DOCSLIB.ORG

١ Topics: Sources of Variation

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
١ Topics: Sources of Variation Islamic University, Gaza - Palestine Topics: • Control Charts for Variables • Some Special Difficulties of Estimating Indirect Costs in Economy Studies • Did it Pay to Use Statistical Quality Control? • Costs and Product Liability • SQC Techniques in Relation to certain Economic Aspects of Product liability • Control Charts for Variables Islamic University, Gaza - Palestine Sources of Variation • Variation exists in all processes. • Variation can be categorized as either; – Common or Random causes of variation, or • Random causes that we cannot identify • Unavoidable • e.g. slight differences in process variables like diameter, weight, service time, temperature Assignable causes of variation • Causes can be identified and eliminated • e.g. poor employee training, worn tool, machine needing repair ١ Islamic University, Gaza - Palestine Control charts identify variation • Chance causes - “common cause” – inherent to the process or random and not controllable – if only common cause present, the process is considered stable or “in control” • Assignable causes - “special cause” – variation due to outside influences – if present, the process is “out of control” Islamic University, Gaza - Palestine Control Charts for x and R Notation and values • Ri = range of the values in the ith sample Ri = xmax - xmin • R = average range for all m samples • is the true process mean • is the true process standard deviation ٢ Islamic University, Gaza - Palestine Control Charts for Xbar and R Statistical Basis of the Charts • Assume the quality characteristic of interest is normally distributed with mean , and standard deviation, . • If x1, x2, …, xn is a sample of size n, then he average of this sample is x x x x x 1 2 n • n • is normally distributed with mean, , and standard deviation, x / n Islamic University, Gaza - Palestine Control Charts for Xbar and R Statistical Basis of the Charts • The probability is 1 - that any sample mean will fall between Z Z 2/ x 2/ n and Z Z 2/ x 2/ n • The above can be used as upper and lower control limits on a control chart for sample means, if the process parameters are known. ٣ Islamic University, Gaza - Palestine Control Charts for Xbar and R Control Limits for the xbar chart UCL x A 2R Center Line x LCL x A 2R • A2 is found in Appendix VI for various values of n. Islamic University, Gaza - Palestine Control Charts for Xbar and R Control Limits for the R chart UCL D4 R Center Line R LCL DR3 • D3 and D4 are found in Appendix VI for various values of n. ٤ Islamic University, Gaza - Palestine Control Charts for Xbar and R Estimating the Process Standard Deviation • The process standard deviation can be estimated using a function of the sample average range. R d2 • This is an unbiased estimator of Islamic University, Gaza - Palestine Control Charts for Variables • To create the centerline of the chart: m Xi X i 1 m ٥ Islamic University, Gaza - Palestine Control Charts for Variables • To find the average range: m R i R i 1 m Islamic University, Gaza - Palestine Control Charts for Variables • Control limits for the R chart: UCLR D4 R LCLR D3R ٦ Islamic University, Gaza - Palestine Control Charts for Variables • Centerline and Control limits for X-bar and S chart (if n 10): m m Xi si i 1 X s i 1 m m UCL B s UCLX X A3 s s 4 LCLs B3 s LCLX X A3 s Islamic University, Gaza - Palestine Distribution of Data • Normal distributions • Skewed distribution ٧ Islamic University, Gaza - Palestine Control Charts for Variables Trial Control Limits • The control limits should be treated as trial control limits. • If this process is in control for the m samples collected, then the system was in control in the past. • If all points plot inside the control limits and no systematic behavior is identified, then the process was in control in the past, and the trial control limits are suitable for controlling current or future production. Islamic University, Gaza - Palestine Control Charts for Variables Trial control limits and the out-of-control process • If points plot out of control, then the control limits must be revised. • Before revising, identify out of control points and look for assignable causes. – If assignable causes can be found, then discard the point(s) and recalculate the control limits. – If no assignable causes can be found then 1) either discard the point(s) as if an assignable cause had been found or 2) retain the point(s) considering the trial control limits as appropriate for current control. ٨ Islamic University, Gaza - Palestine Control Charts for Variables Control Limits, Specification Limits, and Natural Tolerance Limits • Control limits are functions of the natural variability of the process • Natural tolerance limits represent the natural variability of the process (usually set at 3-sigma from the mean) • Specification limits are determined by developers/designers. Islamic University, Gaza - Palestine Control Charts for Variables Control Limits, Specification Limits, and Natural Tolerance Limits • There is no mathematical relationship between control limits and specification limits. • Do not plot specification limits on the charts – Causes confusion between control and capability – If individual observations are plotted, then specification limits may be plotted on the chart. ٩ Islamic University, Gaza - Palestine Rational subgroup from homogeneous lot - Rational subgroup from homogeneous lot : same machine, same operator - Decisions on size of sample empirical judgment + relates to costs • choose n = 4 or 5 use R-chart • when n 10 use s-chart - frequency of taking subgroups often enough to detect process changes - Guideline of sample sizes/frequency using • Say, 4000 parts/day 75 samples • if n = 4 19 subgroups • or n = 5 15 subgroups Islamic University, Gaza - Palestine Control Charts for Variables Rational Subgroups • X bar chart monitors the between sample variability • R chart monitors the within sample variability. ١٠ Islamic University, Gaza - Palestine Control Charts for Variables Guidelines for the Design of the Control Chart • Specify sample size, control limit width, and frequency of sampling • if the main purpose of the x-bar chart is to detect moderate to large process shifts, then small sample sizes are sufficient (n = 4, 5, or 6) • if the main purpose of the x-bar chart is to detect small process shifts, larger sample sizes are needed (as much as 15 to 25)…which is often impractical…alternative types of control charts are available for this situation… Islamic University, Gaza - Palestine Sample Std. Deviation Chart (x - s control chart ) • Both R and s measure dispersion of data • R chart - simple, only use XH (highest) and XL(lowest) • s chart - more calculation - use ALL UCL X A s xi’s more accurate, need x 3 LCL X A s calculate sub-group sample standard x 3 deviation UCLs B4s • When n < 10 R chart LCLs B3s s chart so s • n 10 - s chart better , R not o C4 C4 accurate any more ١١ Islamic University, Gaza - Palestine Control Charts for Variables Guidelines for the Design of the Control Chart • If increasing the sample size is not an option, then sensitizing procedures (such as warning limits) can be used to detect small shifts…but this can result in increased false alarms. • R chart is insensitive to shifts in process standard deviation.(the range method becomes less effective as the sample size increases) may want to use S or S2 chart. • The OC curve can be helpful in determining an appropriate sample size. Islamic University, Gaza - Palestine Control Charts for Variables Guidelines for the Design of the Control Chart Allocating Sampling Effort • Choose a larger sample size and sample less frequently? or, Choose a smaller sample size and sample more frequently? • The method to use will depend on the situation. In general, small frequent samples are more desirable. ١٢ Islamic University, Gaza - Palestine Statistical Control • Statistical Process Control: Statistical evaluation of the output of a process during production • Quality of Conformance: A product or service conforms to specifications Islamic University, Gaza - Palestine Control Chart • Control Chart – Purpose: to monitor process output to see if it is random – A time ordered plot representative sample statistics obtained from an on going process (e.g. sample means) – Upper and lower control limits define the range of acceptable variation ١٣ Islamic University, Gaza - Palestine Statistical Control Abnormal variation Out of due to assignable sources control UCL Mean Normal variation due to chance LCL Abnormal variation due to assignable sources 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample number Islamic University, Gaza - Palestine Statistical Process Control • The essence of statistical process control is to assure that the output of a process is random so that future output will be random. ١٤ Islamic University, Gaza - Palestine Statistical Process Control • The Control Process – Define – Measure – Compare – Evaluate – Correct – Monitor results Islamic University, Gaza - Palestine Statistical Control • Variations and Control – Random variation: Natural variations in the output of a process, created by countless minor factors – Assignable variation: A variation whose source can be identified ١٥ Islamic University, Gaza - Palestine Sampling Distribution Sampling distribution Process distribution Mean Islamic University, Gaza - Palestine Normal Distribution Standard deviation Mean 95.44% 99.74% ١٦ Islamic University, Gaza - Palestine Control Limits Sampling
Load more

Recommended publications
  • 2. Graphing Distributions
    2. Graphing Distributions A. Qualitative Variables B. Quantitative Variables 1. Stem and Leaf Displays 2. Histograms 3. Frequency Polygons 4. Box Plots 5. Bar Charts 6. Line Graphs 7. Dot Plots C. Exercises Graphing data is the first and often most important step in data analysis. In this day of computers, researchers all too often see only the results of complex computer analyses without ever taking a close look at the data themselves. This is all the more unfortunate because computers can create many types of graphs quickly and easily. This chapter covers some classic types of graphs such bar charts that were invented by William Playfair in the 18th century as well as graphs such as box plots invented by John Tukey in the 20th century. 65 by David M. Lane Prerequisites • Chapter 1: Variables Learning Objectives 1. Create a frequency table 2. Determine when pie charts are valuable and when they are not 3. Create and interpret bar charts 4. Identify common graphical mistakes When Apple Computer introduced the iMac computer in August 1998, the company wanted to learn whether the iMac was expanding Apple’s market share. Was the iMac just attracting previous Macintosh owners? Or was it purchased by newcomers to the computer market and by previous Windows users who were switching over? To find out, 500 iMac customers were interviewed. Each customer was categorized as a previous Macintosh owner, a previous Windows owner, or a new computer purchaser. This section examines graphical methods for displaying the results of the interviews. We’ll learn some general lessons about how to graph data that fall into a small number of categories.
    [Show full text]
  • Chapter 16.Tst
    Chapter 16 Statistical Quality Control- Prof. Dr. Samir Safi TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) Statistical process control uses regression and other forecasting tools to help control processes. 1) 2) It is impossible to develop a process that has zero variability. 2) 3) If all of the control points on a control chart lie between the UCL and the LCL, the process is always 3) in control. 4) An x-bar chart would be appropriate to monitor the number of defects in a production lot. 4) 5) The central limit theorem provides the statistical foundation for control charts. 5) 6) If we are tracking quality of performance for a class of students, we should plot the individual 6) grades on an x-bar chart, and the pass/fail result on a p-chart. 7) A p-chart could be used to monitor the average weight of cereal boxes. 7) 8) If we are attempting to control the diameter of bowling bowls, we will find a p-chart to be quite 8) helpful. 9) A c-chart would be appropriate to monitor the number of weld defects on the steel plates of a 9) ship's hull. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Which of the following is not a popular definition of quality? 1) A) Quality is fitness for use. B) Quality is the totality of features and characteristics of a product or service that bears on its ability to satisfy stated or implied needs.
    [Show full text]
  • Section 2.2: Bar Charts and Pie Charts
    Section 2.2: Bar Charts and Pie Charts 1 Raw Data is Ugly Graphical representations of data always look pretty in newspapers, magazines and books. What you haven’tseen is the blood, sweat and tears that it some- times takes to get those results. http://seatgeek.com/blog/mlb/5-useful-charts-for-baseball-fans-mlb-ticket-prices- by-day-time 1 Google listing for Ru San’sKennesaw location 2 The previous examples are informative graphical displays of data. They all started life as bland data sets. 2 Bar Charts Bar charts are a visual way to organize data. The height or length of a bar rep- resents the number of points of data (frequency distribution) in a particular category. One can also let the bar represent the percentage of data (relative frequency distribution) in a category. Example 1 From (http://vgsales.wikia.com/wiki/Halo) consider the sales …g- ures for Microsoft’s videogame franchise, Halo. Here is the raw data. Year Game Units Sold (in millions) 2001 Halo: Combat Evolved 5.5 2004 Halo 2 8 2007 Halo 3 12.06 2009 Halo Wars 2.54 2009 Halo 3: ODST 6.32 2010 Halo: Reach 9.76 2011 Halo: Combat Evolved Anniversary 2.37 2012 Halo 4 9.52 2014 Halo: The Master Chief Collection 2.61 2015 Halo 5 5 Let’s construct a bar chart based on units sold. Translating frequencies into relative frequencies is an easy process. A rela- tive frequency is the frequency divided by total number of data points. Example 2 Create a relative frequency chart for Halo games.
    [Show full text]
  • Bar Charts and Box Plots Normal Poisson Exponential Creating a Simple Yet Effective Plot Requires an 02468 C 1.0 Exponential Uniform Understanding of Data and Tasks
    THIS MONTH a Uniform POINTS OF VIEW Normal Poisson Exponential 02468 b Uniform Bar charts and box plots Normal Poisson Exponential Creating a simple yet effective plot requires an 02468 c 1.0 Exponential Uniform understanding of data and tasks. λ = 1 Min = 5.5 Normal Max = 6.5 0.5 Poisson σμ= 1, = 5 μ = 2 Bar charts and box plots are omnipresent in the scientific literature. 0 02468 They are typically used to visualize quantities associated with a set of Figure 2 | Representation of four distributions with bar charts and box plots. items. Representing the data accurately, however, requires choosing (a) Bar chart showing sample means (n = 1,000) with standard-deviation the appropriate plot according to the nature of the data and the task at error bars. (b) Box plot (n = 1,000) with whiskers extending to ±1.5 × IQR. hand. Bar charts are appropriate for counts, whereas box plots should (c) Probability density functions of the distributions in a and b. λ, rate; be used to represent the characteristics of a distribution. µ, mean; σ, standard deviation. Bar charts encode quantities by length, which is a highly accurate visual encoding and preferred over the angle-based strategy used in to represent such uncertainty. However, because the bars always start pie charts (Fig. 1a). Often the counts that we want to represent are at zero, they can be misleading: for example, part of the range covered sums over multiple categories. There are several options to visualize by the bar might have never been observed in the sample.
    [Show full text]
  • Measurement & Transformations
    Chapter 3 Measurement & Transformations 3.1 Measurement Scales: Traditional Classifica- tion Statisticians call an attribute on which observations differ a variable. The type of unit on which a variable is measured is called a scale.Traditionally,statisticians talk of four types of measurement scales: (1) nominal,(2)ordinal,(3)interval, and (4) ratio. 3.1.1 Nominal Scales The word nominal is derived from nomen,theLatinwordforname.Nominal scales merely name differences and are used most often for qualitative variables in which observations are classified into discrete groups. The key attribute for anominalscaleisthatthereisnoinherentquantitativedifferenceamongthe categories. Sex, religion, and race are three classic nominal scales used in the behavioral sciences. Taxonomic categories (rodent, primate, canine) are nomi- nal scales in biology. Variables on a nominal scale are often called categorical variables. For the neuroscientist, the best criterion for determining whether a variable is on a nominal scale is the “plotting” criteria. If you plot a bar chart of, say, means for the groups and order the groups in any way possible without making the graph “stupid,” then the variable is nominal or categorical. For example, were the variable strains of mice, then the order of the means is not material. Hence, “strain” is nominal or categorical. On the other hand, if the groups were 0 mgs, 10mgs, and 15 mgs of active drug, then having a bar chart with 15 mgs first, then 0 mgs, and finally 10 mgs is stupid. Here “milligrams of drug” is not anominalorcategoricalvariable. 1 CHAPTER 3. MEASUREMENT & TRANSFORMATIONS 2 3.1.2 Ordinal Scales Ordinal scales rank-order observations.
    [Show full text]
  • Chapter 6 Presenting Your Data in Graphic Form Political Orientations
    UNIVARIATE ANALYSIS Chapter 6 Presenting Your Data in Graphic Form Political Orientations Now let’s turn our attention from religion to politics. Some people feel so strongly about politics that they joke about it being a religion. The General Social Survey distribute(GSS) data set has several items that reflect political issues. Two are key political items: POLVIEWS and PARTYID. These items will be the primary focus in this chapter. In the process of examining these variables, we are going to learn not only more about the politicalor orientations of respon- dents to the 2012 GSS but also how to use SPSS Statistics to produce and interpret data in graphic form. You will recall that in the previous chapter, we focused on a variety of ways of displaying univariate distributions (frequency tables) and summarizing them (measures of central ten- dency and dispersion). In this chapter, we are going to build on that discussion by focusing on several ways of presenting your data graphically. We will begin by focusing on two charts thatpost, are useful for variables at the nominal and ordinal levels: bar charts and pie charts. We will then consider two graphs appropriate for interval/ratio variables: histograms and line charts. Graphing Data With Direct “Legacy” Dialogs SPSS Statistics gives us acopy, variety of ways to present data graphically. Clicking the Graphs option on the menu bar will give you three options for building charts: Chart Builder, Interactive, and Legacy Dialogs. These take you to two chart-building methods developed by SPSS over the past 20 years. Chart Builder is the most recent.
    [Show full text]
  • Stacked Bar Charts……………………………………………12
    Effective Use of Bar Charts Purpose This tool provides guidelines and tips on how to effectively use bar charts to communicate research findings. Format This tool provides guidance on bar charts and their purposes, shows examples of preferred practices and practical tips for bar charts, and provides cautions and examples of misuse and poor use of bar charts and how to make corrections. Audience This tool is designed primarily for researchers from the Model Systems that are funded by the National Institute on Disability, Independent Living, and Rehabilitation Research (NIDILRR). The tool can be adapted by other NIDILRR-funded grantees and the general public. The contents of this tool were developed under a grant from the National Institute on Disability, Independent Living, and Rehabilitation Research (NIDILRR grant number 90DP0012-01-00). The contents of this fact sheet do not necessarily represent the policy of Department of Health and Human Services, and you should not assume endorsement by the Federal Government. 1 Overview and Organization Simple Bar Charts……………………………………..……....3 Clustered Bar Charts…………………………………………10 Stacked Bar Charts……………………………………………12 Paired Bar Charts…………………………………………..…14 Simple Bar Chart – Categorical Comparisons A bar chart is basically a vertical column chart oriented horizontally instead. Data values are displayed as horizontal bars. The magnitude of each data element is represented by the length of the bar. Can be used to display values for categorical items (diabetes prevalence by state, hospital performance rankings on a preferred clinical practice measure etc). Shows comparisons among the categorical groups on the measure. Categories displayed on the vertical axis. Simple Bar Chart – Categorical Comparisons Bar charts are preferred over column charts: When the categorical axis labels are lengthy; When you have 12 or more categories; When the metric to be displayed is duration (such as clinic lobby wait time per health center).
    [Show full text]
  • Which Chart Or Graph Is Right for You?
    Which chart or graph is right for you? Tracy Rodgers, Product Marketing Manager Robert Bloom, Tableau Engineer You’ve got data and you’ve got questions. You know there’s a chart or graph out there that will find the answer you’re looking for, but it’s not always easy knowing which one is best without some trial and error. This paper pairs appropriate charts with the type of data you’re analyzing and questions you want to answer. But it won’t stop there. Stranding your data in isolated, static graphs limits the number and depth of questions you can answer. Let your analysis become your organization’s centerpiece by using it to fuel exploration. Combine related charts. Add a map. Provide filters to dig deeper. The impact? Immediate business insight and answers to questions that actually drive decisions. So, which chart is right for you? Transforming data into an effective visualization (any kind of chart or graph) or dashboard is the first step towards making your data make an impact. Here are some best practices for conducting meaningful visual analysis: 2 Bar chart Bar charts are one of the most common data visualizations. With them, you can quickly highlight differences between categories, clearly show trends and outliers, and reveal historical highs and lows at a glance. Bar charts are especially effective when you have data that can be split into multiple categories. Use bar charts to: • Compare data across categories. Bar charts are best suited for data that can be split into several groups. For example, volume of shirts in different sizes, website traffic by referrer, and percent of spending by department.
    [Show full text]
  • Visualiation of Quantitative Information
    Visualisation of quantitative information Overview 1. Visualisation 2. Approaching data 3. Levels of measurement 4. Principals of graphing 5. Univariate graphs 6. Graphical integrity James Neill, 2011 2 Is Pivot a turning point for web exploration? (Gary Flake) (TED talk - 6 min. ) 4 Approaching Entering & data screening Approaching Exploring, describing, & data graphing Hypothesis testing 5 6 Describing & graphing data THE CHALLENGE: to find a meaningful, accurate way to depict the ‘true story’ of the data 7 Clearly report the data's main features 10 Levels of measurement • Nominal / Categorical • Ordinal • Interval • Ratio 12 Discrete vs. continuous Discrete - - - - - - - - - - Continuous ___________ Each level has the properties of the preceding 14 13 levels, plus something more! Categorical / nominal Ordinal / ranked scale • Conveys a category label • Conveys order , but not distance • (Arbitrary) assignment of #s to e.g. in a race, 1st, 2nd, 3rd, etc. or categories ranking of favourites or preferences e.g. Gender • No useful information, except as labels 15 16 Ordinal / ranked example: Ranked importance Interval scale Rank the following aspects of the university according to what is most • Conveys order & distance important to you (1 = most important • 0 is arbitrary through to 5 = least important) e.g., temperature (degrees C) __ Quality of the teaching and education • Usually treat as continuous for > 5 __ Quality of the social life intervals __ Quality of the campus __ Quality of the administration __ Quality of the university's reputation 17 18 Interval example: 8 point Likert scale Ratio scale • Conveys order & distance • Continuous, with a meaningful 0 point e.g. height, age, weight, time, number of times an event has occurred • Ratio statements can be made e.g.
    [Show full text]
  • Which Chart Or Graph Is Right for You? Tell Impactful Stories with Data
    Which chart or graph is right for you? Tell impactful stories with data Authors: Maila Hardin, Daniel Hom, Ross Perez, & Lori Williams January 2012 p2 You’ve got data and you’ve got questions. Creating a Interact with your data chart or graph links the two, but sometimes you’re not sure which type of chart will get the answer you seek. Once you see your data in a visualization, it inherently leads to more questions. Your bar graph reveals that This paper answers questions about how to select the sales tanked in the second quarter in the Southeast. best charts for the type of data you’re analyzing and the A scatter plot shows an unexpected concentration of questions you want to answer. But it won’t stop there. product defects in one category. Donations from older Stranding your data in isolated, static graphs limits the alumni are significantly down according to a heat map. number of questions you can answer. Let your data In each example, your reaction is the same: why? become the centerpiece of decision making by using it Equip yourself to answer these questions by making to tell a story. Combine related charts. Add a map. your visualization interactive. Doing so creates the Provide filters to dig deeper. The impact? Business opportunity for you and others to analyze your data insight and answers to questions at the speed of visually and in real-time, letting you answer questions Which chart or graph is right for you? Tell impactful stories with data Tell Which chart or graph is right for you? thought.
    [Show full text]
  • Bar Charts This Set of Notes Shows How to Construct a Bar Chart Using
    Revised July 2018 Bar Charts This set of notes shows how to construct a bar chart using Stata. It assumes that you have set Stata up on your computer (see the “Getting Started with Stata” handout), and that you have read in the set of data that you want to analyze (see the “Reading in Stata Format (.dta) Data Files” handout). In Stata, most tasks can be performed either by issuing commands within the “Stata command” window, or by using the menus. These notes illustrate both approaches, using the data file “GSS2016.DTA” (this data file is posted here: https://canvas.harvard.edu/courses/53958). Bar charts display differences in means for a quantitative variable across two or more groups, as opposed to histogram comparisons which display percentage distributions of a categorical variable within groups. For example, we can construct a bar chart of the mean hours per day of television viewing by self-attributed class: 1 Simple bar charts can be constructed easily via the Stata command line. The general command structure is graph bar <varname1>, over(<varname2>) where you enter a quantitative variable in place of “varname1" and a categorical variable in place of “varname2". Using the variables in the above graph, you would issue the command graph bar tvhours, over(class) This command produces a bare-bones graph with no enhancements. To enhance and improve the display, it is probably easier to use the Stata menus. For a bar chart, Click on “Graphics” Click on “Bar chart” When you do this, the “graph bar – Bar chart” window shown below opens up: 2 Under “Type of data” select “Graph of summary statistics.” Enter the name of your quantitative variable in the “Variable(s)” box in the middle of the window.
    [Show full text]
  • Performance of Conventional X-Bar Chart for Autocorrelated Data Using Smaller Sample Sizes
    Proceedings of the World Congress on Engineering and Computer Science 2013 Vol II WCECS 2013, 23-25 October, 2013, San Francisco, USA Performance of Conventional X-bar Chart for Autocorrelated Data Using Smaller Sample Sizes D. R. Prajapati Abstract—Control charts are used to determine whether or not a correlation is more often encountered in practice than negative manufacturing or business process is in a state of statistical autocorrelation. control. Various schemes of the standard (Shewhart) X chart for Autocorrelation is inherent to many processes like: autocorrelated data at sample sizes of 2 and 3 are developed and chemical, manufacturing processes and service sectors. When compared with the schemes of the same chart for IID data at charts are applied to the autocorrelated data, the false alarm various process shifts in the process mean. It is clear from the X comparison that the in-control ARL of 370 is achieved by rate increases and performance of the chart is suspected. So employing the X chart for the IID and autocorrelated data but improvement in the (Shewhart) X chart is needed to improve as the level of correlation increases, the performance of its performance for the correlated data. The following section conventional (Shewhart) X chart deteriorates. It is concluded deals with the literature review in this area. that for faster detection in the process mean, the larger sample sizes (n) may be used. Thus the X chart for autocorrelated data B. CONVENTIONAL (SHEWHART) X CHART should be used with carefully and judiciously. Index Terms— Autocorrelated data, In-control ARLs, In conventional X chart, means of small samples are taken at conventional X chart, Out-of control ARLs regular intervals, plotted on a chart, and compared against two limits.
    [Show full text]