Causes of Variation That Can Be Identified and Eliminated Are Called What?
STATISTICAL Process CONTROL
Photo past: Sergej Khakimullin
Traditional quality control is designed to prevent the production of products that do non run across certain acceptance criteria. This could be achieved by performing inspection on products that, in many cases, have already been produced. Action could and then be taken by rejecting those products. Some products would get on to be reworked, a procedure that is costly and time consuming. In many cases, rework is more than expensive than producing the product in the offset place. This situation frequently results in decreased productivity, customer dissatisfaction, loss of competitive position, and higher cost.
To avert such results, quality must be built into the product and the processes. Statistical process control (SPC), a term often used interchangeably with statistical quality command (SQC), involves the integration of quality control into each stage of producing the product. In fact, SPC is a powerful collection 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 decision-making and improving processes. SPC is an important ingredient in continuous process improvement strategies. It uses uncomplicated statistical means to control, monitor, and meliorate processes. All SPC tools are graphical and simple to employ and empathise, as shown in Figure ane.
Understanding VARIATION
The main objective of whatsoever SPC study is to reduce variation. Any process tin can be considered a transformation mechanism of different input factors into a production or service. Since inputs showroom variation, the result is a combined effect of all variations. This, in plough, 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 exist traced or whose causes may exist identified. Equally 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 be represented by a normal distribution. Mutual causes are also called take a chance causes
Figure 1
SPC Tools
of variation. A stable process exhibits simply common causes of variation. The beliefs of a stable process is anticipated or consistent, and the process is said to be in statistical control.
SPECIAL CAUSES OF VARIATION.
Special causes, too called assignable causes of variation, are not part of the process. They can be traced, identified, and eliminated. Control charts are designed to chase for those causes as function of SPC efforts to improve the process. A process 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 Procedure Control (SPC)
TOOLS
Among the many tools for quality improvement, the following are the almost normally used tools of SPC:
- histograms
- cause-and-effect diagrams
- Pareto diagrams
- control charts
- scatter or correlation diagrams
- run charts
- process menses diagrams
Figure i shows the seven basic tools of statistical process control, sometimes known every bit the "magnificent 7."
HISTOGRAMS.
Histograms are visual charts that describe how frequently each kind of variation occurs in a procedure. As with all SPC tools, histograms are more often than not used on a representative sample of output to make judgments about the process as a whole. The tiptop of the vertical confined on a histogram shows how common each blazon of variation is, with the tallest confined representing the most mutual outcomes. Typically a histogram documents variations at between 6 and 20 regular intervals along some continuum (i.e., categories made up of ranges of process values, such every bit measurement ranges) and shows the relative frequency that products autumn into each category of variation.
For example, if a metallic-stamping procedure is supposed to yield a component with a thickness of ten.5 mm, the range of variation in a poorly controlled procedure might be betwixt 9 mm and 12 mm. The histogram of this output would divide information technology 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. Nether a normal distribution (i.due east., a bell curve) the chart would be symmetrical on both sides of the mean, which is normally the centre category. Ideally, the hateful is also well within the specification limits for the output. If the chart is non symmetrical or the mean is skewed, it suggests that the process is particularly weak on one terminate. Thus, in the stamping example, if the chart is skewed toward the lower end of the size calibration, it might mean that the stamping equipment tends to use as well much strength.
Nonetheless, even if the chart is symmetrical, if the vertical bars are all similar in size, or if there are larger confined protruding toward the edges of the chart, it suggests the process is not well controlled. The platonic histogram for SPC purposes has very steep bars in the heart 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 comeback. They get a step further than histograms by focusing the attention on the factors that cause the near trouble in a process. With Pareto charts, facts near the greatest improvement potential can be easily identified.
A Pareto chart is also made upward of a serial of vertical bars. However, in this instance the confined move from left to right in lodge of descending importance, as measured by the percentage of errors caused by each factor. The sum of all the factors generally accounts for 100 per centum of all errors or problems; this is often indicated with a line graph superimposed over the bars showing a cumulative pct as of each successive factor.
A hypothetical Pareto nautical chart might consist of these four explanatory factors, along with their associated percentages, for factory paint defects on a product: extraneous dust on the surface (75 percent), temperature variations (15 per centum), sprayer caput clogs (half dozen percent), and paint conception variations (4 percent). Clearly, these figures suggest that, all things being equal, the most effective stride to reduce paint defects would be to find 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 take the least impact.
CAUSE-AND-EFFECT DIAGRAMS.
Cause-and-effect diagrams, besides called Ishikawa diagrams or fishbone diagrams, provide a visual representation of the factors that near likely contribute to an observed problem or an effect on the procedure. They are technically not statistical tools—information technology requires no quantitative information to create 1—simply they are unremarkably employed in SPC to help develop hypotheses virtually which factors contribute to a quality trouble. In a cause-and-result diagram, the main horizontal line leads toward some effect or outcome, commonly a negative one such as a product defect or returned merchandise. The branches or "bones" leading to the fundamental problem are the principal categories of contributing factors, and within these in that location are oftentimes a variety of subcategories. For case, the main causes of customer turnover at a consumer Isp might fall into the categories of service problems, price, and service limitations. Subcategories under service problems might include busy signals for dial up customers, server outages, e-mail delays, and and then along. The relationships between such factors can be clearly identified, and therefore, problems may exist identified and the root causes may be corrected.
SCATTER DIAGRAMS.
Besprinkle 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 past the X and Y axes, and the pattern of the dots, plotted from sample data involving the two variables, suggests whether or non a statistical relationship exists. The relationship may be that of crusade and upshot or of another origin; the besprinkle diagram just shows whether the relationship exists and how strong information technology is. The variables in scatter diagrams more often than not must be measurable on a numerical scale (east.g., price, altitude, speed, size, age, frequency), and therefore categories similar "present" and "not present" are not well suited for this analysis.
An example would be to study the relationship betwixt product defects and worker experience. The researcher would construct a nautical chart based on the number of defects associated with workers of different levels of experience. If there is a statistical relationship, the plotted data will tend to cluster in certain ways. For case, if the dots cluster around an upward-sloping line or band, it suggests in that location is a positive correlation betwixt the two variables. If it is a downward-sloping line, there may be a negative relationship. And if the information points are spread evenly on the chart with no particular shape or clustering, information technology suggests no human relationship at all. In statistical procedure command, scatter diagrams are unremarkably used to explore the relationships between procedure variables and may lead to identifying possible means to increased process functioning.
CONTROL CHARTS.
Considered by some the most important SPC tool, control charts are graphical representations of process operation over time. They are concerned with how (or whether) processes vary at dissimilar intervals and, specifically, with identifying nonrandom or assignable causes of variation. Control charts provide a powerful belittling tool for monitoring procedure variability and other changes in process mean or variability deterioration.
Several kinds of control charts exist, each with its own strengths. I of the about common is the Χ̅ chart, also known as the Shewhart Χ̅ chart afterward its inventor, Walter Shewhart. The Χ̅ symbol is used in statistics to indicate the arithmetic hateful (average) of a set of sample values (for instance, product measurements taken in a quality control sample). For control charts the sample size is oftentimes quite small, such every bit just four 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, besides as to expected levels of variation nether a normal distribution.
Four values must be calculated before the Χ̅ nautical chart can be created:
- The average of the sample means (designated as Χ̅d̅ since it is an boilerplate of averages)
- The upper control limit (UCL), which suggests the highest level of variation i would await in a stable process
- The lower command limit (LCL), which is the lowest expected value in a stable process
- The boilerplate of range R (labeled R̅), which represents the mean difference betwixt the highest and lowest values in each sample (e.g., if sample measurements were 3.ane, three.3, 3.2, and 3.0, the range would be three.iii - iii.0 = 0.3)
While the values of Χ̅d̅ and R̅ tin can be determined directly from the sample data, computing the UCL and LCL requires a special probability multiplier (oftentimes given in tables in statistics texts) A two . The UCL and LCL judge the distance of three standard deviations above and beneath the mean, respectively. The simplified formulas are as follows:
where Χ̅d̅ is the mean of the sample means
A 2 is a constant 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 as a continuum fabricated upwardly of three parallel horizontal lines, with UCL on summit, Χ̅d̅ in the middle, and LCL on the lesser. The private sample ways (Χ̅) are then plotted along the continuum in the order they were taken (for instance, at weekly intervals). Ideally, the Χ̅ values will stay within the confines of the control limits and tend toward the centre along the Χ̅d̅ line. If, however, individual sample values exceed the upper or lower limits repeatedly, information technology signals that the process is non in statistical control and that exploration is needed to find the crusade. More avant-garde analyses using Χ̅ charts also consider warning limits within the control limits and various trends or patterns in the Χ̅ line.
Other widely used control charts include R charts, which observe variations in the expected range of values and cumulative sum (CUSUM) charts, which are useful for detecting smaller nonetheless revealing changes in a gear up of data.
RUN CHARTS.
Run charts depict procedure behavior against fourth dimension. They are of import in investigating changes in the procedure over time, such as anticipated cycles. Any changes in procedure stability or instability tin can exist judged from a run chart. They may besides exist used to compare 2 separate variables over time to identify correlations and other relationships.
Menses DIAGRAMS.
Procedure flow diagrams or flow charts are graphical representations of a process. They show the sequence of different operations that make upwardly a process. Flow diagrams are important tools for documenting processes and communicating information well-nigh processes. They tin also exist used to identify bottlenecks in a procedure sequence, to identify points of rework or other phenomena in a process, or to define points where data or information virtually procedure performance demand to be collected.
PROCESS Adequacy Assay
Process capability is determined from the full variations that are caused only by common causes of variation later all assignable causes take been removed. It represents the operation of a procedure that is in statistical command. When a process is in statistical command, its performance is predictable and can be represented by a probability distribution.
The proportion of product that is out of specification is a measure of the capability of the process. Such proportion may be determined using the process distribution. If the procedure maintains its status of being in statistical control, the proportion of defective or nonconforming production remains the same.
Before assessing the capability of the procedure, information technology must be brought commencement to a state of statistical control. At that place are several ways to measure out the capability of the process:
USING CONTROL CHARTS.
When the control nautical chart indicates that the process is in a state of statistical control, and when the control limits are stable and periodically reviewed, it can be used to assess the adequacy of the procedure and provide information to infer such capability.
NATURAL TOLERANCE VERSUS SPECIFICATION
LIMITS.
The natural tolerance limits of a process are normally these limits betwixt which the process is capable of producing parts. Natural tolerance limits are expressed as the procedure mean plus or minus z process standard deviation units. Unless otherwise stated, z is considered to be 3 standard deviations.
In that location are iii situations to exist considered that describe the relationship betwixt process natural tolerance limits and specification limits. In case one, 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 situation accommodates, to a certain degree, some shift in the procedure mean or a change in process variability.
In case ii, specification limits are equal to the process natural tolerance limits. This situation represents a critical procedure that is capable of meeting specifications only if no shift in the process mean or a change in process variability takes place. A shift in the process mean or a change in its variability will result in the production of nonconforming products. When dealing with a state of affairs like this, intendance must be taken to avoid producing products that are not conforming to specifications.
In case three, specification limits are narrower than the procedure natural tolerance limits. This situation guarantees the production of products that do not run across the desired specifications. When dealing with this situation, activeness should be taken to widen the specification limits, to change the pattern of the product, and to control the process such that its variability is reduced. Another solution is to look for a different process altogether.
Farther READING:
Fine, Edmund S. "Use Histograms to Assist Data Communicate." Quality, May 1997.
Juran. Joseph M., and A. Blanton Godfrey, eds. Juran'due south Quality Handbook. 5th ed. New York: McGraw-Hill, 1998.
Maleyeff, John. "The Fundamental Concepts of Statistical Quality Command." Industrial Engineering, December 1994. Schuetz, George. "Bedrock SQC." Modern Car Shop, February 1996.
Source: https://www.referenceforbusiness.com/encyclopedia/Sel-Str/Statistical-Process-Control.html
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