Alternative Hypothesis (H1)
The hypothesis that contradicts the null hypothesis in statistical testing. It represents what the researcher is trying to prove or the effect they expect to find.
ANOVA (Analysis of Variance)
A statistical method for comparing means of three or more groups by analyzing variance. Tests whether observed differences between group means are statistically significant.
ARIMA
AutoRegressive Integrated Moving Average. A class of time series models that combines autoregression, differencing, and moving average components for forecasting.
Autocorrelation
The correlation of a time series with its own past and future values. Measures the degree to which current values are related to previous values.
Bagging (Bootstrap Aggregating)
An ensemble method that trains multiple models on random subsets of data (bootstrap samples) and combines their predictions to reduce variance.
Bayes' Theorem
A fundamental theorem relating conditional probabilities. P(A|B) = P(B|A)P(A)/P(B). Forms the basis of Bayesian statistics and inference.
Bias-Variance Tradeoff
The balance between model simplicity (high bias, low variance) and complexity (low bias, high variance). Optimal models minimize total error.
Boosting
An ensemble technique that builds models sequentially, with each new model focusing on correcting errors from previous models.
Censored Data
Observations where the exact failure time is unknown. Right-censored: item hasn't failed by observation end. Left-censored: failure occurred before observation.
Central Limit Theorem
The sampling distribution of the mean approaches a normal distribution as sample size increases, regardless of the population's distribution.
Confidence Interval
A range of values that, with a specified probability (e.g., 95%), contains the true population parameter. Width depends on sample size and variability.
Control Chart
A graph used in SPC to monitor process behavior over time. Contains center line, upper control limit (UCL), and lower control limit (LCL).
Cpk (Process Capability Index)
Measures how well a process meets specifications, accounting for centering. Cpk = min[(USL-μ)/3σ, (μ-LSL)/3σ]. Values >1.33 generally indicate capable processes.
Cross-Validation
A technique for evaluating model performance by partitioning data into training and validation sets multiple times. K-fold CV uses k partitions.
CUSUM Chart
Cumulative Sum control chart. Detects small, sustained shifts in process mean by accumulating deviations from target.
Decision Tree
A predictive model that makes decisions based on a series of questions about feature values. Splits data recursively to maximize information gain or reduce impurity.
Degrees of Freedom
The number of independent values that can vary in a calculation. Affects the shape of distributions used in hypothesis testing (t, chi-square, F).
Design of Experiments (DOE)
A systematic approach to planning experiments that efficiently explores factor-response relationships while controlling for nuisance variables.
Ensemble Methods
Techniques that combine multiple models to produce better predictions than any single model. Includes bagging, boosting, and stacking.
EWMA Chart
Exponentially Weighted Moving Average chart. Weights recent observations more heavily, effective for detecting small process shifts.
Exponential Smoothing
Forecasting method that assigns exponentially decreasing weights to older observations. Includes simple, double (Holt), and triple (Holt-Winters) variants.
Factorial Design
An experimental design that studies all combinations of factor levels. A 2^k design has k factors at 2 levels each.
Failure Rate (Hazard Rate)
The instantaneous rate of failure at time t given survival to t. h(t) = f(t)/R(t). Can be constant, increasing, or decreasing.
F-Distribution
A probability distribution arising as the ratio of two chi-square distributions. Used in ANOVA and regression significance tests.
Feature Engineering
The process of creating new features from raw data to improve model performance. Includes transformations, interactions, and domain-specific features.
Gradient Descent
An optimization algorithm that iteratively adjusts parameters to minimize a loss function by moving in the direction of steepest descent.
Gradient Boosting
A boosting method where each successive model fits the negative gradient of the loss function, effectively fitting residuals.
Hazard Function
See Failure Rate. The conditional probability density of failure at time t given survival to t.
Hypothesis Testing
A statistical procedure for making inferences about population parameters based on sample data. Tests a null hypothesis against an alternative.
Interaction Effect
When the effect of one factor depends on the level of another factor. Detected in factorial designs through analysis of interaction terms.
Kaplan-Meier Estimator
A non-parametric estimator of the survival function that handles censored data. The product-limit estimator.
K-Means Clustering
An unsupervised algorithm that partitions data into k clusters by minimizing within-cluster variance around centroids.
Linear Regression
A method for modeling the relationship between a dependent variable and independent variables using a linear equation. Minimizes sum of squared errors.
Logistic Regression
A classification algorithm that models the probability of binary outcomes using the logistic function. Despite its name, used for classification.
Maximum Likelihood Estimation (MLE)
A method for estimating parameters by finding values that maximize the likelihood of observing the data.
MTBF (Mean Time Between Failures)
For repairable systems, the average time between consecutive failures. Includes repair time in the cycle.
MTTF (Mean Time To Failure)
For non-repairable items, the expected time until failure. MTTF = integral of the reliability function.
Normal Distribution
The bell-shaped probability distribution characterized by mean and standard deviation. Many natural phenomena approximate this distribution.
Null Hypothesis (H0)
The default hypothesis in statistical testing, typically representing no effect or no difference. Rejected only when evidence is sufficient.
Overfitting
When a model learns noise in training data rather than true patterns, resulting in poor generalization to new data. Characterized by low training error but high test error.
p-value
The probability of obtaining results at least as extreme as observed, assuming the null hypothesis is true. Small p-values (typically <0.05) suggest rejecting H0.
PCA (Principal Component Analysis)
A dimensionality reduction technique that transforms data into uncorrelated components ordered by variance explained.
Process Capability
The ability of a process to produce output within specification limits. Measured by Cp, Cpk, Pp, Ppk indices.
Random Forest
An ensemble of decision trees trained on bootstrap samples with random feature subsets. Reduces overfitting through averaging.
R-squared (Coefficient of Determination)
The proportion of variance in the dependent variable explained by the model. Ranges from 0 to 1; higher values indicate better fit.
Regularization
Techniques that constrain model complexity to prevent overfitting. L1 (Lasso) and L2 (Ridge) add penalty terms to the loss function.
Reliability Function R(t)
The probability that an item survives beyond time t. R(t) = 1 - F(t) = P(T > t).
Response Surface Methodology (RSM)
A collection of statistical techniques for exploring relationships between variables and optimizing responses using polynomial models.
Shewhart Chart
The original control chart developed by Walter Shewhart. Uses 3-sigma limits to distinguish common cause from special cause variation.
Standard Deviation
A measure of dispersion representing the average distance of observations from the mean. Square root of variance.
Stationarity
A property of time series where statistical properties (mean, variance) remain constant over time. Required for ARIMA modeling.
Support Vector Machine (SVM)
A classification algorithm that finds the optimal hyperplane maximizing the margin between classes. Can use kernels for non-linear boundaries.
t-Distribution
A probability distribution similar to normal but with heavier tails. Used when sample size is small and population variance unknown.
t-Test
A hypothesis test for comparing means. Variants include one-sample, two-sample (independent), and paired t-tests.
Type I Error
Rejecting a true null hypothesis (false positive). Probability equals significance level α.
Type II Error
Failing to reject a false null hypothesis (false negative). Probability denoted β; power = 1 - β.
Underfitting
When a model is too simple to capture underlying patterns. Characterized by high error on both training and test data.
Variance
A measure of dispersion representing the average squared deviation from the mean. For sample: s² = Σ(xi - x̄)²/(n-1).
Weibull Distribution
A flexible lifetime distribution with shape (β) and scale (η) parameters. β<1: decreasing hazard; β=1: constant (exponential); β>1: increasing hazard.
Western Electric Rules
A set of decision rules for identifying out-of-control conditions on control charts beyond simple limit violations.