CH 10

CONTROL CHARTS - THE VOICE OF THE PROCESS

Control Charts: A time ordered plot of representative sample statistics obtained from an ongoing process (e.g. sample means), used to distinguish between random and nonrandom variability -Each point on the control chart represents a sample of n observations

C-CHART EXAMPLE - Rolls of coiled wire are monitored using a c-chart. Eighteen rolls have been examined, and the number of defects per roll has been recorded in this table. -Is the process in control? Plot the values on a control chart using three standard deviation (z = 3)control limits.

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How much to inspect graph

High cost, low volume items need more intensive inspections -If inspection activities increases, inspection costs increase, but the costs of undetected defects decrease

p-chart control limits

If p is unknown, it can be estimated from samples -IF LCL is negative, use 0.

Mean vs range charts

Mean charts are sensitive to shifts in the process mean vs. Range charts are sensitive to changes in process dispersion -Therefore, use of both charts provide more complete information.

Type II error

Means concluding a process is in control when it is not -The probability of failing to reject the null hypothesis when the null hypothesis is false -Consumer's Risk -beta -Assume H0 = Null Hypothesis (process is in control)

Type 1 error

Means concluding a process is not in control when it actually is -The probability of rejecting the null hypothesis when the null hypothesis is true -Manufacturer's Risk -Assume H0 = Null Hypothesis (process is in control) -alpha

PROCESS CAPABILITY

Once a process has been determined to be stable, it is necessary to determine if the process is capable (>1.33)* of producing output that is within an acceptable range

C-CHART CONTROL LIMITS

is c is unknown--> cbar= number of defects/ number of samples

Process Variability - Issue of Process Control: -Issue of Process Capability:

- Issue of Process Control: Are the variations random? --If nonrandom variation is present, the process is said to be unstable. -Issue of Process Capability: Given a stable process, is the inherent variability of the process within a range that conforms to performance criteria?

Random Variation vs Assignable Variation

- Random: (Common cause) natural variation in the output of a process, created by countless minor factors -Assignable: (Special cause) a variation whose cause can be identified; also a nonrandom variation

PROCESS CAPABILITY - Tolerances or specifications -process variability -process capability

- Tolerances or specifications Range of acceptable values established by engineering design or customer requirements (range of values the units of output must fall to be acceptable) -Process variability Natural or inherent variability in a process (measured by std dev) -Process capability The inherent variability of process output (process width) relative to the variation allowed by the design specification (specification width)

USE A P-CHART

-Use it when the data consists of multiple samples of several observations each -Use it when observations can be placed into two categories:

Inspection Issues (4)

1. How much to inspect and how often 2. At what points in the process to inspect 3. Whether to inspect in a centralized or on-site location 4. Whether to inspect attributes or variables

What points in the process to inspect? (5)

1. raw materials and purchased parts 2. finished products 3. before a costly operation 4. Before an irreversible process 5. before a covering process

Sampling Distribution graph

1. sampling and process distribution have the same mean 2. variability of sampling distribution is less than the variability of process 3. sampling distribution is normal -outside 2 or 3 std dev is nonrandom variations

Quality Control

A process that evaluates output relative to a standard and takes corrective action when output doesn't meet standards

Quality of Conformance

A product or service conforms to specifications -Quality control seeks Quality of Conformance

Run tests

A test for patterns in a sequence - Run: A sequence of observations with a certain characteristic -Even if a process appears to be in control, the data may still not reflect a random process -Analysts often supplement control charts with a run test

- Sampling Distribution:

A theoretical distribution that describes the random variability of sample statistics -The normal distribution is commonly used for this purpose - the larger the sample size, the narrower the sampling distribution relative to sample size

Inspection

An appraisal activity that compares goods or services to a standard - Inspection alone is generally not sufficient to achieve a reasonable level of quality -Most organizations rely upon some inspection and a great deal of process control to achieve an acceptable level of quality.

Control Charts for Attributes

Attributes generate data that are counted. -p-chart: Control chart used to monitor the proportion of defectives in a process -c-chart: Control chart used to monitor the number of defects per unit

Control Charts for Variables -Mean Control Charts

Used to monitor the central tendency of a process -If the standard deviation of the process, i.e. σ is unknown, use the sample range as a measure of process variability.

Control Charts for Variables - Range Control Charts

Used to monitor the process dispersion - Variables generate data that are measured

sample statistics

SPC involves periodically taking samples of process output and computing sample statistics -To judge the randomness of process variation -Sample means -The number of occurrences of some outcome

Control Process Steps required for effective control: (6)

Sampling and corrective action are only a part of the control process

Statistical Process Control (SPC)

Statistical evaluation of the output of a process -SPC is the tool to help in the process -Helps us determine if a process is "in control" or if corrective action is needed

USING MEAN AND RANGE CHARTS -Steps to Determine Initial Control Limits (6)

Step 1: Obtain 20 to 25 samples Step 2: Compute appropriate sample statistics Step 3: Establish preliminary control limits Step 4: Determine if any points fall outside of the control limits -Search for and correct the assignable cause of variation -Assume the process is in control -If you find no out-of-control signals Step 5: Resume the process and collect another set of observations on which to base control limits Step 6: Plot the data on the control chart and check for out-of-control signals

Central Limit Theorem (CLT)

The distribution of sample averages tends to be normal regardless of the shape of the process distribution

Control Limits

The dividing lines between random and nonrandom deviations from the mean of the distribution -Upper control limits (UCL) and lower control limits (LCL) define the range of acceptable variation -between two limits= random -outside or on either limit= nonrandom

MEAN AND RANGE CHARTS - FIGURE B

The mean chart does not detect the change in dispersion, but it is picked up by the range chart.

MEAN AND RANGE CHARTS - FIGURE A

The mean chart picks up shift in process mean, but since dispersion is not changing, the range chart fails to indicate a problem.

USE A C-CHART

Use only when the number of occurrences per unit of measure can be counted and/or non-occurrences cannot be counted.

Range Chart: Control Limits

Used to monitor process dispersion -D3= a control chart factor based on sample size, n -D4= a control chart factor based on sample size, n

Mean Chart: Control Limits

Used to monitor the central tendency of a process -A2= a control chart factor based on sample size, n

(Cp) capability index

used to assess the ability of a process to meet specifications

Whether to inspect in a centralized or on-site location?

whether the advantage of specialized lab tests are worth the time and interruption needed to obtain the results -on-site: quicker decisions, avoidance of introduction of extraneous factors -lab: specialized equipment, more favorable test environment