Talk:Control chart

This article should not be merged. Control charts are a related but very clearly separate issue from the common and special causes from which they arise. -- Phil 20:39, 14 December 2005 (UTC)

Adding example pictures

I think this whole area of different statistical charting could really benefit from some example pictures of the relevant chart. Anyone care to add some example charts? Thanks --Evolve2k 08:05, 6 January 2006 (UTC)

I second that - I'm following the "The Pareto chart is one of the seven basic tools of quality control, which include the histogram, Pareto chart, check sheet, control chart, cause-and-effect diagram, flowchart, and scatter diagram. See Quality Management Glossary." to see all the charts, and most have them, but this does not, and from the description it takes some time to figure out what is displayed, and how.

Other control charts besides Shewhart ones

Shewhart charts are most common in control charting because of their relative simplicity (over other charts), and therefore are an excellent jumping off point. However, there are control charts (CUSUM, EWMA, and multivariate forms of CUSUM, EWMA, and Shewhart charts) which differ considerably from the basic rules being introduced here. The article in its present form is very much targeted to Shewhart control charts and overlooks the fact that there are other types of control charts which also test to see whether a process mean or variance has shifted. Significant amounts of information need to be added to this article, and I envision much of the content presently in this one moving to a new article titled Shewhart control charts. I am going to try to add a little bit to this article to get it started. --Statwizard 15:03, 23 March 2006 (UTC)

Factual error

Statement from article: "In 1938, Shewhart's innovation came to the attention of W. Edwards Deming, then working at the United States Department of Agriculture but about to become mathematical advisor to the United States Census Bureau."

"1925-26 Deming worked at the Hawthorne plant of the Western Electric Company on research with telephone transmitters, thus becoming aware of Shewhart's work." A Brief History of Dr. W. Edwards Deming British Deming Association SPC Press, Inc. 1992

I made that change, but I may have been hasty, since this source mentions nothing about that [1]. I suppose he could have done the research as part of his PhD degree, so I'll look for that. Spalding 18:55, 18 June 2006 (UTC)

This source [2] shows that he spent summers there, so I'll leave the edit. Spalding 19:01, 18 June 2006 (UTC)

The Deming Institute chronology is not intended to be comprehensive. Deming met Shewhart in 1927. The 1930s reference in the article is to the lectures Shewhart made at the USDA which led to Deming editing these for publication as Shewhart's 1939 book. Deming and Shewhart had a history before the lectures at UDSA. Leaders100 19:05, 18 June 2006 (UTC)

Types of Charts Table

The Types of Charts table looks great and provides quick access to the articles on the various types of control charts. However, I'm concerned that it may be inaccurate or, at least, misleading. For instance, anyone reading would believe that Individuals (ImR or XmR) charts can only be used with variable data, but the XmR chart is also a substitute for the attributes charts (p-, np-, u- and c-chart) when the underlying assumptions for those charts are violated.

Any update that I can imagine for this table would make it harder to read, so the question is: do we update it, reduce the level of detail to eliminate the problem, or just leave it?

Alternatively, would it be appropriate to have a "chart chooser" flowchart to help clarify the role of and relationships between the different charts?

Tom Hopper 15:04, 17 March 2010 (UTC) —Preceding unsigned comment added by Thopper (talk • contribs)

• Do you have a source for this? Montgomery specifically calls out this practice in his textbook (Montgomery, Douglas (2005). Introduction to Statistical Quality Control. Hoboken, New Jersey: John Wiley & Sons, Inc. p. 309. ISBN 9780471656319. OCLC 56729567.): "A Misapplication of ${\bar {x}}$ and R Charts" where a consultant recommended using a ${\bar {x}}$ and R chart to plot fraction nonconforming. You'd have a hard time convincing statisticians as the distributions underlying each type of chart are so different (particularly in range of values each can assume, in skewness, in the independence or dependence of the mean and standard deviation).

-- DanielPenfield (talk) 14:32, 18 March 2010 (UTC)

Daniel, Wheeler discusses, briefly, the correct use of attribute charts, and the substitution of individuals and moving range (XmR) charts (not ${\bar {X}}$ and R charts), in Understanding Variation, where he refers to XmR charts as the "swiss army knife" of control charts, and in this SPCToolkit article in Quality Digest, where he states "you can't go far wrong using an XmR chart with count data, and it is generally easier to work with empirical limits than to verify the conditions for a theoretical model." By this statement, he is referring to the fact that dispersion for XmR charts is calculated from the data, while for attributes charts the dispersion is estimated based on the mean. In the book, he gives two examples of count data where the assumptions for attributes charts are violated, producing inappropriate control limits, and shows that the XmR chart provides correct limits. According to the article Selecting the Right Control Chart, which also mentions this issue, the use of XmR charts for count data is also discussed in Wheeler and Poling's Building Continual Improvement, though I do not have a copy to confirm this.

Tom Hopper 18:18, 21 March 2010 (UTC) —Preceding unsigned comment added by Thopper (talk • contribs)

• What are the specific assumptions for which he's constructed examples? I'm talking about the examples you refer to in your statement "In the book, he gives two examples of count data..." Is it the constancy of p, perhaps? -- DanielPenfield (talk) 14:39, 22 March 2010 (UTC)

In the appendix starting on page 140, he gives two examples. In the first, the data is count of on-time shipments per month, where the probability p is not the same for all shipments in a given month. The resulting p-chart limits are too wide, while an XmR chart provides more useful limits. The second example uses data for percent of total shipments by premium freight. Here, the resulting p-chart limits are too narrow, which Wheeler attributes to a large area of opportunity (very high counts) and non-constant probability p.

Tom Hopper 08:48, 23 March 2010 (UTC)

• I was able to take a look at an earlier edition of his book over the weekend. I would consider his position fairly controversial for the reason that it looks like the processes he's trying to monitor are always out-of-control, strictly speaking. Imagine constructing a p-chart from observations randomly drawn from one or the other of two dice: One is a four-sided die and the other is a twenty-sided die and a "nonconformance" is defined as "the die for this particular observation comes up with the number one". So sometimes p = 0.25 and sometimes it's 0.05. Even if he plots these data on an individuals chart, ${\bar {X}}$ will be 0.25 for some samples and 0.05 for others (and the standard deviation will be 0.43 for some samples and 0.22 for others). To work as advertised, control charts must be constructed from identically-distributed observations when the process is deemed "in control". Furthermore, his claim that "the XmR chart will still work because it uses an empirical approach rather than being based on a specific probability model" (from p. 138 of 1993 edition) is also a flat-out contradiction of the individual chart requirement that observations be independent and normally-distributed (that is the specific probability model).

-- DanielPenfield (talk) 14:31, 29 March 2010 (UTC)

I think that, with Wheeler's premium freight data, you're right that p varies from month to month. Frankly, I don't know the best way to address this problem. This automatically implies that either the process is out of control or that we're measuring the wrong characteristic. However, I'm not sure that it's sensible to expect such a process to have a constant p, and I don't know what other characteristic would be better to measure.

Wheeler's statement about an empirical approach is referring to the measure of dispersion and therefore the control limits, and not to the general use of a probability model, though he has argued that XbarR and XmR charts are not dependent on specific probability models, and should not be. With XmR charts the measure of dispersion is based on the measured variance in the data; with the attribute charts, the measure of dispersion is based solely on ${\bar {p}}$. For this reason, the XmR is more robust to violations of the assumption of normality than the attribute charts are to violations of the assumption of their underlying distribution.

Coincidentally, this is covered in a recent Quality Digest article, Some Problems with Attribute Charts.. It's probably better for me to just refer you to that article than to rehash the author's arguments.

Tom Hopper 08:58, 2 April 2010 (UTC)

In thinking further about this, it occurs to me that one of the pillars of Wikipedia is to present information from a neutral point of view. We have, here, a well-referenced practice (I'll summarize it with "when in doubt, use XmR charts") that has been advocated by authoritative members of the community for over a decade. Rather than discussing the theoretically soundness of the practice, shouldn't this information be included to maintain Wikipedia's neutrality?

From a personal perspective, this is a very interesting discussion, and I'd like to continue it for my own personal development. I'm just not sure that it's serving Wikipedia's interests at this point. Tom Hopper 06:39, 7 April 2010 (UTC) —Preceding unsigned comment added by Thopper (talk • contribs)

• Going back to your original statements, then:

Your comment	My response
"However, I'm concerned that it may be inaccurate or, at least, misleading."	I think we've established that it's entirely accurate. The apparent "inaccuracy" stems from Wheeler's assertion that it's reasonable to apply control charts to processes for which the observations aren't identically distributed. Other approaches that are orthodox where Wheeler's is not include Shewhart's original proposal for control charts which required computing an empirical probability mass function and setting control limits at percentiles of that. Another reasonable approach would be to find some way (Ishikawa's stratification) to separate the observations into streams that are reasonably expected to be drawn from identically-distributed random variables and control chart each stream. But both of those require time, effort, and discipline which most organizations just don't have, so Wheeler presents an approach that runs contrary to statistical theory, trumpeting its advantages without informing his audience of its disadvantages.
"For instance, anyone reading would believe that Individuals (ImR or XmR) charts can only be used with variable data, but the XmR chart is also a substitute for the attributes charts (p-, np-, u- and c-chart) when the underlying assumptions for those charts are violated."	We've established that there are several problems with Wheeler's suggestion that we use XmR in these types of situations, specifically: Fraction nonconforming can only assume values between 0 and 1; obsverations for variables charts can assume any real value. XmR assumes that the observations are normally-distributed, fraction nonconforming is most assuredly not normally distributed, and, as you can read in Binomial distribution, they're only reasonably close for a large sample size (the rational subgroup that results in a single observation) or when p is neither close to 0 nor close to 1. Wheeler is advocating the use of XmR for situations for which it wasn't designed (viz., observations that are not from identically distributed random variables)
"Any update that I can imagine for this table would make it harder to read, so the question is: do we update it, reduce the level of detail to eliminate the problem, or just leave it?"	If the practice is widespread, it should be included as a footnote with the explanation that such uses won't perform as advertised and aren't supported by statistical theory. If you were to include it in the table (which I think you shouldn't), you absolutely must emphasize that Wheeler is advocating its use for processes whose observations are not drawn from identically-distributed random variables, which again, is a fundamental requirement for any control chart to work at its advertised levels of type I and type II error.

-- DanielPenfield (talk) 14:13, 7 April 2010 (UTC)

Sources

Note the following statement: "If the process is in control, all points will plot within the control limits.". Also below in same paragraph: "Note that with three sigma limits, one expects to be signaled approximately once out of every 370 points on average, just due to common-causes.". So, process can be in control and not all points will plot within the control limits. —Preceding unsigned comment added by 208.44.254.2 (talk) 12:32, 21 September 2010 (UTC)