our products meet specifications. In the most general terms, there are two obstacles on the way to achieve product quality: (1) deviations from target specifications, and (2) excessive variability around target specifications. In order to indicate these variations in quality the control chart analysis and presentation of data is used. A control chart is a statistical tool used to distinguish between variation in a process resulting from common causes and variation resulting from special causes. It presents a graphic display of process stability or instability over time. One goal of using a Control Chart is to achieve and maintain process stability. Process stability is defined as a state in which a process has displayed a certain degree of consistency in the past and is expected to continue to do so in the future. This consistency is characterized by a stream of data falling within control limits.

Control limits represent the limits of variation that should be expected from a process in a state of statistical control. When a process is in statistical control, any variation is the result of common causes that effect the entire production in a similar way. It is important to understand that control limits should not be confused with specification limits, which represent the desired process performance.

In the use of statistical methods to control product quality, statistical quality control techniques are the tools used to achieve cost reduction and quality improvement. This is particularly true in the first stages of the use of statistical methods; as managers dealing with quality matters acquire advanced statistical knowledge.

Project Objective

The main objective of this project is to provide the collaborating companies with an important tool such as statistical quality control techniques. Any company interested in performing a quality improvement project will have the opportunity to visit my website and be provided with all the knowledge necessary to carry out their projects. The companies will benefit from using our Control Chart techniques when they want to:

· Monitor process variation over time.

· Differentiate between special cause and common cause variation.

· Assess the effectiveness of changes to improve a process.

· Communicate how a process performed during a specific period.

The power of using our techniques lies in the ability to separate out assignable causes of quality variation. This makes possible the diagnosis and correction of many production troubles and often brings substantial improvements in product quality and reduction of spoilage and rework. Moreover, by identifying certain of the quality variations as inevitably chance of variations, the control chart will tell quality management when to leave a process alone and thus prevent unnecessary frequent adjustments that tend to increase the variability of the process rather than to decrease it.

Project Methodology

An important distinction in the technical language of statistics is that between variables and attributes. When a record is made of an actual measured quality characteristic, such as a dimension expressed in thousandths of an inch, the quality is said to be expressed by variables. Variable data are measured on a continuous scale. For example: time, weight, distance or temperature can be measured in fractions or decimals. The possibility of measuring to greater precision defines variable data. When a record shows only the number of articles conforming and the number of articles failing to conform to any specified requirements, it is said to be a record by attributes. Attribute data are counted and cannot have fractions or decimals. Attribute data arise when you are determining only the presence or absence of something: success or failure, accept or reject, correct or not correct. For example, a report can have four errors or five errors, but it cannot have four and a half errors.

The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit and a lower line for the lower control limit. These lines are determined from historical data. By comparing current data to these lines, managers can draw conclusions about whether the process variation is consistent or in control or is unpredictable or out of control which means it is affected by special causes of variation.

When dealing with a quality characteristic that is a variable, it is a standard practice to control both the mean value of the quality characteristic and its variability. Control of the process average or mean quality level is usually with the control chart for means, or the x bar chart. The control of the process range is done by using the control chart for range, or the R chart. The X bar chart is developed from the average of each subgroup data. The R chart is developed from the ranges of each subgroup data, which is calculated by subtracting the maximum and the minimum value in each subgroup.

Many quality characteristics cannot be conveniently represented numerically. In such cases, each item inspected is classified as either conforming or nonconforming to the specifications on that quality characteristic. Quality characteristics of this type are called attributes. Examples are nonfunctional semiconductor chips, warped connecting and rods. The following are the type of attribute charts:

p charts

This chart shows the fraction of nonconforming or defective product produced by a manufacturing process. It is also called the control chart for fraction nonconforming. It is based on the Binomial distribution.

c Charts

This shows the number of defects or nonconformities produced by a manufacturing process. It is based on the Poisson distribution.

u Charts

This chart shows the nonconformities per unit produced by a manufacturing process.

Quality Improvement Project Procedure When doing a quality improvement project the following is the procedure managers must take:

1. Choose the appropriate control chart for your data.

2. Determine the appropriate time period for collecting and plotting data.

3. Collect data, construct your chart and analyze the data.

4. 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.

Determining Out of Control Signals:

· A single point outside the control limits.

· Two out of three successive points are on the same side of the centerline

· Four out of five successive points are on the same side of the centerline

· 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

· Obvious consistent or persistent patterns that suggest something unusual about your data and your process

When analyzing the variable control chart, the R chart must be analyzed first to determine if it is stable. If there are out of control points, those points are to be discarded from the data and the new data is plotted again to see if the remaining points on the chart are stable now. If stable, the X bar is analyzed and if out of control points are found, the same procedure is done as for the R chart.

Variable Control Chart Analysis - X&R bar charts-Case Study #1

The following process has been chosen to be analyzed statistically. This process could have been chosen from the collaborating companies or any company using our services.

“A small electronic device is designed to emit a timing signal of 200 milliseconds duration. In the production of these devices, subgroups of five were taken at periodic intervals and tested. The data was collected in order to do a quality improvement project”.

According to the data obtained a variable control chart analysis will be performed. The results of inspection of the 125 of these devices and their calculations and analysis can be found in the following link.

Attribute Control Chart Analysis - p Variable Chart- Case Study #2

The following is the case study taken from one of the companies that use our tools for their projects:

"The same electronic company decides to manufacture 1550 devices in 25 days. The manager decides to manufacture 50 batches per day for the 25 days. A p chart is used to monitor the proportion of failing devices. Fifty batches are examined, and the failures in each batch are counted".

When gathering the data, there is a single observation for each batch. The variable batch identifies the subgroup sample and is referred to as the subgroup variable. The subgroup variable contains the number of nonconforming items in each subgroup sample. Variable subgroup sizes are undesirable but when dealing with processes where the whole batch is nonconforming or where errors such as color and dimension are part of the process. When collecting the data, the variation in the number inspected per day could be result of different failures that could not be accounted as one failure. This will cause day to day variations in the data. For this case, as the subgroup size changes each day, the trial central line and control limits must be calculated each day.
In this case, as the production quantities vary from day to day, the subgroup sizes will also be variable.
When the p chart was constructed, it appeared that two fraction defective from subgroups 7 and 17 fell above the upper control limit. An investigation could find no assignable cause for the defective percentage in those subgroups; and therefore, it could be assumed that these values were a rare but normal effect of the random variability of the process.
After recomputing the new control limits, these data are plotted on the control chart again. Here, we noticed that none of the points fell outside of any of the variable control limits and that there are no long sequences of points on the same side of the center line. It can, therefore, be concluded that the process is in control.
A point on the p chart falling above the upper control limit represents an abnormally high value of fraction defective for the process, and this condition should be investigated. However, a point falling below the lower control limit would seem to represent an abnormally low fraction defective, which is a desirable condition.
The control charts and the results for the p variable chart can be found in the following link.

p Variable Chart

Attribute Control Chart Analysis - np Constant Chart- Case Study #3

When the subgroup size is constant, it is possible to construct a control chart for the actual number of defectives in the sample.
For each subgroup the proportion nonconforming is calculated
This kind of chart could be used by companies during the start up phase of a new product or process when the process is very inconsistent
Companies may prefer to use this control chart to measure their operations quality performance
The np chart is never used when the subgroup size is variable. However, when the subgroup is constant, the np chart may be easier to interpret the p chart
The following is the case study taken from one of the companies that use our tools for their projects:

" A company is interested in measuring their quality performance in the assembly department for their clinical units. They inspected 12 samples of 350 units and then the number of nonconforming units were registered".

The results of the calculations for these data can be found in the following link.

Constant Attribute Chart

Attribute Control Chart Analysis - c Control Chart- Case Study #4

The letter c is used to represent the number of defects
The appropriate distribution for the number of defects is the Poison Distribution
In using the chart for defects, it is important to know that the inspection unit may be a single unit of product, or it may be a subgroup consisting of several individual units
When using this chart, it does not matter how we define the subgroup or inspection unit, it is imperative that its size remain constant
When the subgroup size does vary, a modification of the c chart, called the u chart may be used

"On final inspection, hand held calculators are tested and inspected for loose connections, scratches, dents, and any other defects that would interfere with their operation, or make them unacceptable to a customer".

The results of the calculations for these data can be found in the following link.

c Control Chart Analyses

Attribute Control Chart Analysis - u Control Chart- Case Study #5

The following case will be analyzed and the use of the u control will be shown:

" A company manufactures cabinets for 19 in. color television receivers. The production quantity varies from day to day. Each day's output is inspected for defects in the cabinet finish".

The result of the calculations for these data can be found in the following link.

u Control Chart Analyses

Summary

Determining the capability of a process is vital information for the quality improvement operations of any company. Control charts are a highly specialized tool that indicate a process performance according to the characteristics of the process. It is important to understand the processes to be analyzed and the kind of control chart to be utilized.

The main purpose of using this extraordinary tool is simply to extract samples of a certain size from any ongoing production process. Then produce line charts of the variability in those samples, and consider their closeness to target specifications. If a trend emerges in those lines, or if samples fall outside pre-specified limits, then we declare the process to be out of control and take action to find the cause of the problem.

Further Work Needed

It is extremely important for managers to carry out quality improvement projects in their companies in order to satisfy customers needs. Statistical control analysis offers a great advantage to those companies that apply this knowledge. Therefore, there should an on going effort from management to have this terrific tool as part of their daily tasks.

Bibliography

CD-ROM by Ranky, Paul, G.: An Introduction to Total Quality Management & Control
Quality Control, Dale H. Besterfield: 7thth edition, Upper saddle River, N.J