Samah

• Quality Control


  Lecture 4: Theorems of Probability
• Theorems of Probability


  Example 6
• Example 6


  1. Assume that in Example Problem of Example 5, the first part was not returned to the box before the second part was selected

  2. What is the probability?

  
• Probabilities to calculate


  • Probability of choosing both parts from supplier Z
  • Probability of choosing both nonconforming parts
  • Probability of choosing both conforming parts
  • Probability of choosing both conforming parts from supplier X
• Tutorial


  Example (Homework)
• Distribution of marks obtained by 1200 students

  • Below 40
  • Above 80
  • Between 40 and 100

  
• Example 7


  If the 261 parts described in Table 5-1 are contained in a box, what is the probability that two randomly selected parts (with replacement) will have one conforming part from supplier X and one conforming part from supplier Y or supplier Z?
• Example 8


  An oil company is bidding for the rights to drill a well in field A and a well in field B
• Probabilities to calculate


  • Probability of a successful well in field A
  • Probability of a successful well in field B
  • Probability of both a successful well in field A and a successful well in field B
  • Probability of at least one successful well in the two fields together
  • Probability of no successful well in field A
  • Probability of no successful well in field B
  • Probability of no successful well in the two fields together (calculate by two methods)
  • Probability of exactly one successful well in the two fields together
• bago pa man = before
• tulad niya = like him/her
• sa kabila ng lahat = despite everything
• kung saan man = wherever
• Process control


  Monitoring during the production process
• Acceptance sampling procedure

  Inspection before and after production
• Lot-by-lot acceptance sampling by attributes


  Most common type of sampling
• Lot-by-lot acceptance sampling by attributes

  1. Predetermined number of units (sample) from each lot inspected by attributes

  2. If number of nonconforming units less than prescribed minimum, lot accepted; if not, lot not accepted
• Acceptance sampling


  Can be used for number of nonconforming units or nonconformities per unit
• Lot-by-lot acceptance sampling by attributes

  • Lot size, N = 9000
  • Sample size, n = 300
  • Acceptance number, c = 2
• Situations where acceptance sampling is most likely to be used


  • When test is destructive, sampling necessary
  • Cost of 100% inspection high relative to cost of passing nonconforming unit
  • Many similar units to be inspected, fatigue and boredom cause higher percentage of nonconforming material to be passed
  • Information on producer's quality not available
  • Automated inspection not available
• Lot formation


  • Lots should be homogeneous
  • Lots should be as large as possible
• Representative sample


  Sample units selected for inspection should be representative of the entire lot - random sampling
• Courses of action for non-accepted lots

  • Passed to production facilities, non-conforming units sorted by production personnel
  • Rectified at consumer's plant by personnel from producer's or consumer's plant
  • Returned to producer for rectification
• Single sampling


  One sample taken from lot, decision to accept or not accept based on inspection results of that sample
• Double sampling


  Initial sample, decision based on inspection results whether to accept lot, not accept lot, or take another sample<|>If quality very good, lot accepted on first sample and second sample not taken<|>If quality very poor, lot not accepted on first sample and second sample not taken<|>Only when quality level neither very good nor very bad is second sample taken
• Multiple sampling

  Continuation of double sampling, three, four, five or more samples can be established, sample sizes much smaller
• Sequential sampling


  Items sampled and inspected one after another, cumulative record maintained, decision made to accept or not accept lot as soon as sufficient cumulative evidence
• All four types of sampling plans can give the same results, type of plan based on factors other than effectiveness
• Factors determining type of sampling plan


  • Simplicity
  • Administrative costs
  • Quality information
  • Number of units inspected
  • Psychological impact
• Process Capability


  The natural variation of a process should be small enough to produce products that meet the standards required. A process in statistical control does not necessarily meet the design specifications.

  
• Process capability


  A measure of the relationship between the natural variation of the process and the design specifications
• Control limits are established as a function of the average


  Specification is the permissible variation in the size of the part and for individual values and established by design engineers, at this time, to obtain a better understanding of individual values and average values

  
• Figure (1) shows that there are a large number of individual values and subgroup averages
• Both distributions (individual values and subgroup averages) are normal in shape
• The control limits, process spread, distribution of individual values are interdependent
• Control charts cannot determine whether the process is meeting specification
• Process spread

  Process capability, equal to 6σ
• Tolerance


  The difference between specifications
• When the tolerance is established by the design engineer without regard to the spread of the process, undesirable situations can result
• Case I: When the process capability is less than the tolerance 6σ<USL-LSL


  1. Process is in control

  2. No difficulty encountered even when there is a substantial shift in the process mean