Chapter 10 Quality control

Statistical Process Control

(SPC) Quality control seeks quality of conformance: a product or service conforms to specifications A tool used to help in this process is SPC: Statistical evaluation of the output process Helps us decide if a process is in control or if corrective action is needed

2 basic questions concerning variability

1) Issue of process control: are the variations random? if nonrandom variation is present, the process is said to be unstable 2) Issue of process capability: given a stable process, is the inherent variabliity of the process within a range that confroms to performance criteria?

Quality control

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

Sampling Distribution

A theoretical distrib that describes the random variability of sample stats The normal distribution is commonly used for this purpose

Control Chart

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

Inspection

An appraisal activity that compares goods or services to a standard Issues: 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

Managerial considerations

At what points in the process to use control charts What size samples to take What type of control chart to use Variables Attributes

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

Steps for effective control

Define: What is to be controlled? Measure: How will measurement be accomplished? Compare: There must be a standard of comparison Evaluate: Establish a definition of out of control Correct: Uncover the cause of nonrandom variability and fix it Monitor: Verify that the problem has been eliminated

Centralized vs. on site inspection

Effects on cost and level of disruption are a major issue in selecting centralized vs. on site inspection

Run Tests

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 Run test A test for patterns in a sequence Run Sequence of observations with a certain characteristic

Variables generate data that are measured

Mean control charts Used to monitor the central tendency of a process. "x- bar" charts Range control charts Used to monitor the process dispersion R charts

Process Capability

Once a process has been determined to be stable, it is necessary to determine if the process is capable of producing output that is within an acceptable range Tolerances or specifications Range of acceptable values established by engineering design or customer requirements Process variability Natural or inherent variability in a process Process capability The inherent variability of process output (process width) relative to the variation allowed by the design specification (specification width)

Variation

Random (common cause) variation: Natural variation in the output of a process, created by countless minor factors Assignable (special cause) variation: A variation whose cause can be identified, a non random variation

Sampling and Sampling distribution

SPC involves periodically taking samples of process output and computing sample stats: Sample means The # of occurences of the same outcome Sample stats are used to judge the randomness of process variation

improving process capability

Simplify Standardize Mistake-proof Upgrade equipment Automate

Centralized inspection

Specialized tests that may best be completed in a lab, more specialized testing equipment, more favorable testing enviro

Central Limit Theorem

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

Control Limits

The dividing lines between random and nonrandom deviations from the mean of the distribution Upper and lower control limits define the range of acceptable variation

Using Mean and range charts

To determine initial control limits: Obtain 20 to 25 samples Compute appropriate sample statistics Establish preliminary control limits Determine if any points fall outside of the control limits If you find no out-of-control signals, assume the process is in control If you find an out-of-control signal, search for and correct the assignable cause of variation Resume the process and collect another set of observations on which to base control limits Plot the data on the control chart and check for out-of-control signals

Type I Error

Type I error 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

Type II error

Type II error 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

Use a c chart when

Use only when the number of occurrences per unit of measure can be counted; non-occurrences cannot be counted. Scratches, chips, dents, or errors per item Cracks or faults per unit of distance Breaks or Tears per unit of area Bacteria or pollutants per unit of volume Calls, complaints, failures per unit of time

Use a p chart when

When observations can be placed in to 2 categories Good or bad, pass or fail, operate or don't When the data consists of mult samples of several observations of each

On-site

quicker decisions are rendered, avoid intro of extraneous factors, quality at the source

Typical inspection points

raw materials and purchased parts finished products before a costly operation before an irreversible process before a covering process