Quality Control

// Temperature readings (°C) from sensor on production line
val sensorReadings = doubleArrayOf(
    155.2, 154.8, 156.1, 155.5, 154.3, 155.9, 155.0, 156.3, 154.7, 155.4,
    155.8, 154.5, 156.0, 155.3, 154.9, 155.7, 155.1, 156.2, 154.6, 155.6,
    155.3, 154.4, 155.8, 162.5, 155.1, 155.7, 154.2, 155.5, 155.9, 141.3
)
// Two potential outliers: 162.5 and 141.3

val summary = sensorReadings.describe()

summary.mean
summary.standardDeviation
summary.min // check for unusually low values
summary.max // check for unusually high values
summary.interquartileRange

val zScores = sensorReadings.zScore()

val anomalyIndices = zScores.indices.filter { kotlin.math.abs(zScores[it]) > 3.0 }
val anomalies = anomalyIndices.map { sensorReadings[it] }

val lowerBound = sensorReadings.quantile(0.01)
val upperBound = sensorReadings.quantile(0.99)

val outliers = sensorReadings.filter { it < lowerBound || it > upperBound }

val centerLine = sensorReadings.mean()
val sigma = sensorReadings.standardDeviation()

val upperControlLimit = centerLine + 3 * sigma
val lowerControlLimit = centerLine - 3 * sigma

val outOfControl = sensorReadings.filter { it > upperControlLimit || it < lowerControlLimit }

val morningBatch = doubleArrayOf(
    155.2, 154.8, 156.1, 155.5, 154.3, 155.9, 155.0, 156.3, 154.7, 155.4
)
val eveningBatch = doubleArrayOf(
    155.8, 154.5, 156.0, 155.3, 154.9, 155.7, 155.1, 156.2, 154.6, 155.6
)

// Check normality
shapiroWilkTest(morningBatch).pValue
shapiroWilkTest(eveningBatch).pValue

// Check variance homogeneity
leveneTest(morningBatch, eveningBatch).pValue

// Compare means
val batchComparison = tTest(morningBatch, eveningBatch)
batchComparison.pValue
batchComparison.isSignificant() // false means no significant shift

val batch1 = doubleArrayOf(155.2, 154.8, 156.1, 155.5, 154.3)
val batch2 = doubleArrayOf(155.9, 155.0, 156.3, 154.7, 155.4)
val batch3 = doubleArrayOf(155.8, 154.5, 156.0, 155.3, 154.9)

val anova = oneWayAnova(batch1, batch2, batch3)
anova.fStatistic
anova.pValue

// Exclude known outliers for fitting
val cleanReadings = sensorReadings.filter { it in 150.0..160.0 }.toDoubleArray()

val fitted = NormalDistribution(
    mu = cleanReadings.mean(),
    sigma = cleanReadings.standardDeviation()
)

val ks = kolmogorovSmirnovTest(cleanReadings, fitted)
ks.pValue // high p-value supports the normal process model

val temperatureSensor = doubleArrayOf(
    155.2, 154.8, 156.1, 155.5, 154.3, 155.9, 155.0, 156.3, 154.7, 155.4
)
val pressureSensor = doubleArrayOf(
    2.12, 2.08, 2.15, 2.11, 2.05, 2.14, 2.09, 2.16, 2.07, 2.10
)
val flowRateSensor = doubleArrayOf(
    45.1, 44.8, 45.5, 45.2, 44.5, 45.4, 44.9, 45.6, 44.7, 45.3
)

temperatureSensor.describe()
pressureSensor.describe()
flowRateSensor.describe()

// Correlation matrix — identifies linked parameters
val matrix = correlationMatrix(temperatureSensor, pressureSensor, flowRateSensor)
// matrix[0][1] = temperature-pressure correlation
// matrix[0][2] = temperature-flow correlation
// matrix[1][2] = pressure-flow correlation