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Questions tagged [quality-control]

Quality Control relates to statistical methods used for monitoring, maintaining, and/or improving either the statistical quality control of a process or the capability of a process. Use for questions about 6 sigma.

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Rejection of samples suspected of not coming of the target population

Say, there is a stationary process that should resemble a Gaussian distribution with 'known' mean and variance. Iid samples in triplicates (or n-plicates) are taken from it. It is also known that ...
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How to calculate the process control limits when there is not much data left?

Context: To compute the "Process Control" limits, I am following the Stacey Barr's blog. My question: After detecting the signal, if I don't have enough data points left in my dataframe, for ...
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Hotelling's $T^2$ chart for subgroups with unequal size

I have been reading about Hotelling's $T^2$ control charts and I'm unsure on how to deal with the case where the mean observations come from unequal-sized subgroups. Consider $m$ observations $\mathbf{...
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Possible reason for the Central Limit Theorem not to apply?

I have a multi-generator process which generates around 1200 data points per minute consisting of ~80 processes which contribute more or less evenly to the data points. Each singular process should in ...
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Selecting the Lag and then Aggregating the Data to Control Chart Autocorrelated Extrusion Data?

I have wall thickness data from an extruded product. I understand that for use in a control chart (XmR) that data from extruded products will be autocorrelated. My data was sampled every 5 seconds ...
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Correct setup for a Bayesian gamma model

I am interested in understanding how center volume affects a quality metric in a healthcare application. Each program's performance is reported as an observed/expected (O/E) ratio where the expected ...
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Within-group and between-group variation in real life processes?

In the context of Statistical Process Control (SPC), control charts are used to monitor a process over time and detect shifts in the mean or variation. The traditional Shewhart $\bar{X}$ charts makes ...
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How to statistically discover significant process change effectiveness?

I am currently working on a project where I need to assess the effectiveness of changes made in a production process. Our initial success rate was 50%, and after making some alterations, we've ...
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Single control limits for process with various subgroup sizes

I have a production process, which produces one or more goods on a certain day. For this example, assume the weight of the produced good is consistenlty measured. However, the operators can ofcourse ...
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Extended gage R&R for attribute data

I would like to see a worked example of doing an expanded gage R&R study. Expanded means the gage is varied, as well as the parts, operators, and trials that vary in a standard GR&R study. ...
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Statistical Approaches for Interpreting Weekly Changes in a Percentage Metric

Overview Each week we have some number of trials and successes, and we track the percentage of successes each week, this is our metric. Made up example: A loan company - each week we get some ...
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Different methods to calculate standard deviation

I am doing a study using Statistical Process Control and have to calculate the standard deviation. I am aware of a number of ways to do this. The first method is using the sum of squares (classic ...
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Linear Model + tolerance intervals: How to show that when a condition is fulfilled for a tool it is also fulfilled for another related tool?

The problem Imagine that you have two different tools that produce data at given time points $t_1,...,t_m$. Suppose that we only have access to the mean and standard deviation of the data at each time ...
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Statistic for assessing quality of dose response curve (fit with logistic regression)

I want to assess the quality of a 4-parameter logistic regression fit on dose response data. I am in the process of assessing the quality of some compound screening data. This is characterising the ...
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Equivalence of two processes or implication that one is better than the other

The problem Two different tools $M1$ and $M2$ are supposed to deliver a certain amount of volume of a liquid but in different ways. Furthermore, the efficacity of the tools to deliver this volume ...
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Questions about Using Monte Carlo simulation to determine the control limits of control chart

The Montacaro simulation method is used to solve the control limit of the control chart, how to determine the randomly generated data streams, and whether it needs to be generated according to the ...
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The link between AQL, RQL and the reliability of a process

The problem is to distinguish between the definitions of AQL, RQL and reliability in the field of quality control. Let us just pose the context. We wish to calculate the reliability of a manufacturing ...
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Does the rules "7 or more consecutive points on one side" in Statistical Process Control take in account the amount of data point?

I'm reading on Control chart rules and there is a rule which says: "7 or more consecutive points on one side" in considered "out of control". However, does it take into account the ...
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Difference between anomaly detection and data quality check

I am a beginner in ML and in my company i have been asked to come up with models that can check if there are data quality issue in any given table. It will be an unsupervised learning task and I only ...
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Control Chart: Nelson alternating rule

The Nelson rules for control charts describe patterns, which are "special" and need our attention. One of these rules is the "alternation rule". According to Nelson it is "...
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What is the proper test to determine if a result is above the normal set of values?

I'm a chemist who has been asked to put my statistics hat on, and I'm looking for some help. Situation: Every month we get a report with the number of guest complaints for each item we sell. Each ...
Kat's user avatar
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Repeats vs Replications

I've seen e.g. the minitab explanation on this topic which isn't bad but though, in the end, I can't explain which statistical term or the like I would (or could) investigate with each of them. I ...
Ben's user avatar
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2 votes
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Multiple Comparisons Problem in Control Charts

I have been taught control charts (or Shewhart charts) as a statistical tool to detect processes which are out of control. One particular case was by taking $k$ samples of size $n$ from a process over ...
ZirconPetrichor's user avatar
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Experiment design useful when objects change / will be replaced in each trial run?

I want to perform some studies on how material thickness, type of material, humidity and temperature influence tensile strength. While I was thinking about useful designs I was wondering whether a ...
Ben's user avatar
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Average Sample Size For Curtailed Double Sampling Plan

I am currently implementing double sampling. The goal is to accept or reject a lot by only sampling a few instances from it. In a two-stage testing procedure (double sampling) one first draws a ...
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Packages for experiment design with multiple levels?

I'm aware of e.g. FrF2 which allows to create 2-level experiment designs. I'm also aware of e.g. gen_design or optFederov which seem to consider multiple levels but when using these I always receive ...
Ben's user avatar
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269 views

Does it make sense to calculate Relative Standard Error using population parameters?

Relative Standard Error (RSE) is one of the main measures to assess the quality of survey indicators. If only sample data are available, RSE can be computed using estimated mean $\bar{y}$ and ...
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What is the rationale of using 2.66 times moving range for control limits in individual control charts?

The Wikipedia says "If the data are normally distributed with standard deviation $\sigma$ then the expected value of $\overline {MR}$ is $d_{{2}}\sigma =2\sigma /{\sqrt \pi }$." https://en....
hehe's user avatar
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How many values should one validate to achieve a desired confidence?

If I have a set of 100 values which have been programmatically calculated and I would like to validate those calculations by performing them manually, how many manual calculations would I need to do ...
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determining the sample size for quality test

It has been a long time since I did statistics in uni and I have a "simple problem" that I need solving. I need to determin for a sample size for a limited population of documents ( lets say ...
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What are the suitable methods for statistical process control with non normally distributed data such as proportion?

Is there anyone familiar with statistical process control charts? The usual control limits +-3SD are based on normal distribution. What are the common methods for dealing with non-normally distributed ...
hehe's user avatar
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What are the best-practices for validating phone records? [closed]

I have a bunch of telephone data including information on call start time, end time, and duration. I am trying to evaluate the quality of the dataset to determine if the phone call data are legitimate ...
324's user avatar
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How to determine the lifetime?

I want to determine the average expected lifetime of devices of which I have data. This data comprises ~4500 generators of which ~3800 died and the others are still alive. Furthermore, I have ...
Ben's user avatar
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3 votes
1 answer
1k views

Using standard deviation to calculate Control Limits for Individual Control Chart

To compute the control limits using the 3 sigma rule, the standard deviation is usually approximated by the formula: $\sigma=\frac{\overline{MR}}{1.128}$, where $\overline{MR}$ is the average of all ...
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Is it better to use the prediction interval or the RMSE?

I use a measurement technique $X$ to assess if a good is within production specifications during its manufacturing. $X$ is slow but precise. I wish to find out if I can use a measurement technique $Y$ ...
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1 vote
1 answer
2k views

three sigma vs six sigma

I wonder about the meaning of the term six sigma. It describes a process/production with (mostly) zero defects. You can see here: source: https://www.dummies.com/article/business-careers-money/...
Ben's user avatar
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3 votes
1 answer
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How to estimate probable response times, from previous samples?

I'm a IT manager that deals with delays from various departments in a purchase process. In a given phase we have 25 handovers and thus 25 response times. So many variable times (and without SLA) ...
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Which control charts to use to track mortality

I am trying to implement control charts in my organization (healthcare) to track various quality outcomes. The first one i want to do is mortality( # patient deaths/ month(or week) ). I have a data ...
Tars's user avatar
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1 vote
1 answer
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Sample size and type of hypothesis test for QC of products (frozen cattle embryos)

I have a question regarding sample size and type of hypothesis test to be used. I am currently working on buying beef cattle embryos from overseas. The livestock department in my country is going to ...
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57 views

Why does the X-bar control chart not use control limits from the t distribution

In univariate statistical process control, for the $\bar{X}$ chart with $n$ subgroups each of $m$ samples, we calculate the center line, upper and lower control limits using this equation (1): Here, $...
Migwell's user avatar
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Find control chart limits based on existing data

I'd like to produce a control chart that tells me if a given process will be within bounds in the future or not. Currently, the process gives me simple timeseries data, per minute ...
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Hotelling T squared seemingly useless at detecting a mean shift

I am trying to develop a single-sample Hotelling $T^2$ test in order to implement a multivariate control chart, as described in Montgomery, D. C. (2009) Introduction To Statistical Quality Control, ...
Migwell's user avatar
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statistical process control for non normal time series

Let us say I have several KPI measurements per month. There may be different numbers of measurements per month but there are more than 30. The monthly distributions do not look normally as shown in ...
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1 vote
1 answer
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XmR charts for several measures at the same day/month

Xmr charts are often used in statistical process control (see for example). They make sense, but I wonder what one does, if one has several measure per day/month etc. Should one just use the average (...
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Setting limits for process control of low probability error

I have a process which produces plastic parts. I have a requirement that states that the weight shall be > x grams. So far I have measured each individual part produced (around 250 pieces) and ...
Antti Stålnacke's user avatar
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How to find value of omega in CUSUM?

I am trying to understand CUSUM or Cumulative Sum Control Chart. In the example on above linked Wikipedia page, the formula for high CUSUM value indicating positive ...
rnso's user avatar
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Using an old trained model on a new data - comparing two populations

I have two populations with the same set of features. The range of the features' values is also the same. I trained Random Forest Algorithm on the first population. Thus, I wonder whether or not I can ...
Inna 's user avatar
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1 answer
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Can CUSUM be used to detect anomalies in clustered data?

I am looking at approaches to detect anomalies in network traffic in terms of packets being sent with a very short inter-arrival time (IAT). Said differently, the longer (possibly) uniform IATs would ...
Jonathan Dunne's user avatar
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1 answer
200 views

What do the letter and the subscript in the Shewhart's control chart constants ($A_2, A_3, c_4, c_5, \ldots$) mean?

The expected value of the sample standard deviation is $$E(s) = c_4(n)\sigma$$ where $$ c_4(n) = \sqrt{2\over n-1}{\Gamma({n\over2})\over\Gamma({n-1\over2})} $$ The page on Wikipedia led me ...
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3 votes
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Find a single-sampling plan for which $p_1=0.02$, $\alpha=0.01$,$p_2=0.06$ and $\beta=0.10$

I am not sure where to start. My previous lecture gave very limited information on what to do here, so my current toolbox only consists of these formulas: $$1-\alpha=\sum_{d=0}^{c} {n \choose d}p_1^d(...
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