Chapter 10 Operations: Quality Control

types II errors

-concluding a process is in control when it is not -in other words, the error is concluding nonrandom variations are not present, when they are -in practice, two-sigma limits and three-sigma limits are commonly used without specifically referring to the probability of a type II error

type I error

-concluding a process is not in control when it actually is -in other words, the "error" is concluding that non randomness is present when only randomness is present it is also referred to as an alpha risk, where alpha is the sum of the probabilities in the to tails

control process

-define -measure -compare -evaluate -correct -monitor results

limitations of capability indexes

-process may not be stable -process output may not be normally distributed -process not centered but Cp is used

a sampling distribution and a process distribution

1- both distributions have the same mean 2- the variability of the sampling distribution is less than the variability of the process 3- the sampling distribution is normal. this is true even if the process distribution is not normal

determining initial control limits

1- obtain 20 to 25 samples. compute the appropriate sample statistics for each sample 2- establish preliminary control limits using the formulas 3- determine if any points fall outside the control limits 4- if you find no out-of-control signals, assume that the process is in control. if not, investigate and correct assignable causes of variation. then resume the process and collect another set of observations upon which control limits can be based 5- plot the data on the control chart and check for out-of-control signals

where to inspect in the process

many operations have numerous possible inspection points it is important to restrict inspection efforts to the points where they can do the most good in manufacturing, some of the typical inspection points are -raw materials and purchased parts -finished products -before a costly operation -before an irreversible process -before a covering process

mean and range charts

mean charts are sensitive to shifts in the process mean, whereas range charts are sensitive to changes in process dispersion use of both charts provides more complete information than either chart along

central limit theorem

the distribution of sample averages tends to be normal regardless of the shape of the process distribution the larger the sample size, the narrower the sampling distribution

define

the first step is to define in sufficient detail what is to be controlled

chance or random variations

the natural or inherent process variations in process output

process variability

the natural or inherent variability in a process it is measured in terms of the process standard deviation

sampling and sampling distribution

the sample statistics exhibit variation, just as processes do the variability of sample statistics can be described by its sampling distribution, a theoretical distribution that describe the random variability of sample statistics

statistical process control

there are four commonly used control charts -two for variables -two for attributes attribute data are counted variable data are measured

compare

there must be a standard of comparison that a can be used to evaluate the measurements

counting runs

to determine whether any patterns are present in control chart data, one must transform the data into both As and Bs, and Us and Ds, and then count the number of runs in each case these numbers must then be compared with the number of runs that would be expected in a completely random series

monitor results

to ensure that corrective action is effective, the output of a process must be monitored for a sufficient period of time to verify that the problem has been eliminated

run tests: two tests

two useful run tests involve examination of the number of runs up and down and runs above and below the median

use of c-charts

use only when the number of occurrences per unit of measure can be counted; nonoccurrence cannot be counted -scratches, chips, dents -cracks or faults -breaks or tears -bacteria or pollutants -calls, complaints the underlying sampling distribution is the Poisson distribution -use of the Poisson distribution assumes that defects occur over some continuous region and that the probability of more than one defect at any particular point is negligible

range control charts

used to monitor process dispersion; they are sensitive to changes in process dispersion control limits for range charts are found using the average sample range in conjunction with these formulas KNOW MORE ON SLIDE

correct

when a process is judged out of control, corrective action must be taken

use of p-charts

when observations can be placed into two categories -good or bad -pass or fail -operate or don't operate when the data consists of multiple samples of several observations each the theoretical basis for a p-chart is the binomial distribution, although for large sample sizes, the normal distribution provides a good approximation to it the center line on a p-chart is the average fraction defective in the population, p the standard deviation of the sampling distribution when p is known KNOW

evaluate

management must establish a definition of out of control

quality of conformance

a product or service conforms to specifications

assignable variation

a second kind of variability in process output, whose cause can be identified "special variation"

control chart

a time-ordered plot of sample statistics, which was developed by walter shewhart -used to distinguish between random variability and nonrandom variability it has upper and lower limits, called control limits that define the range of acceptable variation for the sample statistic

process variability

all processes generate output that exhibits some degree of variability

mean control chart

based on normal distribution if the standard deviation of the process is unknown, another approach is to use the sample range as a measure of process variability KNOW MORE ON SLIDE 22

run test

checks for patterns in a sequence of observations -analysts supplement control charts help to detect abnormalities in a process and provides insights into correcting a process that is out of control

c-chart

control chart used to monitor the number of defects per unit

p-chart

control chart used to monitor the proportion of defectives in a process

run tests

control charts test for points that are too extreme to be considered random however, even if all points are within the control limits, the data may still not refectory a random process in fact, any sort of pattern in the data would suggest a nonrandom process

run

defined as a sequence of observations with a certain characteristic, followed by one or more observations with a different characteristic -the characteristic can be anything that is observable

capability analysis

determination of whether the variability inherent in the output of a process that is in control falls within the acceptable range of variability allowed by the design specifications for the process output if it is within the specifications, the process is said to be capable if it is not, the manager must decide how to correct the situation

run tests distinguish

distinguishing chance variability from patters requires use of the sampling distributions for median runs and up/down runs. both distributions are approximately normal. if the observed number of runs falls in the range, there are probably no nonrandom patterns for observed numbers of runs beyond such limits, we begin to suspect that patterns are present to few or too many runs can be an indication of non randomness

process capability ratio

if the process is centered, use process capability ration Cp = specification with / process with

nonrandom variation

indicated when a point is observed that is outside the control limits, or a run test produces a large z-value managers should have response plans to investigate cause may be a false alarm (type I error) may be assignable variation

process capability definition

inherent variability of process output relative to the variation allowed by the design specifications

process control

monitoring during the production process

process capability

once the stability of a process has been established, it is necessary to determine if the process is capable of producing output that is within an acceptable range three commonly used terms refer to the variability of the process output

measure

only those characteristics that can be counted or measured are candidates for control

acceptance sampling

quality assurance that relies primarily on inspection of lots (batches) of previously produced items

tolerances or specifications

range of acceptable values established by engineering design or customer requirements

control charts for attributes

recap: attributes generate data that are counted for example, the number of defective items in a sample is counted, whereas the length of each item is measured

control charts for variables

recap: variables generate data that are measured mean control charts -used to monitor the central tendency of a process range control charts -used to monitor the process dispersion

centralized vs. on-site inspection

some situations require that inspections be performed on site at other times, specialized tests can best be performed in a lab -performing medical tests -analyzing food samples -testing metals for hardness -running viscosity tests on lubricants

statistical process control

statistical evaluation of the output of a process during production

control limits

statistical limits that reflect the extent to which sample statistics such as means and ranges can vary due to randomness alone