Reliability Engineering Statistics (2026)

Build a foundation in reliability engineering statistics by exploring population, sample, parameter, statistic, and measures of central tendency and dispersion, including the coefficient of variation, with downloadable Excel templates.

Explore the Greek alphabet as symbols, including alpha, beta, delta, zeta, eta, lambda, mu, iota, sigma, chi, and theta, and learn how capital and lowercase sigma convey constants and variables.

Learn to sample from a population to infer parameters using statistics such as mean, median, mode, and standard deviation; distinguish discrete from continuous data and recognize mu, x-bar, sigma, s.

Learn to analyze continuous data in Excel by computing descriptive statistics and building a histogram to illustrate the probability density function across value ranges.

Explore variance and standard deviation as measures of dispersion in population and sample contexts. Learn their formulas and how Excel computes population and sample standard deviations, including n minus one.

Explain variance, range, and the coefficient of variation as key dispersion measures, defining range as the difference between the largest and smallest values, and cov as standard deviation over mean.

Compare the distribution of subgroup averages to that of individuals, noting the same overall mean. Analyze range and standard deviation, and preview the central limit theorem.

Explore distribution shape through kurtosis, focusing on leptokurtic, mesokurtic, and platykurtic forms, alongside center (mu, x-bar) and spread (range, standard deviation, variance), to characterize normality.

Explore the central limit theorem, showing how subgroup averages form a normal distribution regardless of the parent distribution, and apply the formula for the standard deviation of averages.

Access a downloadable glossary of terminology for reliability engineering, covering descriptive statistics, environmental stress screening, and gamma distribution, with a pdf resource of about 120 terms across seven pages.

Practice basic statistics with Excel by deriving summary statistics, creating data visualizations, and solving problems from a three-slide PowerPoint deck, including an embedded central limit theorem video.

Explore probability concepts alongside statistics, covering sample space, unions, intersections, Venn diagrams, conditional probability, and combinations and permutations, then apply reliability block diagrams in reliability engineering.

Define a random variable as a function on a sample space and distinguish discrete from continuous cases, using coin toss outcomes and counted or measured data as examples.

Learn how probability assigns a number to simple events and estimates it from repeated trials, using coin flips and a six-sided die to illustrate outcomes and limits.

Explore sample space and simple events, define probability between 0 and 1, and compare independent and dependent draws using replacement vs no replacement with a bag of balls.

Explore the union and intersection of events in a sample space, describing all points in A or B and only those in both, with complements and probability.

Explore conditional probability and how A changes when B occurs; use P(A|B)=P(A∩B)/P(B) with sampling without replacement and employment scenarios.

Learn to apply the multiplication rule for independent events, where the probability of A and B equals the product of their probabilities, illustrated by two relays in series yielding 0.72.

Use probability trees to compute the probability of at least one hit from two missiles, with independent missiles and a dependent case, yielding 0.9775.

Explore reliability block diagrams in Excel, building series and parallel models to calculate system reliability and run what-if scenarios with reusable data models.

Learn how to analyze an R out of n reliability system using binomial distribution and the n choose r combinations to compute the probability that at least r components function.

Reinforce probability concepts with a practice exercise set, using a PowerPoint slide deck of problems and solutions to work through on your own, covering the section's range of skills.

Study probability distributions—normal, exponential, Poisson, and binomial—across discrete and continuous data, and master the four functions: density, cumulative distribution function, reliability, and hazard, with Excel practice datasets.

Explore how engineering variation is described by probability distributions, including discrete and continuous types. Learn how pdfs and cdfs quantify the likelihood of outcomes and intervals.

Explore how the pdf, cdf, reliability (survival) function, and hazard function interrelate in reliability engineering. Use a five-year life example to see how survival declines and hazard rises with time.

Define reliability as the probability a system performs satisfactorily for a time under stated conditions. Relate the reliability function to time and performance and show normal, exponential, and Weibull distributions.

Explain how mean life depends on the underlying distribution, comparing exponential and normal time-to-failure, and show why mean life alone can mislead reliability assessments.

Explore discrete probability distributions through coin tosses, dice sums, and frequency analyses, illustrating how to build and read discrete probability functions, sample spaces, and relative frequencies from real-world data.

Explore the binomial distribution as a two-outcome reliability model (operable or failed). Compute the probability of x occurrences in n trials using p and q = 1−p with p^x q^{n−x}.

Explore the binomial distribution by computing the pdf for a 25-device sample with failure probability 0.02, yielding zero failures 0.60, one failure 0.30, and more than one 0.0886.

Master three approaches to hypergeometric problems—manual factorial calculations, Excel-based factorial formulas, and the hypergeometric dist function—and distinguish PDF from CDF with practical examples.

Explore continuous probability distributions with probability density functions, their cumulative distribution and reliability functions, and see how parameters shape models like normal, log-normal, exponential, and Weibull.

Explore the Poisson distribution as a discrete model for rare events, computing probabilities with p(x)=e^{-lambda} lambda^x/x!, and compare pdf and cdf using a bank example.

Apply the Poisson distribution continued with tabulated cumulative distribution functions to compute zero, one, and more-than-one failure probabilities for samples using lambda = np (e.g., n=25, p=0.02).

Explore how to compute the Poisson pdf and cdf in Microsoft Excel, adjusting lambda to see its effect on the mean and distribution.

Explain the normal distribution's symmetry around the mean and its standard deviation, its pdf and cdf, and how z-scores relate area under the curve to 68-95-99.73 percent ranges.

Examine the normal distribution and its key functions—the pdf, cdf, reliability function, and hazard function—using z-scores and Excel to analyze survival curves.

Apply the standardized normal distribution to compute areas under the curve with the z score formula, using package weights and tensile strength of metal extrusion as examples.

Apply normal distribution concepts to a ten-component reliability example, using z values, pdf, cdf, and the reliability and hazard functions to compute reliability at 100 hours and 150 hours.

Compare normal and exponential distributions by plotting their cdfs and reliability functions, highlighting how the mean and lambda shape the percentage below or above the average.

Explore the exponential reliability function, the survival probability, and its relation to the CDF. Compute reliability at 1000 hours with lambda 0.00053, yielding about 59% uptime.

Explore the discrete geometric distribution modeling the number of trials until the first success in independent Bernoulli trials, with pdf, cdf, reliability, and hazard functions.

Study the exponential reliability model: mean time to failure is 1/λ. Apply a three-unit railway example to compute no failure and no more than one or two failures via binomial.

Explore the exponential distribution's hazard rate, which is constant and memoryless, meaning the next-interval failure probability stays the same, with applications to electronic components and the bathtub curve.

Explore the Weibull distribution, a flexible model for failure times and lifetimes in reliability engineering, life data analysis, and survival analysis.

Explore how the Weibull shape parameter beta and the scale parameter eta shape the pdf, reliability, and failure rate, highlighting infantile, random, and wear out regimes.

Explore the Weibull distribution as a versatile model for time-to-failure, with beta as shape and eta as scale, and apply to compute the PDF, CDF, and reliability function.

Apply the most likely estimator to estimate Weibull parameters from censored data. Learn to use Excel solver to optimize these parameters via six steps, from problem definition to result interpretation.

Explore the lognormal distribution and its relation to the normal, transform data to log values, and compute pdf, cdf, reliability and hazard for failure-time data using practical examples.

Explore chi square distribution as sum of squares of k degrees of freedom standard normals. Use it in goodness-of-fit tests and confidence intervals for standard deviation of a normal distribution.

Explore goodness of fit tests that determine if observed data fit a distribution using chi-square statistics, observed versus expected frequencies, and the null hypotheses at a chosen significance level.

Apply chi-square goodness of fit in reliability engineering by comparing observed transistor failures to an expected 12 per 1000 hours in Excel, using degrees of freedom and a 5% alpha.

Engage with extensive practice exercises on probability distributions to reinforce learning, tackle the most challenging section with numerous examples and problems, and deepen understanding of the topic.

Explore sampling plans to determine how many samples to pull from a population, enabling quick, data-driven inferences for quality and manufacturing reliability engineering.

Explore sampling characteristics and how inferential statistics guide sampling plans to balance cost and uncertainty, including acceptance criteria like C equals zero for lots.

Determine the sample size for scenarios: mean, p hat with known and unknown values, and differences of two means or two proportions, using margins of error and 95% confidence intervals.

Determine minimum sample sizes for estimating population proportions and the difference of means or proportions with a 95% confidence interval and specified margin of error, including when P is unknown.

Compute sample sizes for variable data under a normal distribution using the z-based formula for 95% confidence and margin of error, with a four tons per hour shift example.

Work through a single practice problem on sampling plans, using a 99% confidence interval to calculate the margin of error in a circuit board reliability test and review the solution.

Apply hypothesis testing as a decision-making tool rooted in probability distributions for reliability, quality, and analytics, using t, z, F tests and paired comparisons.

Explore hypotheses and hypothesis testing, including null hypothesis (H0), alternative (Ha), and type I and II errors with alpha. Use a buns production example to test if average equals 1000.

Identify type one and type two errors from the null hypothesis using an operating characteristic curve in acceptance sampling. Explain alpha risk and two types of correct and incorrect decisions.

Explore the seven-step framework for hypothesis testing, including null and alternative hypotheses, one- or two-tailed tests, alpha, critical values, and the t test with its distribution.

Assess whether a new pig feed boosts four-week weight gain through a t test example; with t=1.36 below 1.796, the result fails to reject the null at 5%.

Apply a two-tailed t test to assess the supplier's claimed mean hardness of 65, using n=25, df=24, and a 5% significance; reject the null when t is -4.18.

Use the z test for means with known population standard deviation to compare a sample mean of 1.88 to 1.84 (n=64, sigma=0.04). Reject the null for a two-tailed 5% test.

Explore the non-pooled t test for comparing means with unequal variances, using A1 and A2 to compute degrees of freedom and assess vendor diaphragm thicknesses at a 0.10 level.

Explore the paired comparison test, a t test variation that reduces sampling variation by using the same vehicles with and without the additive, to assess fuel economy.

Compare two machines' variability with an f test of standard deviations to assess process quality. Accept the null that sigma1 equals sigma2 at alpha 0.10, indicating similar variability.

Use hypothesis tests for proportions with one- and two-sample z tests to compare defect rates in vendor claims and cross-machine data.

Explore nonparametric statistics in reliability engineering statistics without assuming a data model, and apply methods such as Mann-Whitney, Kruskal-Wallis, Mood's median, Wilcoxon signed rank, and Kaplan-Meier estimators.

Explore inferential statistics and hypothesis testing in reliability engineering statistics with nonparametric methods, focusing on null and alternative hypotheses and evaluating whether observed sample differences reflect real population differences.

Explores the trade-offs between parametric and nonparametric methods for statistical decision making, examining assumptions of independence, normality, and equal variances, and comparing common parametric tests with distribution-free peers.

Explore the Anderson-Darling test for normality, using skewness and kurtosis checks, visual inspection, SPC charts, and central limit theorem considerations to assess fit against normal, lognormal, exponential, and weibel distributions.

Explain the sign test, a non-parametric method for comparing two related samples by the direction of changes; p=0.5 under no bias, per John Arbuthnot.

Explore Wilcoxon signed rank test, a non-parametric alternative to t test for paired data, using differences, ranks, and signed-rank sums to test if the median difference is zero under symmetry.

Explain the Mann-Whitney U-test, a non-parametric alternative to the t-test, using ranking and totals of two independent groups to assess whether central tendencies differ in two-tailed test at 5% significance.

Discover the Friedman test, a non-parametric alternative to repeated measures ANOVA, using ranked data across eight athletes over a three hour test to assess performance.

Explore Spearman rank correlation, a nonparametric measure of rank correlation for monotonic relationships. In a ten-athlete example, compute d and d^2, compare with Pearson, and interpret a high correlation.

Apply nonparametric methods to censored data using the Kaplan-Meier estimator and understand type I and type II censoring in reliability testing, including B10 life and practical test designs.

This lecture explains the Kaplan-Meier estimator for reliability data with right censoring, and walks through a stepwise calculation and a correction factor to produce a reliability curve.

Explore the Kaplan-Meier estimator in Excel to analyze censored data and describe reliability trends across a testing cycle using a stair-step calculation and a correction factor.

Wrap up nonparametric statistics by guiding you through a Mood's median nonparametric test case study. Use the downloadable Excel workbook and slide deck to practice in Excel, with solutions provided.

Discover statistical process control for reliability engineering, using control charting and run charts to visualize data and perform descriptive statistics, then apply process capability analysis with cp and ppk indexes.

Explore basic statistical process control for reliability, focusing on control charts, x-bar and R charts, subgroup data, capability analysis, and the difference between control and specification limits.

Explore how to interpret control charts, identify out-of-control signals like jumps and shifts, assess recurring patterns and external influences, and consider measurement discrimination and when to reset control limits.

Explore capability analysis by comparing specification limits to the process range, using CPK and PPK to gauge potential and actual performance.

Learn to evaluate process capability using PPK and PP upper/lower from a pin sample in Excel, by computing the sample mean and standard deviation and comparing spec and process ranges.

Explore confidence intervals as a key tool in inferential statistics, using sample data to estimate population parameters and to determine a range likely to contain the true mean.

Compute point estimates for the mean and standard deviation from a five-unit sample using x-bar and s. Build interval estimates from failure-time data, yielding bounds around 156 to 161 hours.

Show how the sample mean serves as a point estimate for mu, with x bar as estimator, and use average and range charts and standard deviation charts to reflect efficiency.

Learn to construct confidence intervals for the mean using the central limit theorem, the standard error, and z-values to set confidence levels. See a 90% example around 27.5 with ±0.18.

Compute 90% and 95% confidence intervals for the mean with known standard deviation under a normal distribution, using alpha significance and samples to bound the population parameter mu.

Apply the t distribution to compute a mean confidence interval when the standard deviation is unknown, using n minus one degrees of freedom, illustrated with a 61-sample brass plug.

Use the chi-square distribution to construct a confidence interval for the standard deviation of a normal distribution, with 27 samples (s = 6.43) yielding 95% CI about 5.06 to 8.81.

Compute confidence intervals for population proportions using PS, P, n, and alpha with PS ± z alpha/2 sqrt( PS(1-PS)/n ); illustrated by 421/500 (95%) and 16/200 (90%) examples.

Calculate statistical tolerance intervals for the normal curve using x bar and s, for two-sided or one-sided limits, guided by appendix K tables from the Certified Reliability Engineer Handbook.

Calculates 99% reliability intervals with the normal distribution, z-scores, and k tables for mean 1067 hours and standard deviation 45.6, giving 950–1184 hours.

Revisit the exponential distribution in reliability engineering, defining mean time to failure theta, mean time between failures for repairable items, constant failure rate lambda, and censored data methods for estimation.

Compute confidence intervals for the exponential mean using chi-square methods, handling time censored and failure censored data, with a 90% interval illustrated from a 4/10 failure example.

Learn how to compute the required sample size for reliability testing with no failures, using the log(alpha)/log(RL) formula to demonstrate 0.95 reliability at 0.90 confidence.

Engage with confidence intervals practice exercises using the slide deck and Excel files to reinforce sample size calculations and data visualization in reliability engineering statistics.

Congratulates learners on completing the reliability engineering statistics course and highlights lifetime access to videos, Excel templates, and updates, plus instructor Q&A support for applying tools to future projects.

Explore additional udemy courses on reliability and statistics, including quality engineering statistics, root cause analysis and the eight d corrective action process, and lean six sigma green belt 2025 edition.