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PROCESS IMPROVEMENT

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... Qual Mgmt. PROCESS IMPROVEMENT & CONTROL. Problem Prevention And. Process Improvement. Process Capability Studies. Control Charts For Attributes. Control Charts ... – PowerPoint PPT presentation

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Title: PROCESS IMPROVEMENT


1
PROCESS IMPROVEMENT CONTROL
  • Problem Prevention And
  • Process Improvement
  • Process Capability Studies
  • Control Charts For Attributes
  • Control Charts For Variables

2
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

3
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)

4
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

5
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

6
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

7
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

8
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

9
PROCESS CAPABILITY INDICES
  • A more appropriate index may be either
    single-sided or target-sensitive

10
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

11
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

12
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

13
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

Excel
14
REDUCING THE TYPE II ERROR
  •  If sample means are gathered, than
  • Suppose now that the mean shifted k standard
    deviations (s remains unchanged)

Excel
15
REDUCING THE TYPE II ERROR
  • The distribution of the sample means will also
    have shifted

Excel
16
REDUCING THE TYPE II ERROR
  • The probability of a Type II error (?) will then
    be

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17
REDUCING THE TYPE II ERROR
18
REDUCING THE TYPE II ERROR
  • So, we have

19
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

Excel
20
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

21
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

Excel
22
SETTING CONTROL LIMITS (SUMMARY)
  • For an quality characteristic Y that has a
    sampling statistic Y-bar, determine
  • Then set

23
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

24
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

25
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

26
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

27
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

28
RUN RULES FOR CONTROL CHARTS
  • To detect trends
  • Rule 4 Out of control if 7 consecutive points
    increase/decrease a ? 0.0080

29
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

30
RUN RULES FOR CONTROL CHARTS
  • To detect stratification
  • Rule 6 Out of control if 14 consecutive points
    fall in either A a 0.0048
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