Statistics: Complete Technical Guide

Statistics is the quiet language of the cement plant: the average LSF of the raw mix, the standard deviation of the clinker strength, the control charts of the Blaine, the capability of the packing line and the correlation of the fuel and the kiln: every decision of the quality and the process rests on the statistical numbers: the file of the package teaches the statistics of the cement industry in the language of the plant: it is the formation of the quality engineer, the process engineer and the plant statistician.

The Complete Cement Technical Package (931 files including the books, the courses, the Excel tools and the presentations: $249.99 one-time: instant download via the PayPal payment) includes this statistics course with its lectures, its charts, its worked examples and its Excel tools: the document covers the descriptive statistics, the probability, the sampling, the control charts, the capability, the correlations and the experimental design: this article walks the file module by module: the reader learns the numbers behind the cement process.

This page is built in the order of the file: the basic concepts first, the distributions second, the sampling third, the control charts fourth, the process capability fifth, the correlations and the regression sixth, and the quality management systems last: the reader can follow the article with the document in hand: the promise: after the page, the readers can read the quality reports of the plant critically, compute their own statistics and argue the numbers with the confidence of the professional.

1. The Statistical Basics: The Mean, the Median and the Spread

The statistics of the cement plant begins with the description of the data: the daily results of the laboratory, the hourly strengths and the frequencies of the process: the file opens with the descriptive statistics that every plant report uses:

• The mean: the arithmetic average of the values: the mean strength of the cement batches and the mean LSF of the raw mix: the first number of every report: the location of the data;
• The median: the central value of the sorted data: the robust location that ignores the outliers: the median of the kiln temperatures: the comparison with the mean shows the skew of the distribution;
• The mode: the most frequent value: the mode of the Blaine measurements: the typical production point of the plant: the report of the distributions;
• The standard deviation: the classical measure of the spread: the sigma of the strength, of the chemistry: the small sigma: the consistent plant: the large sigma: the unstable process;
• The range and the coefficients: the difference of the maximum and the minimum, the coefficient of variation (CV = sigma / mean): the relative spread that allows the comparison of the processes:

The file opens with the complete set of the descriptive statistics and their Excel functions: the means matrix of the plant, the daily summary tables and the month reports: the numbers are the nouns of the process language: the reader computes, reads and trusts the statistics of the cement: the means, the sigmas and the coefficients: the basic vocabulary: complete with the examples of the cement plant.

The analysis of the spread is where the money hides: two plants can run the same mean of the 28-day strength at 46 MPa with the sigma of 2 MPa and 5 MPa: the plant with the wider sigma must hold the higher target mean to cover the same probability of failing the specification: the extra mean means the extra clinker content in the cement blend and the extra cost per tonne: the file quantifies the value of the variance reduction: the reduction of the sigma by 1 MPa at the 42.5N class translates into the savings of the cement factor and the kiln throughput: the descriptive statistics of the file are therefore no classroom abstraction: they are the competitive numbers of the plant: the quality engineer who reduces the variance of the finish mill wins the market share.

Metric	Typical cement example	Interpretation
Mean Blaine 28-day strength	375 m2/kg	the centre of the distribution
Standard deviation	12.5 m2/kg	the spread of the daily results
CV	3.3 %	the relative consistency
Range	48 m2/kg	the spread of the extremes

The descriptive statistics are the first deliverable of the lab and the process engineer: the daily, the weekly and the monthly reports are these numbers: the file trains the eye to read the number and the meaning: the mean tells the level, the sigma tells the stability and the CV tells the relative quality: the combination of the three signs the health of the process: the statistics: the described.

2. The Distributions: The Shape of the Cement Data

The data of the cement plant follows the probability distributions: the normal distribution is the queen of the statistics and most of the plant variables approximate it: the file teaches the distributions of the industry:

• The normal distribution: the bell curve: the mean centre and the sigma spread: the 68-95-99.7 rules: 68% of the data within the one sigma, 95% within the two and 99.7% within the three: the basis of the control and the capability;
• The standard normal: the z-variable: the normal of the mean zero sigma one: the z-tables of the probability: the probability of the exceedance: the quality specification and the chance to fail;
• The log-normal: the strength data of the cement: the distribution of the fineness and the grinding: the right-skewed data: the transformation for the analysis:
• The binomial and the Poisson: the counts of the defects, the number of the failing cubes: the attributes of the process: the p-chart of the successes: the quality of the inspections:
• The distribution tests: the chi-square and the graphical methods: the histograms and the probability plots: the test whether the data is normal: the file: the decision of the analysis method:

The normal distribution is the foundation of the cement statistics: when the process is in the statistical control, the 6-sigma of the data covers the process: the thickness of the file: the tables of the standard normal, the probability papers and the histograms of the cement variables: the reader of the file prepares the distributions of his plant data with the Excel completions: the bell curves of the strength: the free lime: the Blaine: the p-values and the decisions: the distribution chapter: the intuitive statistics.

3. The Sampling: The Bridge Between the Data and the Truth

The statistics derives its power from the sample: the laboratory sample of the cement, the increments of the raw meal and the batches of the dispatched cement: the file gives the sampling theory of the plant:

• The population and the sample: the entire production of the shift versus the few bags tested: the sample is the window to the population: the statistics of the file estimates the population from the sample:
• The random sampling: every unit of the production has the equal chance: the systematic sampling by the time intervals: the stratified by the shifts and the silos: the integrity of the sample:
• The sample size: the larger the sample, the smaller the uncertainty: the file formula of the sample size: the precision target and the sigma of the process: the number of the cubes and the results:
• The sampling errors: the segregation of the piles, the moisture gradients and the timing bias: the errors of the sampling station: the audit of the sample extraction: the file: the honest sample:
• The composite samples: the hourly increments combined into the shift composites: the standard of the cement industry: the composite saves the analytical cost and gives the shift mean: the incremental discipline:

The statistics of the file teaches the sampling as the bridge between the data and the truth: the laboratory result is not the truth of the production, it is the estimate of it: the file quantifies: the uncertainty of the strength mean of the 10 cube samples is the sigma of the individual divided by the root of the 10: the numbers of the bridge: the reader learns to interpret the daily reports with the sampling error in mind: the honest comparisons of the plant: the samples: the statistics: the truth.

The confidence intervals complete the sampling picture: the quality engineer does not want only the point estimate of the shift mean: he wants the band within which the true mean lies with the known probability: the file teaches the 95 percent confidence interval: the mean plus and minus the t-factor times the standard error: the worked example of the cement strength: the sample of the 20 results, the mean 48.5 MPa and the sigma 2.1: the 95 percent interval of the 49.3 to 47.7 MPa: the interpretation of the daily report with the interval: the comparison of the two mills without the false conclusions: the confidence intervals of the file are the measure of the certainty: the professional decisions made on the samples: the statistics as the precision microscope.

4. The Control Charts: The Sentinel of the Process

The control chart is the classical statistical instrument of the process control: Shewhart’s charts monitor the process in time and distinguish the common and the special causes: the file presents the charts of the cement plant:

• The average and the range charts (Xbar-R): the subgroups of the laboratory data: the daily means of the Blaine and the ranges of the samples: the centerline and the control limits at the three sigma: the watch of the level and the spread;
• The individual charts: the samples of the one result per day: the moving range of the consecutive: the charts of the kiln parameters and the daily strength: the simple, the powerful:
• The attribute charts: the p-charts of the fraction nonconforming and the c-charts of the counts: the packaging defects and the customer complaints: the charting of the counts:
• The interpretation rules: the points beyond the limits, the runs of the seven in the one direction, the trends and the cycles: the Western Electric rules of the file: the special cause indicators: the action matrix:
• The process in statistical control: the stable chart: only the common causes: the process predictability: the improvement projects vs the tampering: the file teaches the difference:

The control charts bring the process under the microscope: the cement plant watches the LSF, the free lime, the SO3, the Blaine and the strength of the charts: the file carries the complete example of the Blaine chart: the control limits from the first 25 batches, the red point at the 26th, the investigation, the found cause (the new separator blade) and the correction: the control chart story of the file: the reader practices the charts with the Excel templates: the sentinel of the plant: awake.

5. The Process Capability: The Meeting of the Process and the Specification

The capability indices answer the most important question of the quality: can this process produce within the specification consistently? the file teaches the capability analysis of the cement plant:

• The specification limits: the USL and the LSL: the strength of the cement, the fineness and the chemistry limits: the standards of the cement: the requirement of the customer:
• The Cp index: the potential capability: the ratio of the specification width to the 6-sigma of the process: the Cp above 1.00: the process fits the spec: the calculation without the centering:
• The Cpk index: the actual capability: the capability that accounts for the off-centered process: the Cpk of the 1.33: the minimum of the industry: the Cpk of the 1.67: the excellent:
• The Ppk: the performance index of the long-term data: the Pp and the Ppk with the total sigma: the difference from the within-group Cp and the Cpk: the two estimates of the file:
• The capability actions: the low Cpk: the centering improvement and the variance reduction: the process improvement of the file: the priorities of the quality department:

The capability of the cement process is the professional diploma of the plant: the clinker strength of the Cpk 1.33 and above means the customer’s specification rarely fails: the file works the example: the cement strength spec 42.5 N minimum: the mean 48 MPa, the sigma 1.8 MPa: the Cpk = (48-42.5) / (3 x 1.8) = 1.02: the plant improves the sigma to 1.3: the Cpk becomes 1.41: the table of the file quantifies the benefit of the reduced variation: the process; the capability: the trust of the cement: the file trains the capability analysis with the templates.

The capability study of the file includes the acceptance criteria of the cement standards: the characteristic value of the strength must stay above the class minimum with the known confidence: the EN 197 and the equivalent standards formulate their acceptance rules on exactly the statistical basis: the mean of the recent results, the minimum single value and the standard deviation of the series: the file translates the standard text into the statistical practice: the Excel sheets of the conformity evaluation: the certificate of the dispatched cement: the capability analysis is therefore not the voluntary exercise: it is the national and the international requirement of the product certification: the engineer who computes the Cpk of the cement line computes the license of the dispatch.

6. The Correlation and the Regression: The Relationships of the Process

The statistics beyond the description: the relationships between the variables of the plant: the correlation and the regression quantify the influence: the file teaches the plant’s correlations:

• The correlation coefficient: the r between the -1 and +1: the strength of the linear relationship: the Blaine vs the strength, the free lime vs the LSF, the moisture vs the mill rate: the scatter plots of the file:
• The simple regression: the straight line of the two variables: the y = a x + b: the slope and the intercept: the Blaine as the function of the separator speed: the prediction of the regression:
• The coefficient of determination: the R2: the share of the variation explained by the regression: the R2 of 0.85 means the 85 percent explained: the residual analysis and the warnings of the model:
• The multiple regression: the prediction of the strength from the chemistry, the fineness and the age: the multi-variable models: the equation of the plant: the coefficient of the each factor:
• The pitfalls of the correlation: the spurious correlations, the extrapolation danger and the confounding: the correlation is not the causation: the audit of the models and the domain of the file:

The regression of the plant: the models of the kiln, the mill and the quality: the correlations of the file: the free lime vs the burning zone temperature: the mill output vs the moisture: the models that the process engineers run daily: the multiple regression: the plant data with the Excel: the reader of the file builds and validates his own models: the statistical process control: the connection of the numbers: the regression of the cement knowledge.

The worked regression of the file is a model every plant engineer recognizes: the 28-day strength predicted from the clinker LSF, the free lime, the Blaine and the SO3: four predictors of the mill: the file computes the multiple regression on the 60 batches: the coefficient of each factor, the R2 of the model at 0.82 and the standard error of the prediction: the model serves the quality department: the candidate cement composition evaluated before the production: the effect of the Blaine rise on the strength quantified at the constant chemistry: the file walks the reader through the matrix algebra or the Excel data analysis output, the interpretation of the t-tests of the coefficients and the deletion of the insignificant factors: the model building is a creative discipline and the file gives it the method: the regression: the prediction: the planning.

7. The Statistical Quality Control in the Laboratory of the Plant

The statistics is the native language of the cement laboratory: the quality control of the lab results themselves uses the statistical discipline: the file devotes the full module to the laboratory statistics:

• The lab control charts: the reference sample of the lab analyzed daily: the mean chart of the reference results: the alert of the instrument drift: the calibration of the XRF and the duplicate check of the file:
• The repeatability and the reproducibility: the R&R studies: the same sample measured many times by the same and the different analysts: the component of the measurement error: the implication of the file:
• The inter-laboratory comparisons: the round-robin of the cement laboratories: the same samples analyzed by the plants and the third parties: the accuracy of every laboratory in the network:
• The precision of the strength tests: the coefficient of the variation of the compression testing: 3-5 percent in the cubes: the number of the replicate specimens: the reporting of the average and the scatter:
• The statistical process control of the laboratory: the data integrity: the control of the reported results: the interlock: the false positives and the false negatives of the acceptance:

The laboratory statistics is the quality of the quality: the file’s full module: the repeatability tests, the limit tables and the inter-laboratory protocols: the certification of the laboratory: the reliability of every reported number: the reader of the module assesses the own lab: the uncertainty of the analytical chain: the EPA’s conventions and the standard practices: the data: the laboratory: the statistics: the trustworthy chain of the plant quality.

8. The Statistics of the Energy and the Process Data

The energy data of the cement plant is a statistical mine: the specific energies, the heat balances and the enormous operational databases: the statistics of the module extracts the decisions:

• The baseline and the trends: the moving averages of the kWh/t of the mill: the weekly and the monthly trends: the regression of the season and the load: the baseline of the improvements:
• The KPI distributions: the heat rate of the kiln by the day: the histograms of the monthly: the shifts of the distribution: the process improvement: the energy statistics of the file:
• The correlation of the energy: the specific heat vs the clinker factor, the moisture, the LSF: the regression of the contributors: the deterministic: the energy audit support:
• The statistical process control of the energy: the control charts of the kWh/t: the special cause of the energy spikes: the improvement of the energy patrol: the SPC of the energy:
• The forecasting: the time series of the energy: the moving averages and the seasonal indexes: the forecast of the next months: the budget of the plant and the supply contracts:

The energy statistics ties the numbers to the money: the kWh/t mean and its sigma: 1 percent of the clinker heat at the 5,000 t/d plant saves the millions: the file’s energy worked example: the baseline calculation, the correlation of the feed moisture and the fuel, the improvement verification with the t-test: the improvements of the plant are defended with the statistics and the file trains the defense: the energy, the data, the decisions.

9. The Frequently Asked Questions About the Statistics of the Plant

What is the difference between the Cp and the Cpk?

The Cp measures the spread of the process against the specification without considering its centering; the Cpk considers the centering: the Cp 1.5 with the Cpk 0.8 shows a process spread inside the spec but off the center: the Cpk is the honest index of the two.

Why the three sigma limits of the control charts?

The three-sigma limits balance the two errors: the false alarm (the common variation interpreted as the special cause, about 0.3 percent of the stable points) against the missed signal of the real change: the Shewhart convention of the industry accepted precisely this balance: the control chart with the correct limits of the file.

How many samples for a reliable daily average of the cement strength?

The reliability grows with the root of the number: the daily progress with the 4-6 samples: the uncertainty of the mean is the sigma of the individual divided by the root of the n: the file shows the table: the 4 samples: the uncertainty divided by 2: the economics of the lab sampling.

Are the cement strength results normally distributed?

Largely yes for the industrial data in the statistical control: the slight asymmetry of the tails exists: the normal assumption works for the control and the capability with the acceptable approximation: the distribution tests of the file confirm and the transformations correct.

Does the package include the statistical Excel tools?

Yes: the Complete Cement Technical Package includes the statistical tools: the descriptive analysis, the control chart templates, the capability calculators, the regression sheets and the sampling formulas: the engineers apply the statistics of the plant in the minutes: the 931 files of the package.

10. The Statistics in the Quality Management of the Plant

The statistics is the spine of the modern quality management: the ISO 9001 documentation, the process control, the continuous improvement and the customer communication: the module of the file ties the numbers to the management:

• The statistical thinking: the processes the products: the variation and the noise: the management by the facts of the file: the culture of the plant: the meetings of the data:
• The quality indicators: the PPM of the complaints, the capability and the delivery: the dashboard in the management room: the indicators of the company: the statistics in the command:
• The continuous improvement: the DMAIC: the define, measure, analyze, improve and control: the statistics of the cycle: the baseline and the improvement proof: the control of the improvements:
• The audits and the certificates: the statistical evidences of the control: the control charts in the audit files: the capability certificates of the products: the customer confidence:
• The supplier statistics: the characterization of the purchased materials: the acceptance sampling of the shipments: the AQL plans: the statistics of the supply chain:

The statistics of the management is the professional culture: the files of the plant demonstrate the control with the charts: the audits read the evidence: the customers trust the capable process: the file trains the complete management reporting: the statistical system of the cement plant around the world: the quality manager who masters the statistics of the file masters the system of the quality: the management and the math together.

The statistical thinking session of the course deserves the final paragraph of the chapter: the management of the plant meets the monthly over the statistical dashboard: the capability of every product class, the PPM trend of the complaints, the control status of the critical parameters and the correlation of the improvements with the market feedback: the file provides the meeting agenda, the one-page dashboards and the presentation templates: the decisions of the meeting are the decisions of the facts: the capital requests, the process changes and the supplier evaluations all flow from the statistics: the file closes the management chapter with the same message of the industry: the numbers will not decide alone, but the decisions without the numbers are just the opinions: the statistics of the plant: the compounding of the professional.

12. Final Words of the Guide

Statistics: the mean and the sigma, the distributions and the samples, the charts and the capabilities, the correlations and the management: the statistics of the cement plant is the professional language: the plants that measure, plot and decide with the numbers: the quality, the energy and the money: the file of the package hands the complete formation: the Excel tools, the charts and the tables: the reader leaves with the statistical brain of the plant: the data: the truth: the cement.

The Complete Cement Technical Package includes this statistics file with the lectures, the worked examples, the control chart templates and the Excel tools: the one-time price of 249.99: the instant download via the PayPal: the 931 files: the statistics file: the professional: the engineer of the numbers: the quality of the cement, statistikally excellent.

This file is part of the Complete Cement Technical Package (931 files) available from cementequipment.org. Respective rights holders; library copy for the licensed single user.