CONTROL CHARTS IN QUALITY CONTROL

CONTROL CHARTS / SHEWHART CHARTS(Tools in Conveying Quality Control Concepts in Construction)

Submitted by: GALANO, GLENN PAUL E.MUROS, JUCEL A.BS Architecture 5-2

Submitted to:ARCH. EMILIE T. GARCIAApproved Specialization 3 Class Adviser

Date Submitted:JANUARY 7, 2016

Definition of Control ChartControl charts, also known as Shewhart charts (after Dr. Shewhart) or process-behavior charts, is one of the seven basic tools of quality. These are statistical tools used in quality control to (1) analyze and understand process variables, (2) determine process capabilities, and to (3) monitor effects of the variables on the difference between target and actual performance.Control charts indicate data points, upper and lower control limits, and often include a central (average) line, to help detect trend of plotted values. These charts visually display the fluctuations of a particular process variable, such as temperature, in a way that lets the quality control engineer easily determine whether these variations fall within the specified process limits. If all data points are within the control limits, variations in the values may be due to a common cause and process is said to be in control. If data points fall outside the control limits, variations may be due to a special cause and the process is said to be out of control.

Father of Control ChartDr. Walter Andrew Shewhart (March 18, 1891 March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control. He invented the control chart.Bell Telephones engineers had been working to improve the reliability of their transmission systems. In order to impress government regulators of this natural monopoly with the high quality of their service, Shewhart's first assignment was to improve the voice clarity of the carbon transmitters in the company's telephone handsets. Later he applied his statistical methods to the final installation of central station switching systems, then to factory production. When Dr. Shewhart joined the Western Electric Company Inspection Engineering Department at the Hawthorne Works in 1918, industrial quality was limited to inspecting finished products and removing defective items. That all changed on May 16, 1924. George D. Edwards, Dr. Shewharts boss, recalled that Shewhart prepared a little memorandum only about a page in length. About a third of that page was given over to a simple diagram which at this modern era would be recognize as a schematic control chart. That diagram, and the short text which preceded and followed it, set forth all of the essential principles and considerations which are involved in what professionals know today as process quality control.Shewhart's work pointed out the importance of reducing variation in a manufacturing process and the understanding that continual process-adjustment in reaction to nonconformance actually increased variation and degraded quality. In 1931, he published a book entitled Economic Control of Quality of Manufactured Product which summarized the methods and work that he has done.

In-depth Background of Control ChartsA process may either be classified as in control or out of control. The boundaries for these classifications are set by calculating the mean, standard deviation, and range of a set of process data collected when the process is under stable operation. Then, subsequent data can be compared to this already calculated mean, standard deviation and range to determine whether the new data fall within acceptable bounds.For good and safe control, subsequent data collected should fall within three standard deviations of the mean. Control charts build on this basic idea of statistical analysis by plotting the mean or range of subsequent data against time. For example, if an engineer knows the mean (grand average) value, standard deviation, and range of a process, this information can be displayed as a bell curve, or population density function (PDF). The image above shows the control chart for a data set with the PDF overlay.The centerline is the mean value of the data set and the green, blue and red lines represent one, two, and three standard deviations (represented with Greek letter sigma ) from the mean value. In generalized terms, if data points fall within three standard deviations of the mean (within the red lines), the process is considered to be in control.

Functions of Control ChartsThere are several functions of a control chart: It centers attention on detecting and monitoring process variation over time. It provides a tool for ongoing control of a process. It differentiates special from common causes of variation in order to be a guide for local or management action. It helps improve a process to perform consistently and predictably to achieve higher quality, lower cost, and higher effective capacity. It serves as a common language for discussing process performance.

Purpose of Control ChartsThe main purpose of using a control chart is to monitor, control, and improve process performance over time by studying variation and its source. Another purpose is to allow simple detection of events that are indicative of actual process change. This simple decision can be difficult where the process characteristic is continuously varying. The control chart provides statistically objective criteria of change. When change is detected and considered good its cause should be identified and possibly become the new way of working, where the change is bad then its cause should be identified and eliminated.

Chart UsageIf the process is in control (and the process statistic is normal), 99.7300% of all the points will fall between the control limits. Any observations outside the limits, or systematic patterns within, suggest the introduction of a new (and likely unanticipated) source of variation, known as a special-cause variation. Since increased variation means increased quality costs, a control chart signaling the presence of a special-cause requires immediate investigation. This makes the control limits very important decision aids. The control limits provide information about the process behavior and have no intrinsic relationship to any specification targets or engineering tolerance. In practice, the process mean (and hence the center line) may not coincide with the specified value (or target) of the quality characteristic because the process design simply cannot deliver the process characteristic at the desired level.

Principles of Variation Every process is subject to variation. More variation in the process means more loss to the society. Two types of causes affect variation. These are: Common Cause (also known as chronic or chance cause) The cumulative effect of many small and individually uncontrollable causes of variation in a process. This expresses the effect (characteristic) negatively. Special Cause (also known as sporadic or assignable cause) One of a few causes of variation that result in a large variation in the process. Action on variation entirely depends on type of cause identified.

Common Cause vs. Special CauseCommon CauseSpecial Cause

Consists of many individual causesConsists of one or few causes

Results in relatively smaller variationResults in large variation

Process need not be tampered withProcess need to be investigated and corrected

Process is considered stableProcess is unstable

Types of Data Used in Control Charts Variable Data Data that can be measured E.g. weight, height, length, hardness, diameter, angle Attribute Data Data that can be counted E.g. defects, scratches, dent, spatters, blow, holes, cracks

Variable Control Charts vs. Attribute Control ChartsSometimes, the quality control engineer has a choice between variable control charts and attribute control charts. Attribute control charts have the advantage of allowing for quick summaries of various aspects of the quality of a product, that is, the engineer may simply classify products as acceptable or unacceptable, based on various quality criteria. Thus, attribute charts sometimes bypass the need for expensive, precise devices and timeconsuming measurement procedures. Also, this type of chart tends to be more easily understood by managers unfamiliar with quality control procedures; therefore, it may provide more persuasive (to management) evidence of quality problems.Variable control charts however are more sensitive than attribute control charts. Therefore, variable control charts may alert us to quality problems before any actual "unacceptables" (as detected by the attribute chart) will occur. Douglas Montgomery, a name known in Industrial Statistics, remarked that the variable control charts were the leading indicators of trouble that will sound an alarm before the number of rejects (scrap) increases in the production process.

Common Types of Control ChartsThe types of charts are often classified according to the type of quality characteristic that they are supposed to monitor: as mentioned from above, there are the variable control charts and the attribute control charts. Specifically, the following charts are commonly constructed for controlling variables: Xbar Chart: In this chart, the sample means are plotted in order to control the mean value of a variable (e.g., size of piston rings, strength of materials, etc.). R Chart: In this chart, the sample ranges are plotted in order to control the variability of a variable. S Chart: In this chart, the sample standard deviations are plotted in order to control the variability of a variable. S**2 Chart: In this chart, the sample variances are plotted in order to control the variability of a variable.For controlling quality characteristics that represent attributes of the product, the following charts are commonly constructed: C Chart: In this chart, the number of defectives (per batch, per day, per machine, per 100 feet of pipe, etc.) are plotted. This chart assumes that defects of the quality attribute are rare, and the control limits in this chart are computed based on the Poisson distribution (distribution of rare events). U Chart: In this chart, the rate of defectives, that is, the number of defectives divided by the number of units inspected (the n; e.g., feet of pipe, number of batches) are plotted. Unlike the C chart, this chart does not require a constant number of units, and it can be used, for example, when the batches (samples) are of different sizes. Np Chart: In this chart, the number of defectives (per batch, per day, per machine) are plotted, as seen in the C chart. However, the control limits in this chart are not based on the distribution of rare events, but rather on the binomial distribution. Therefore, this chart should be used if the occurrence of defectives is not rare (e.g., they occur in more than 5% of the units inspected). For example, we may use this chart to control the number of units produced with minor flaws. P Chart: In this chart, the percent of defectives (per batch, per day, per machine, etc.) are plotted, as seen in the U chart. However, the control limits in this chart are not based on the distribution of rare events but rather on the binomial distribution (of proportions). Therefore, this chart is most applicable to situations where the occurrence of defectives is not rare (e.g., we expect the percent of defectives to be more than 5% of the total number of units produced).

Sample Size and SubgroupingThere are a few key conditions that must be met when constructing control charts: The initial predictions for the process must be made while the process is assumed to be stable. Because future process quality will be compared to these predictions, they must be based off of a data set that is taken while the operation is running properly. Multiple subsets of data must be collected, where a subset is simply a set of n measurements taken over a specific time range. The number of subsets is represented as k. A subset average, subset standard deviation, and subset range will be computed for each subset. From these subsets, a grand average, an average standard deviation, and an average range are calculated. The grand average is the average of all subset averages. The average standard deviation is simply the average of subset standard deviations. The average range is simply the average of subset ranges.

The upper and lower control limits for the process can then be determined from this data: Future data taken to determine process stability can be of any size. This is because any point taken should fall within the statistical predictions. It is assumed that the first occurrence of a point not falling within the predicted limits shows that the system must be unstable since it has changed from the predictive model. The subsets are defined, based on the data and the process. For example, if you were using a pH sensor, the sensor would most likely output pages of data daily. If you know that your sensor has the tendency to drift every day, you might select a 30 minute subset of data. If it drifts monthly you might set your subset to be 24 hours or 12 hours. Finally, the population size N is assumed to be infinite. Alternatively, if the population is finite but the sample size is less than 5% of the population size, we can still approximate the population to be near infinite. That is, n/N