Control Charts - Science topic

I did not say that. I said that in other disyribution you cannot calculate with the laws of the normal distributions. I have given example with the uniform distribution. Give a concrete example with exponential distribution.and show me the meaning of the sigma and SD.

I'm not sure, but I think you did a great job of answering your own question... 'Charting the afterlife?" Answer; Why?' Somethings can't be known. Or, even if we were explained, would we have a hope of understanding the answer? Every morning on the way to work I ask the Universe for a special watch over some friends and family (including my most recent 'best friend' Chihuahua) who have 'recently' passed. I know that they are soaring the Universe as Light Beings and I am a bit jealous of all they will see and re-understand. But charting the afterlife... it's like charting the Universe itself accurately. THEY could do it, but we can't even imagine what it looks like in totality. MY opinion, of course.

Excellent contribution, Bill, and particularly pleasing to see Homer Sarasohn's contribution recognised and positioned appropriately in the chronology.

With great pleasure

The cusum or cusumq tests work for mean https://en.m.wikipedia.org/wiki/CUSUM and variance https://www.statstodo.com/CUSUMVariance.php. It was designed for assessing breakpoint/change points in control charts. Best,

The conditional expected delay, CED(t), is the expected number of samples to obtain an out-of-control signal given that the process shift occurs at time t and there were no previous false alarms.

The zero state ARL is CED(1). The steady state ARL is the limit of CED(t) as t increases.

The zero state ARL can be very misleading. If the process shift is assumed to occur immediately as monitoring begins then all data values could be weighted equally. This leads to essentially the progressive mean chart.

For delayed shifts, data should not be weighted equally. Recent data should be given more weight as with the EWMA statistic,

Because the zero state ARL performance can be very misleading, the steady-state performance is preferred. It is unrealistic to assume any shift must occur immediately.

My dear brother Prof. Aslam,

Thank you for sending me this question.

Let us revisit the basic definition of run length (RL) i.e. the number of samples until an out of control (OOC) signal is observed. Let us agree that no matter what chart you are working with (Shewhart, EWMA or CUSUM) the definition of RL doesn't change.

Having said that, now let us talk about the distribution of this variable RL in following 2 scenarios:

(1) Shewhart Xbar Chart

In case of Shewhart chart, this RL variable is the number of trials (no. of plotted Xbars in terms of control charting) until first success. In control charting our success is observing an OOC signal. It is to be noted here that in Shewhart structure, these trials are independent Bernoulli trials having fixed probability of success i.e. getting a OOC signal at i^th sample is independent of what was the outcome of previous samples, and the probability of a point falling outside limits (say p) is constant for each trial. According to probability theory, in a sequence of independent Bernoulli trials, the random variable number of trials until first success follows a geometric distribution. Moreover, the mean of geometric distribution is 1/p. That is why, in Shewhart structure we can simply find the probability of success (i.e. probability of statistic falling outside the limits) and take its reciprocal to get the average of variable RL which we denote by ARL.

(2) EWMA Xbar Chart

In case of EWMA chart, this RL variable is again the number of plotted EWMA statistics until a OOC signal is observed. Note here that in this sequence, the trials are not independent Bernoulli trials i.e. EWMA statistic falling inside/outside the limits at i^th sample is not independent of what was the outcome of previous samples. More precisely, if EWMA statistic at 7^th sample is plotted very close to center line, it is less likely that it will go OOC on the 8^th sample. Similarly, if EWMA₇ is plotted very close to UCL, there are more chances of EWMA₈ going outside the limits. This means that the result of 8^th trial is dependent on the outcome of 7^th trial. As the trials are not independent, so this RL variable (number of trials until first success) will not follow a geometric distribution and hence the mean of RL will not be 1/p.

I hope this clarifies the things once and for all.

Hussain Ali

Please see useful document below:

Best Regards

Martin

I have written some MATLAB codes on this subject. I can give them to interested researchers upon request.

I think it is better to write the code by yourself.

Control charts are process behaviour charts that help us understand if the process/activity is in state of statistical control. Depending on the type of measurement various charts are available. If the measurement type is qualitative, then attributes chart is used and when quantitative variables chart is used.

This should be of help:

Minitab is the best software for all quality related activities and it is easy to use also.

Thanks dear Mohad. I really appreciate.

As you have mentioned that you found some out of control data, it clearly indicates that your problem is to set the control limits for the process. This is called phase-I or the base period. In the base period , when the process shows points beyond control limits, it is required to find whether they are due to assignable causes or not. It requires to remove those points from the analysis. Then one goes into phase-II where the chart will be used to monitor the process.

Also, do not get confused with specification limits and control limits. Because I found some practioners are confused between USL and LSL with UCL and LCL. Please refer to Statistical quality conrol book by DCMontgomery for better understanding.

Both the FDA and the EU as well as many other agencies/governments do have control programs for monitoring residues in food.

Over the past years these programs have been expanded and refined.

What items are then still missing in your view?

the Sigma One to Sigma Six levels describes the maximum number of defects per million in a system or process. There is, therefore, a strong relation between this and the overall accuracy percentage expected from the system or process. For example, the Three Sigma approach expects a maximum of 66.8K errors per million. This translates to 93.3% accuracy expectation for any given process or system. On the other hand the Six Sigma expects a maximum of 3.4 errors per million. This translates to 99.999997% accuracy expectation for a given process or system.

@Uditha Samarakoon

Plotly is D3 based so take a look here;

Or here;

You also can parse your json to javascript object, like here;

You can use D3 (https://d3js.org/). It is a javascript library for graphs. However, for real-time applications, I believe that you need use AJAX.

Please see this link for the cite:

Best, David Booth

If you are an R user, then install my R package "spc" and call the function mewma.arl() to calculate the ARL. I also want to to promote my paper Knoth (2017), ARL Numerics for MEWMA Charts, Journal of Quality Technology 49(1), 78-89. Eventually, the methods in use are (i) Monte-Carlo simulation (utilized by the inventors of MEWMA), (ii) Markov chain approximation (Runger/Prabhu 1996 and more; free software is available), (iii) numerical solution of integral equation (Rigdon 1995; for the in-control ARL is free software available; Minitab and Statistica offer it as well).

Thanks David

I will take a look at your proposal

Kindest regards

yes, k-means is a good clustering algorithm and you can use it to obtain two levels

There are several normalization techniques reported in literature , are you trying to build a classifier or a forecasting engine. To construct any supervised learning engine you require normalise data, for better accuracy. How you obtained that data is not normalised...

HI

Hope the following link may help you

Before you throw away the Poisson Plot be sure to check the "Goodness-of-Fit Test for Poisson" in the Stat > Basic Statistics menu and then check the P-Value generated. Same for the "Chi-Square Goodness-of-Fit Test". In these cases, a low p-value suggests that your data do not follow those distributions. Hope that helps.

Hello Rahmat: You might find the answer in "On the evaluation of control chart limits based on predictive distributions" by Ulrich Menzefricke. The author proposes control limits by normal approximation to the beta-binomial (when n*p1 > 5). See page 1439. Hope this helps. Regards

Hello,

You are looking for surveys  on Concept drift, in predictive analytics and machine learning, the concept drift means that the statistical properties of the target variable, which the model is trying to predict, change over time in unforeseen ways. I would suggest one of   João Gama 's papers. Dr Gama is one of the well known researchers in the  change detection field; you can find what you'r searching for here :

best,

Shewhart control chart can be use for controling and monitring process i.e. quality characteristics. and then when you can apply your case under three circumstance.

What do you expect from using control chart,

it depens on what kind of your data used variable or attribute, you will choose the suitable control chart, and then construct control chat for variable or attribute.

The CL, UL and LU Results will be availble.

Whereas, Mann-Kendall trend test is non-parametice statistics test, i.e. parameters are not avialble, and the set of data is small.

again, what do you expect form Mann-Kendall trend test,

the result of this test shows only whether the the result of this data significant or not.

It is a common practice to use Exponentailly Weighted Moving Average control charts on the residuals from a time series model. When the smoothing parameter lambda is set to 1, the EWMA charts becomes a Shewhart chart.  If the time series model is correct, then the residuals are independent from each other, which is a requirement in a Shewhart chart.

If the process is "highly conforming", do you still need to use a control chart to monitor it? If Yes, then for normally distributed random variables being monitored, you could use a basic Shewhart chart for the mean and a chart of the standard deviation. Due to the high level of confomance, there may be no need for the more sensitive procdedures, such as EWMA or CUSUM chart for the mean nd one for the standard deviation or maybe ln(variance) as some have proposed.

If the data are non-normal, consider using the corresponding nonparametric control charts. If you have count data, a different chart is more suitable.

Your question does not tell us much about the process. 

Dear Antonio, 

Are you familiar with these papers?

Razieh -

It seems that perhaps your application here is for a univariate time series for which you have no other data to do anything more complex.  If your current value is "missing," then that sounds like you are really saying that you need a forecast.   And because you have no clearly defined patterns established in your time series, the simplest format for "exponential smoothing" may be as good as you can do, at least for now.  It will put the strongest influence on the most recent data that you do have. 

Jim 

This is a very important question. Researchers should examin the pattern and volume of the missing data before doing the final analyses. runing descriptive statistics can show where are the missings, so the researcher can look at the cases and the variables and observe any pattern or volume of missings. for example, if the same question has a large amount of missings, then there is a possible problem in this question that the participants did not understand, or did not like, or the question was unclear by wording or typing.

Usually Missing at random is better than non random because at random means that the missings is distributed over the different variables in small scale and can be replaced by many methods {Replacing missing is an Art and it take long time to be mentioned here}. however, if the missing is estimated to be too much, and this too much depends on the sample size and the type of the study, then missing becomes a serious problem.

I also needed a chart like that, but a better way is to take samples of the wastwater to be treated and carry out jar test experiments in the lab with different coagulants (could be organic or inorganic or even both depending on the quality of your water) and do different doses and assess coagulant and/or optimal dose based on things like settlability and clarity of your water etc. and of course measure your parameters of interest at the end such as pH, conductivity, COD, ions etc. 

you can start with widely used coagulants which are inorganic like ferric chloride/aluminium sulphate

I agree...but it's important to take into account the difference between ARL in control (ARLi) and ARL out of control (ARLo). On the one hand the ARLi should be as big as possible because you want the minimum number of false alarms (for a Shewhart type control chart ARLi=370). And on the other hand the ARLo should be as small as possible because you want to detect the process goes out of control as soon as possible.

If you are a beginner practitioner read this:

Montgomery, D. C. (2009). Introduction to Statistical Quality Control. John Wiley & Sons Incorporated.

And for the advanced ones:

Klein, M. (2000). Two alternatives to the Shewhart (X)over-bar control chart. Journal of Quality Technology, 32(4), 427–431.

Could you please be more specific? What do you mean by "How could I build my control chart."? What type of control chart? For averages? For a range? for a variance? for a standard deviation? for a percentile? for the shape parameter of the Weibull distribution? For its scale parameter? ... Each one of these charts requires a lot of statistical work and design.

I suggest you two strategies:

First:

Conduct a correlation test to discover a period where it will can be considered null. You can use the Gausian curve for Hypotesis test, using arctg funcion to fit the correlation in Gausian curve.

With this period, you can control the data with an usual control chart, just as Individual Mobile Range (IMR).

Second:

You can use a correlalated data and "force" a rational subgroup collecting data in group from the process in litte interval of time, and then, in a bigger interval.

For Example, you can collect three data in 15 min of interval of each one, and set a subgroup, and after 4 hours, repeat the process. In this way, you can use Xbarr/R control chart.

That is the order() - function:

x = c(-1, 5, 0, 3, 1, -2)

> rank(x) # "classical" ranking

[1] 2 6 3 5 4 1

> order(x) # anti ranking

[1] 6 1 3 5 4 2

> rank(-x) # reverse "classical" ranking

[1] 5 1 4 2 3 6

best,

Rainer