chapter 5 tqm

• Statistics


  The science concerned with the collection, organization, analysis, interpretation, and presentation of data
• The use of statistical methods in quality dates back to 1903 at the Bell Telephone system
• In the 1920s, Bell Labs thought that statistical tools would have applications in the factory, and began to experiment with statistical sampling, eventually leading to the development of control charts
• Experiment


  A process that results in some outcome
• Outcome


  The result that we observe, e.g. the number of defective parts in the sample or the length of time until the bulb fails
• Sample space


  The collection of all possible outcomes of an experiment
• Probability


  The likelihood that an outcome occurs
• Probabilities are presented mathematically as fractions (½, ¼, ¾) or as decimals (0.25, 0.50, 0.75, 0.90) between zero and 1
• A probability of 0 means that something never happen; and a probability of 1 indicates that something will definite happen
• Event


  A collection of one or more outcomes from a sample space, e.g. finding 2 or fewer defectives in the sample of 10, or having a bulb burn for more than 1000 hours
• Complement of an event A (Ac)

  Consists of all outcomes in the sample space not in A
• Mutually exclusive events


  Events that have no outcomes in common
• Calculating Probabilities

  1. Rule 1: The probability of any event is the sum of the probabilities of the outcomes that compose that event

  2. Rule 2: The probability of the complement of any event A is P(Ac) = 1 - P(A)

  3. Rule 3: If events A and B are mutually exclusive, then P(A or B) = P(A) + P(B)

  4. Rule 4: If two events A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) - P(A and B)
• Conditional probability


  The probability of occurrence of one event A, given that another event B is known to be true or have already occurred

  
• Independent events


  Two events A and B are independent if P(A | B) = P(A)
• Random variable


  A numerical description of the outcome of an experiment
• Probability distribution


  A characterization of the possible values that a random variable may assume along with the probability of assuming these values
• Cumulative distribution function


  Specifies the probability that the random variable X will assume a value less than or equal to a specified value, x, denoted as P(X ≤ x)
• Important Probability Distributions


  • Discrete: Binomial, Poisson
  • Continuous: Normal, Exponential
• Sampling Methods


  • Simple Random Sampling
  • Stratified Sampling
  • Systematic Sampling
  • Cluster Sampling
  • Judgment Sampling
• Design of Experiments (DOE)

  A systematic, efficient method that enables scientists and engineers to study the relationship between multiple input variables (aka factors) and key output variables (aka responses)
• DOE is a structured approach for collecting data and making discoveries
• When to use DOE

  • To determine whether a factor, or a collection of factors, has an effect on the response
  • To determine whether factors interact in their effect on the response
  • To model the behavior of the response as a function of the factors
  • To optimize the response
• Ronald Fisher first introduced four enduring principles of DOE in 1926: the factorial principle, randomization, replication and blocking
• Generating and analyzing these designs relied primarily on hand calculation in the past; until recently practitioners started using computer-generated designs for a more effective and efficient DOE
• Why use Design for Experiment (DOE)

  • DOE is useful in driving knowledge of cause and effect between factors
  • To experiment with all factors at the same time
  • To run trials that span the potential experimental region for our factors
  • In enabling us to understand the combined effect of the factors
• If DOE does not exist, experiments are likely to be carried out via trial and error or one-factor-at-a-time (OFAT) method