PROCESS IMPROVEMENT

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PROCESS IMPROVEMENT CONTROL

• Problem Prevention And
• Process Improvement
• Process Capability Studies
• Control Charts For Attributes
• Control Charts For Variables

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PROBLEM PREVENTION AND PROCESS IMPROVEMENT I

• Is It Working? Can It Work Better?
•  Process Capability Studies
• Control Charts
• Mistakes To Avoid, And Their
• Statistical Equivalents
• Run Rules For Control Charts

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IS IT WORKING? CAN IT WORK BETTER?

• Problem detection prevention
• Assignable variation detection
• Tools useful only for stable, capable processes
• Process improvement
• Assignable variation removal
• Tools useful for stable capable or
  unstable/incapable processes
• PDCA cycle (conversion of unassignable to
  assignable variation)

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PROCESS CAPABILITY STUDIES

• Used to ensure that a process is capable of
  making the part to spec when no assignable
  variation is present
• Define
• µ, s -- Mean, standard deviation of QC for
  stable process
• m -- Target value of QC
• UNL, LNL -- Upper, lower natural limits
• USL, LSL -- Upper, lower spec limits

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NATURAL, CONTROL, AND SPECIFICATION LIMITS

• Specification limits
• Define an acceptable part
• m -- target value
• USL (LSL) -- upper (lower) spec limit
• Natural limits
• Range we can expect with only unassignable
  variation
• µ -- mean value of QC
• UNL (LNL) -- upper (lower) natural limit
• To manufacture quality parts, we need
• LSL lt lt LNL lt UNL lt lt USL

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NATURAL, CONTROL, AND SPECIFICATION LIMITS

• Control limits
• Range of values we use to warn us that assignable
  variation is present
• UCL (LCL) -- upper (lower) control limit
• To detect assignable variation before it becomes
  a problem, we need
• LSL lt lt lt lt LCL lt UCL lt lt lt lt USL
• So we have
• LSL lt lt LNL lt lt LCL lt UCL lt lt UNL lt lt USL

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PROCESS CAPABILITY INDICES

• Natural limits (quantitatively) defined
• A normally distributed qc from a stable process
  will fall within the natural limits 99.73 of the
  time
• This implies that the natural limits are
•  UNL µ 3s
•  LNL µ - 3s
• The basic process capability index is thus

• Generally OK if Cp gt 1.33

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PROCESS CAPABILITY INDICES

• Consider our bags of sugar
• m 10 lbs
• LSL, USL 9.5, 10.5 lbs
• m 10.1 lbs
• s 0.1 lbs

• The results look ok, but the results are
  misleading since Cp is target insensitive

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PROCESS CAPABILITY INDICES

• A more appropriate index may be either
  single-sided or target-sensitive

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CONTROL CHARTS

• A control chart is an aid to determine if
  assignable variation is present
• UCL-- upper control limit for QC
• LCL -- lower control limit for QC

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CONTROL CHARTS

• If an observation falls inside the limits
• Conclude process is in control
• If an observation falls outside the limits
• Conclude process is out of control

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MISTAKES TO AVOID, THEIR STATISTICAL
EQUIVALENTS

• Need to set control limits to minimize two types
  of mistakes
• Type I -- conclude we're out of control when
  we're in control (false alarm)
• Type II -- conclude we're in control when we're
  out of control (overlooked problem)
• Probability of each type of mistake
• Type I -- a Type II -- b
• This is standard hypothesis testing with the
  following null hypothesis
• H0 the process is in control

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SETTING CONTROL LIMITS

• Focus on minimizing likelihood of Type I error
  first
• If control limits set to /- 3 standard
  deviations, probability of a Type I error
  0.0027 lt 1
• To control the likelihood of a Type II error
• Use n observations instead of 1
• For a variable QC, the resulting distribution of
  sample means is
• Normally distributed
• Same mean (µ)
• Smaller variance

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REDUCING THE TYPE II ERROR

•  If sample means are gathered, than

• Suppose now that the mean shifted k standard
  deviations (s remains unchanged)

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REDUCING THE TYPE II ERROR

• The distribution of the sample means will also
  have shifted

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REDUCING THE TYPE II ERROR

• The probability of a Type II error (?) will then
  be

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REDUCING THE TYPE II ERROR
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REDUCING THE TYPE II ERROR

• So, we have

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REDUCING THE TYPE II ERROR

• What is the probability that, if the bag-filling
  process went out of control and the true mean
  bag weight shifted to 10.1 lbs, we would not
  detect the shift on the next sample?
• n 5
• m 10
• s 0.1

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AVERAGE RUN LENGTH

• An alternative way of thinking about the
  likelihood of Type I and Type II errors for
  control charts
• On average, how often will I get a false alarm
  (Type I error)?
• On average, how long will it take to detect of
  shift of k standard deviations in the mean? (Type
  II error)
• The expected length of time until a control limit
  is violated is the average run length

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AVERAGE RUN LENGTH

• For a standard control chart with 3-sigma control
  limits, the frequency of a Type I error is

• The ARL to detect a shift k in the process mean
  depends on b.

• Which depends on the sample size n and how big
  the shift k is

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SETTING CONTROL LIMITS (SUMMARY)

• For an quality characteristic Y that has a
  sampling statistic Y-bar, determine

• Then set

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CONSTRUCTING CONTROL CHARTS

• Same procedure applies for all charts
• Determine sampling plan (sample size, frequency)
• Collect 25 samples
• Estimate necessary parameters of sampling
  distribution (usually the mean and standard
  deviation)
• Calculate UCL and LCL
• Plot data
• Determine if process was in control
• If yes,
• Use chart to monitor process
• If no,
• Improve process, collect more data, recompute
  control limits, or
• all of the above

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RUN RULES FOR CONTROL CHARTS

• Run rules based on more than one observation may
  be used to decrease b without increasing a
• Define "zones" on the chart as follows
• A zones -- between 0 and 1 s from mea
• B zones -- between 1 and 2 s from mean
• C zones -- between 2 and 3 s from mean

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RUN RULES FOR CONTROL CHARTS

• To detect freaks
• Rule 1 Out of control if 2 of 3 consecutive
  points fall in same C or beyond a 0.0016

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RUN RULES FOR CONTROL CHARTS

• To detect freaks
• Rule 2 Out of control if 4 of 5 consecutive
  points fall in same B or beyond a 0.0028

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RUN RULES FOR CONTROL CHARTS

• To detect shifts
• Rule 3 Out of control if 7 consecutive points
  fall on one side of mean a 0.0080

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RUN RULES FOR CONTROL CHARTS

• To detect trends
• Rule 4 Out of control if 7 consecutive points
  increase/decrease a ? 0.0080

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RUN RULES FOR CONTROL CHARTS

• To detect mixtures
• Rule 5 Out of control if 5 consecutive points
  fall in either B or beyond a 0.0032

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RUN RULES FOR CONTROL CHARTS

• To detect stratification
• Rule 6 Out of control if 14 consecutive points
  fall in either A a 0.0048