Chapter 22: Statistical Process Control

Question 1

Prevention approach

Answer 1

Instead of inspecting the product, inspecting the process to determine when the process starts producing units that do not conform to specifications.

Uses hypothesis testing concepts

Allows for earlier correction

Question 2

Sources of variation

Answer 2

Chance

Assignable variation

Question 3

Chance

Answer 3

Aka common variation

Caused by a number of randomly occuring events that are part of the production process and generally cannot be eliminated without changing the process

Question 4

Assignable variation

Answer 4

Aka special variation

Variation causes by specific events/factors that are frequently temporary and can usually be identified and eliminated (malfunctions)

Question 5

When production process is under control

Answer 5

Only sources of variation in the random variable are due to chance.

Each distribution has the same shape, mean, standard deviation

Products all fall within designated specification limits

Question 6

When production process is out of control

Answer 6

When product falls outside of designated specification limits

When the process distribution changes and varies between individual instabces

Question 7

Common ways for processes being out of control

Answer 7

• level shift
• instability
• trend
• cycle

Question 8

Out of control process: Level shift

Answer 8

A change in the mean of the process distribution

Potential causes: machine breakdown, new machine or operator, environmental change

Question 9

Out of control process: instability

Answer 9

When process standard deviation increases (wider variation)

Potential causes: problem with machinery, materials, tools, operators

Question 10

Out of control process: trend

Answer 10

When there is a slow, steady shift in the process distribution mean in either direction.

Potential causes: irregular maintenance (residue/dirt buildup, loss of lubricant), operator fatigue

Question 11

Our of control process: cycle

Answer 11

Repeated series of small observations followed by large observations

Potential causes: environmental changes, worn parts, operator fatigue

Question 12

Control chart

Answer 12

Statistical method used to detect problems in processes, a plot of statistics over time

Question 13

Elements of a control chart

Answer 13

Centerline
Upper and lower control limits
- if all points are randomly distributed between control limits then process is under control

Question 14

Standard error of sample mean of x

Answer 14

Standard deviation / square root of b

Question 15

Difference between statistical process control and hypothesis testint

Answer 15

Hypothesis testing - determination about a single fixed parameter

SPC - determination about a variable process distribution (dynamic process distribution with parameters subject to possible shifts)

Question 16

Factors determining the sample size and frequency for a control chart

Answer 16

• costs or type I and Type II errors
• length of production run
• typical change in the process distribution when process goes out of control

Use Operating Characteristic (OC) curve

Question 17

Operating Characteristics curve

Answer 17

OC curve

Plotted probabilities of one characteristic given another characteristic

Question 18

Probability of a type II error

Answer 18

Probability the control chart will be unable to detect a shift of k # of standard deviations in the process mean on the first sample after the shift has occured

Question 19

Average run length

Answer 19

ARL

The expected number of samples that must be taken before the chart indicates that the process has gone out of control (erroneously)

ARL=1/P

P= probability that a sample mean falls outside the control limits (probability of type II error)

Question 20

Control charts for variables

Answer 20

Control charts for interval data

Question 21

Control charts for attributes

Answer 21

For categorical data (defective vs non- defective

Question 22

Ways to judge if a change in process distribution has occured (interval data)

Answer 22

• xbar chart: determine whether the distribution means have changed
• S (standard deviation) or R (range) chart: to determine if profess standard deviation has changed

SPC often uses range calcuations instead of standard deviations (sample range to estimate standard deviation)

Question 23

Estimator of the mean of the distribution

Answer 23

Denoted by x with two bars

The mean of the sample mean so:

Sum of all values of the means for each sample / k number of samples

Used to estimate the mean of the process distribution

Question 24

Standard deviation for process distribution

Answer 24

Denoted as S

Calculate sample variance (s^2) for each sample

To compute pooled standard deviation take the square root of (the sum of all variances divided by the number of samples)

Used to estimate the standard deviation of the profess distribution

Question 25

Centerline and control limits for xbar chart

Answer 25

Centerline= mean of the sample means (x with two bars)

Control limit = mean of the sample mean +/- 3* (standard deviation of process distribution divided by the square root of n (number of observations in each sample))

Question 26

zones of the xbar chart

Answer 26

Divisions of area between the centerline and control limits

C zones: areas within one standard deviation of the center line

B zones: areas between one and two standard errors of the center line

A zones: areas between two and three standard errors of the center line

Width of zones = one standard error

Question 27

finding the standard error of xbar

Answer 27

the difference between the upper and lower control limits divided by 6

Question 28

Pattern tests indicating a process is out of control

Answer 28

Patterns that are rare events and unlikely to occur if the process is under control

1- one point beyond zone A
2- nine points in a row in zone C or beyond on one side of the centerline
3- six increasing or decreasing points in a row
4- fourteen points in a row alternating up and down
5- two out of three points in a row in zone A on the same side of the centerline
6- four out of five points in zone B or A on the same side of the centerline
7- fifteen points in a row in zone C on both sides of the centerline
8- eight points in a row beyond zone C on both sides of the centerline

Question 29

Mintab’s rules

Answer 29

Eight pattern tests for xbar charts

No pattern tests for S and R charts

Four pattern tests for p charts

Question 30

S chart

Answer 30

Graphs sample standard deviations to determine if the process distribution standard deviation has changed

Similar format to xbar chart with centerline and control limits

If no points outside the control limits no evidence to believe the standard deviation has changed over the period (however points below lower control limit may be desirable : standard deviation decreasing)

Question 31

Using xbar and S charts

Answer 31

In practice used together

Xbar chart uses S to calculate control limits and zone boundaries, so if S is our of control then the control limits in xbar will be skewed

S drawn first

Original structure made while process known to be in control and then further data points potted as time continues to monitor process

Question 32

Process capability index

Answer 32

Measures the capability of the process to produce units whose dimensions fall within specifications

Cp= (USL-LSL)/(6sd)

Theoretical process capacity = (upper minus lower specification limit)/ (6 * standard deviation)

Issue- parameter of standard deviation generally unknown

Question 33

Actual process capability

Answer 33

Use xbarbar and S from control chart

CPL (lower) = (xbarbar - LSL)/ 3S

CPU (upper) = (USL - xbarbar)/3S

Process capability index is the smaller of the two

Question 34

Reducing process variation

Answer 34

Experimenting with the “four Ms” and examining the results using a control chart

• machines
• materials
• methods
• manpower