How Do You Know Iif a Process Has Statistical Control

STATISTICAL PROCESS CONTROL

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Photo by: Sergej Khakimullin

Traditional quality control is designed to forbid the production of products that practice not run across certain acceptance criteria. This could be achieved by performing inspection on products that, in many cases, have already been produced. Activeness could so be taken by rejecting those products. Some products would go on to be reworked, a process that is costly and time consuming. In many cases, rework is more expensive than producing the product in the beginning place. This state of affairs frequently results in decreased productivity, client dissatisfaction, loss of competitive position, and higher price.

To avoid such results, quality must be congenital into the product and the processes. Statistical process command (SPC), a term ofttimes used interchangeably with statistical quality control (SQC), involves the integration of quality control into each stage of producing the product. In fact, SPC is a powerful drove of tools that implement the concept of prevention as a shift from the traditional quality by inspection/correction.

SPC is a technique that employs statistical tools for controlling and improving processes. SPC is an important ingredient in continuous process improvement strategies. It uses unproblematic statistical means to control, monitor, and ameliorate processes. All SPC tools are graphical and elementary to use and understand, as shown in Effigy i.

UNDERSTANDING VARIATION

The chief objective of whatsoever SPC written report is to reduce variation. Any procedure tin be considered a transformation mechanism of different input factors into a production or service. Since inputs exhibit variation, the issue is a combined issue of all variations. This, in turn, is translated into the product. The purpose of SPC is to isolate the natural variation in the procedure from other sources of variation that can be traced or whose causes may be identified. As follows, there are two different kinds of variation that affect the quality characteristics of products.

COMMON CAUSES OF VARIATION.

Variation due to mutual causes are inherent in the process; they are inevitable and can exist represented by a normal distribution. Mutual causes are as well called chance causes

Effigy one
SPC Tools

of variation. A stable process exhibits simply common causes of variation. The behavior of a stable procedure is anticipated or consequent, and the process is said to be in statistical control.

SPECIAL CAUSES OF VARIATION.

Special causes, besides chosen assignable causes of variation, are non part of the process. They tin be traced, identified, and eliminated. Control charts are designed to chase for those causes as part of SPC efforts to amend the process. A procedure with the presence of special or assignable cause of variation is unpredictable or inconsistent, and the procedure is said to be out of statistical control.

STATISTICAL PROCESS Control (SPC)
TOOLS

Among the many tools for quality improvement, the following are the about commonly used tools of SPC:

• histograms
• cause-and-effect diagrams
• Pareto diagrams
• command charts
• scatter or correlation diagrams
• run charts
• process flow diagrams

Effigy ane shows the vii basic tools of statistical process command, sometimes known every bit the "magnificent 7."

HISTOGRAMS.

Histograms are visual charts that depict how often each kind of variation occurs in a process. Equally with all SPC tools, histograms are generally used on a representative sample of output to make judgments about the process as a whole. The height of the vertical bars on a histogram shows how common each type of variation is, with the tallest confined representing the most common outcomes. Typically a histogram documents variations at betwixt 6 and 20 regular intervals forth some continuum (i.east., categories made upwards of ranges of process values, such equally measurement ranges) and shows the relative frequency that products fall into each category of variation.

For instance, if a metallic-stamping procedure is supposed to yield a component with a thickness of 10.v mm, the range of variation in a poorly controlled process might exist between 9 mm and 12 mm. The histogram of this output would divide it into several equal categories within the range (say, by each one-half millimeter) and show how many parts out of a sample run fall into each category. Under a normal distribution (i.e., a bell bend) the chart would be symmetrical on both sides of the hateful, which is unremarkably the center category. Ideally, the mean is also well within the specification limits for the output. If the nautical chart is not symmetrical or the mean is skewed, it suggests that the process is peculiarly weak on one cease. Thus, in the stamping example, if the chart is skewed toward the lower end of the size scale, information technology might mean that the stamping equipment tends to employ too much force.

Still, even if the chart is symmetrical, if the vertical bars are all similar in size, or if in that location are larger bars protruding toward the edges of the chart, it suggests the process is not well controlled. The ideal histogram for SPC purposes has very steep bars in the center that drop off quickly to very modest confined toward the outer edges.

PARETO CHARTS.

Pareto charts are another powerful tool for statistical process control and quality improvement. They go a step further than histograms by focusing the attention on the factors that cause the virtually problem in a process. With Pareto charts, facts most the greatest improvement potential can be hands identified.

A Pareto chart is besides fabricated upwardly of a series of vertical bars. However, in this case the bars motility from left to right in order of descending importance, as measured by the per centum of errors acquired by each gene. The sum of all the factors more often than not accounts for 100 percent of all errors or problems; this is often indicated with a line graph superimposed over the bars showing a cumulative percentage as of each successive factor.

A hypothetical Pareto nautical chart might consist of these four explanatory factors, along with their associated percentages, for mill pigment defects on a production: extraneous grit on the surface (75 percent), temperature variations (15 percent), sprayer head clogs (6 percentage), and paint formulation variations (4 percent). Clearly, these figures suggest that, all things beingness equal, the well-nigh effective step to reduce paint defects would be to detect a procedure to eliminate dust in the painting facility or on the materials before the process takes place. Conversely, haggling with the paint supplier for more than consistent paint formulations would have the least impact.

Cause-AND-EFFECT DIAGRAMS.

Cause-and-issue diagrams, too called Ishikawa diagrams or fishbone diagrams, provide a visual representation of the factors that most likely contribute to an observed problem or an effect on the process. They are technically non statistical tools—it requires no quantitative data to create one—simply they are unremarkably employed in SPC to help develop hypotheses about which factors contribute to a quality problem. In a crusade-and-effect diagram, the main horizontal line leads toward some upshot or outcome, commonly a negative one such as a product defect or returned merchandise. The branches or "bones" leading to the central problem are the principal categories of contributing factors, and within these there are oft a diversity of subcategories. For instance, the main causes of customer turnover at a consumer Net service provider might fall into the categories of service problems, price, and service limitations. Subcategories under service problems might include busy signals for punch up customers, server outages, e-mail delays, and and so forth. The relationships betwixt such factors can exist clearly identified, and therefore, problems may be identified and the root causes may be corrected.

SCATTER DIAGRAMS.

Scatter diagrams, also chosen correlation charts, show the graphical representation of a relationship between two variables as a series of dots. The range of possible values for each variable is represented by the Ten and Y axes, and the blueprint of the dots, plotted from sample data involving the two variables, suggests whether or not a statistical human relationship exists. The relationship may be that of crusade and effect or of some other origin; the scatter diagram simply shows whether the relationship exists and how strong it is. The variables in scatter diagrams more often than not must exist measurable on a numerical scale (e.1000., toll, distance, speed, size, age, frequency), and therefore categories like "present" and "not nowadays" are not well suited for this analysis.

An example would be to study the human relationship between product defects and worker feel. The researcher would construct a chart based on the number of defects associated with workers of different levels of experience. If at that place is a statistical relationship, the plotted information will tend to cluster in certain ways. For case, if the dots cluster around an upward-sloping line or band, information technology suggests there is a positive correlation between the two variables. If it is a downward-sloping line, there may exist a negative relationship. And if the data points are spread evenly on the chart with no particular shape or clustering, information technology suggests no relationship at all. In statistical procedure control, scatter diagrams are normally used to explore the relationships between procedure variables and may pb to identifying possible ways to increased procedure performance.

CONTROL CHARTS.

Considered by some the near of import SPC tool, control charts are graphical representations of process operation over time. They are concerned with how (or whether) processes vary at unlike intervals and, specifically, with identifying nonrandom or assignable causes of variation. Control charts provide a powerful analytical tool for monitoring process variability and other changes in process mean or variability deterioration.

Several kinds of command charts exist, each with its own strengths. One of the well-nigh common is the Χ̅ chart, also known as the Shewhart Χ̅ chart after its inventor, Walter Shewhart. The Χ̅ symbol is used in statistics to indicate the arithmetic mean (average) of a set of sample values (for example, product measurements taken in a quality control sample). For control charts the sample size is oftentimes quite pocket-size, such every bit but iv or five units chosen randomly, but the sampling is repeated periodically. In an Χ̅ chart the boilerplate value of each sample is plotted and compared to averages of previous samples, as well as to expected levels of variation nether a normal distribution.

4 values must be calculated before the Χ̅ nautical chart tin be created:

1. The average of the sample means (designated as Χ̅d̅ since it is an average of averages)
2. The upper control limit (UCL), which suggests the highest level of variation i would expect in a stable procedure
3. The lower control limit (LCL), which is the everyman expected value in a stable process
4. The average of range R (labeled R̅), which represents the mean departure betwixt the highest and lowest values in each sample (e.m., if sample measurements were 3.ane, iii.3, 3.2, and 3.0, the range would be 3.3 - iii.0 = 0.3)

While the values of Χ̅d̅ and R̅ can be adamant directly from the sample data, calculating the UCL and LCL requires a special probability multiplier (oft given in tables in statistics texts) A ₂ . The UCL and LCL guess the distance of 3 standard deviations in a higher place and below the mean, respectively. The simplified formulas are equally follows:

where Χ̅d̅ is the mean of the sample means
A ₂ is a abiding multiplier based on the sample size
R̅ is the hateful of the sample ranges

Graphically, the control limits and the overall mean Χ̅d̅ are fatigued every bit a continuum made up of iii parallel horizontal lines, with UCL on peak, Χ̅d̅ in the eye, and LCL on the bottom. The individual sample means (Χ̅) are and so plotted forth the continuum in the order they were taken (for case, at weekly intervals). Ideally, the Χ̅ values will stay inside the confines of the control limits and tend toward the middle forth the Χ̅d̅ line. If, however, individual sample values exceed the upper or lower limits repeatedly, information technology signals that the procedure is non in statistical control and that exploration is needed to find the cause. More than avant-garde analyses using Χ̅ charts also consider warning limits within the control limits and diverse trends or patterns in the Χ̅ line.

Other widely used command charts include R charts, which observe variations in the expected range of values and cumulative sum (CUSUM) charts, which are useful for detecting smaller nevertheless revealing changes in a fix of data.

RUN CHARTS.

Run charts depict process behavior against time. They are important in investigating changes in the process over fourth dimension, such as predictable cycles. Any changes in process stability or instability can exist judged from a run chart. They may likewise be used to compare two separate variables over time to identify correlations and other relationships.

Menses DIAGRAMS.

Procedure flow diagrams or menstruation charts are graphical representations of a process. They show the sequence of different operations that make upwards a process. Flow diagrams are important tools for documenting processes and communicating information near processes. They tin also be used to place bottlenecks in a process sequence, to place points of rework or other phenomena in a process, or to define points where data or data about process performance need to be collected.

Process CAPABILITY ANALYSIS

Procedure capability is determined from the total variations that are acquired only by common causes of variation later all assignable causes take been removed. Information technology represents the performance of a process that is in statistical control. When a process is in statistical control, its performance is predictable and can exist represented by a probability distribution.

The proportion of production that is out of specification is a measure of the capability of the process. Such proportion may exist determined using the process distribution. If the procedure maintains its status of being in statistical control, the proportion of defective or nonconforming product remains the aforementioned.

Before assessing the capability of the procedure, information technology must be brought commencement to a state of statistical control. There are several means to measure out the capability of the process:

USING Control CHARTS.

When the command chart indicates that the procedure is in a land of statistical command, and when the control limits are stable and periodically reviewed, information technology can be used to assess the adequacy of the process and provide data to infer such capability.

NATURAL TOLERANCE VERSUS SPECIFICATION
LIMITS.

The natural tolerance limits of a process are ordinarily these limits between which the process is capable of producing parts. Natural tolerance limits are expressed as the process mean plus or minus z process standard departure units. Unless otherwise stated, z is considered to be three standard deviations.

There are three situations to exist considered that describe the relationship between process natural tolerance limits and specification limits. In case 1, specification limits are wider than the process natural tolerance limits. This situation represents a process that is capable of meeting specifications. Although not desirable, this state of affairs accommodates, to a certain caste, some shift in the process hateful or a modify in process variability.

In case two, specification limits are equal to the process natural tolerance limits. This situation represents a critical process that is capable of coming together specifications only if no shift in the process mean or a modify in process variability takes place. A shift in the process mean or a change in its variability volition event in the production of nonconforming products. When dealing with a situation like this, care must be taken to avoid producing products that are not conforming to specifications.

In case three, specification limits are narrower than the process natural tolerance limits. This state of affairs guarantees the product of products that do not meet the desired specifications. When dealing with this situation, action should exist taken to widen the specification limits, to change the design of the production, and to control the process such that its variability is reduced. Another solution is to look for a dissimilar process altogether.

Farther READING:

Fine, Edmund S. "Utilise Histograms to Help Information Communicate." Quality, May 1997.

Juran. Joseph M., and A. Blanton Godfrey, eds. Juran'south Quality Handbook. fifth ed. New York: McGraw-Loma, 1998.

Maleyeff, John. "The Central Concepts of Statistical Quality Control." Industrial Engineering science, December 1994. Schuetz, George. "Bedrock SQC." Modern Car Shop, February 1996.

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Source: https://www.referenceforbusiness.com/encyclopedia/Sel-Str/Statistical-Process-Control.html

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