Pemodelan Kualitas Proses Kode Matakuliah Pertemuan : I0092 – Statistik Pengendalian Kualitas :2 Learning Objectives 2 Stem-and-Leaf Display •Easy to find percentiles of the data; see page 43 3 Plot of Data in Time Order Marginal plot produced by MINITAB •Also called a run chart 4 Histograms – Useful for large data sets •Group values of the variable into bins, then count the number of observations that fall into each bin •Plot frequency (or relative frequency) versus the values of the variable 5 Histogram for discrete data 6 7 Numerical Summary of Data 8 9 10 The Box Plot (or Box-and-Whisker Plot) 11 Comparative Box Plots 12 Probability Distributions 13 14 Sometimes called a probability mass function Sometimes called a probability density function Will see many examples in the text 15 16 17 18 19 20 21 22 The Hypergeometric Distribution 23 24 The Binomial Distribution Basis is in Bernoulli trials The random variable x is the number of successes out of n Bernoulli trials with constant probability of success p on each trial 25 26 27 28 The Poisson Distribution Frequently used as a model for count data 29 30 The Pascal Distribution The random variable x is the number of Bernoulli trials upon which the rth success occurs 31 • When r = 1 the Pascal distribution is known as the geometric distribution • The geometric distribution has many useful applications in SQC 32 The Normal Distribution 33 34 35 36 Original normal distribution Standard normal distribution 37 38 39 • Practical interpretation – the sum of independent random variables is approximately normally distributed regardless of the distribution of each individual random variable in the sum 40 The Lognormal Distribution 41 42 43 The Exponential Distribution 44 Relationship between the Poisson and exponential distributions 45 The Gamma Distribution 46 • When r is an integer, the gamma distribution is the result of summing r independently and identically exponential random variables each with parameter λ • The gamma distribution has many applications in reliability engineering; see Example 2-121, text page 71 47 The Weibull Distribution 48 • When β = 1, the Weibull distribution reduces to the exponential distribution 49 • Determining if a sample of data might reasonably be assumed to come from a specific distribution • Probability plots are available for various distributions • Easy to construct with computer software (MINITAB) • Subjective interpretation 50 Normal Probability Plot 51 52 Other Probability Plots • What is a reasonable choice as a probability model for these data? 53 54 55 56