KRM8 Chapter 6 - Process Performance and QualityQuality tools for Evaluating & controlling Performance
Checklist: A form used to record the frequency of occurrence of certain service or product characteristics related to performance.
Histogram: A summarization of data measured on a continuous scale, showing the frequency distribution of some quality characteristic (the central tendency and dispersion of the data).
Bar chart: A series of bars representing the frequency of occurrence of data characteristics measured on a yes-or-no basis.
Pareto Chart: A bar chart on which factors are plotted in decreasing order of frequency along the horizontal axis.
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Bar Chart
The manager of a neighborhood restaurant is concerned about rising customer complaints. He would like to present his findings in a way that his employees will understand.
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Evaluating Performance
Scatter-diagram: A plot of two variables showing whether they are related.
Cause-and-effect diagram: A diagram that relates a key performance problem to it’s potential causes.
Sometimes called the fishbone diagram.
Graphs: Representation of data in a variety of pictorial forms, such as line charts and pie charts.
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Checker Board Airlines
Passenger processing at gate
They decide to use the following tools:
.
B. Discolored fabric /// 3
C. Broken fiber board //// //// //// ////
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First Second Third
Process Performance
Defects: Any instance when a process fails to satisfy its customer.
Most experts estimate that the losses due to poor performance and quality range from 20 to 30 % of gross sales
These costs can be broken down into 4 major categories
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Costs of Poor
Prevention costs are associated with preventing defects before they happen.
Appraisal costs are incurred when the firm assesses the performance level of its processes.
Internal failure costs result from defects that are discovered during production of services or products.
External failure costs arise when a defect is discovered after the customer receives the service or product.
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Prevention costs
Includes cost of redesigning the process to remove the causes of poor performance
Redesigning the service or product to make it simpler to produce
Training employees in the methods of continuous improvement
Working with suppliers to increase the quality of purchased items or contracted services
In order to improve performance firms must invest additional time effort and money.
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Appraisal costs
As preventive measures improve performance appraisal cost decrease because fewer resources are needed for quality inspections and subsequent search for cause of any problems that are detected.
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Internal failure costs
Two main categories –
Rework some aspect of the service must be performed again or a defective item must be rerouted to some previous operations to correct the defect
Scrap incurred when a defective item is unfit for further processing
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External failure costs
Dissatisfied customers talks about bad service or product to their friends
Consumer protection groups may take up the issue . alert the media
The potential impact on future profits is difficult to assess, but with out doubt external failure cost can erode market share and profits.
Encountering defects and correcting them after the product is in customers hands is costly
external failure cost also include warranty service and litigation costs.
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Statistical process control is the application of statistical techniques to determine whether a process is delivering what the customer wants.
Acceptance sampling is the application of statistical techniques to determine whether a quantity of material should be accepted or rejected based on the inspection or test of a sample.
Variables: Service or product characteristics that can be measured, such as weight, length, volume, or time.
Attributes: Service or product characteristics that can be quickly counted for acceptable performance.
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Sampling
Sampling plan: A plan that specifies a sample size, the time between successive samples, and decision rules that determine when action should be taken.
Sample size: A quantity of randomly selected observations of process outputs.
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Sample Means and
the Process Distribution
Sample statistics have their own distribution, which we call a sampling distribution.
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Sampling Distributions
A sample mean is the sum of the observations divided by the total number of observations.
The distribution of sample means can be approximated by the normal distribution.
Sample Mean
n = total number of observations
x = mean
Sample Range
The range is the difference between the largest observation in a sample and the smallest.
The standard deviation is the square root of the variance of a distribution.
where
xi = observations of a quality characteristic
x = mean
Process Distributions
A process distribution can be characterized by its location, spread, and shape.
Location is measured by the mean of the distribution and spread is measured by the range or standard deviation.
The shape of process distributions can be characterized as either symmetric or skewed.
A symmetric distribution has the same number of observations above and below the mean.
A skewed distribution has a greater number of observations either above or below the mean.
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Causes of Variation
Two basic categories of variation in output include common causes and assignable causes.
Common causes are the purely random, unidentifiable sources of variation that are unavoidable with the current process.
If process variability results solely from common causes of variation, a typical assumption is that the distribution is symmetric, with most observations near the center.
Assignable causes of variation are any variation-causing factors that can be identified and eliminated, such as a machine needing repair.
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Assignable Causes
The red distribution line below indicates that the process produced a preponderance of the tests in less than average time. Such a distribution is skewed, or no longer symmetric to the average value.
A process is said to be in statistical control when the location, spread, or shape of its distribution does not change over time.
After the process is in statistical control, managers use SPC procedures to detect the onset of assignable causes so that they can be eliminated.
Location
Spread
Shape
Control Charts
Control chart: A time-ordered diagram that is used to determine whether observed variations are abnormal.
A sample statistic that falls between the UCL and the LCL indicates that the process is exhibiting common causes of variation; a statistic that falls outside the control limits indicates that the process is exhibiting assignable causes of variation.
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Control Chart Examples
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Type I and II Errors
Control charts are not perfect tools for detecting shifts in the process distribution because they are based on sampling distributions. Two types of error are possible with the use of control charts.
Type I error occurs when the employee concludes that the process is out of control based on a sample result that falls outside the control limits, when in fact it was due to pure randomness.
Type II error occurs when the employee concludes that the process is in control and only randomness is present, when actually the process is out of statistical control.
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Statistical Process
Control Methods
Control Charts for variables are used to monitor the mean and variability of the process distribution.
R-chart (Range Chart) is used to monitor process variability.
x-chart is used to see whether the process is generating output, on average, consistent with a target value set by management for the process or whether its current performance, with respect to the average of the performance measure, is consistent with past performance.
If the standard deviation of the process is known, we can place UCL and LCL at “z” standard deviations from the mean at the desired confidence level.
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Where
X = central line of the chart, which can be either the average of past sample means or a target value set for the process.
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=
=
=
The control limits for the R-chart are UCLR = D4R and LCLR = D3R
where
R = average of several past R values and the central line of the chart.
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Example 6.1
West Allis is concerned about their production of a special metal screw used by their largest customers. The diameter of the screw is critical. Data from five samples is shown in the table below. Sample size is 4. Is the process in statistical control?
1
0.5027 – 0.5009 = 0.0018
2 0.5021 0.5041 0.5024 0.5020
3 0.5018 0.5026 0.5035 0.5023
4 0.5008 0.5034 0.5024 0.5015
5 0.5041 0.5056 0.5034 0.5039
Special Metal Screw
R = 0.0021
x = 0.5027
Example 6.1
Size of and LCL for LCL for UCL for
Sample x-Charts R-Charts R-Charts
(n) (A2) (D3) (D4)
2 1.880 0 3.267
3 1.023 0 2.575
4 0.729 0 2.282
5 0.577 0 2.115
6 0.483 0 2.004
7 0.419 0.076 1.924
8 0.373 0.136 1.864
9 0.337 0.184 1.816
10 0.308 0.223 1.777
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Example 6.1
Size of and LCL for LCL for UCL for
Sample x-Charts R-Charts R-Charts
(n) (A2) (D3) (D4)
2 1.880 0 3.267
3 1.023 0 2.575
4 0.729 0 2.282
5 0.577 0 2.115
6 0.483 0 2.00
=
=
=
Eliminate the problem Repeat the cycle
Example 6.1
Control Charts
for Attributes
p-chart: A chart used for controlling the proportion of defective services or products generated by the process.
z = normal deviate (number of standard deviations from the average)
p = p(1 – p)/n
n = sample size
p = central line on the chart, which can be either the historical average population proportion defective or a target value.
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Hometown Bank
Example 6.3
The operations manager of the booking services department of Hometown Bank is concerned about the number of wrong customer account numbers recorded by Hometown personnel.
Each week a random sample of 2,500 deposits is taken, and the number of incorrect account numbers is recorded. The results for the past 12 weeks are shown in the following table.
Is the booking process out of statistical control? Use three-sigma control limits.
2
n = 2500
Example 6.3
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c-chart: A chart used for controlling the number of defects when more than one defect can be present in a service or product.
The underlying sampling distribution for a c-chart is the Poisson distribution.
The mean of the distribution is c
The standard deviation is c
A useful tactic is to use the normal approximation to the Poisson so that the central line of the chart is c and the control limits are
UCLc = c+z c and LCLc = c−z c
c-Charts
Example 6.4
In the Woodland Paper Company’s final step in their paper production process, the paper passes through a machine that measures various product quality characteristics. When the paper production process is in control, it averages 20 defects per roll.
Set up a control chart for the number of defects per roll. Use two-sigma control limits.
b) Five rolls had the following number of defects: 16, 21, 17, 22, and 24, respectively. The sixth roll, using pulp from a different supplier, had 5 defects. Is the paper production process in control?
c = 20
z = 2
16
Example 6.4
Sample Number
Process Capability
Process capability is the ability of the process to meet the design specifications for a service or product.
Nominal value is a target for design specifications.
Tolerance is an allowance above or below the nominal value.
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Process Capability Index, Cpk, is an index that measures the potential for a process to generate defective outputs relative to either upper or lower specifications.
Process Capability Index, Cpk
We take the minimum of the two ratios because it gives the worst-case situation.
Cpk = Minimum of
Upper specification – x
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Process capability ratio, Cp, is the tolerance width divided by 6 standard deviations (process variability).
Process Capability Ratio, Cp
Using Continuous Improvement to Determine Process Capability
Step 1: Collect data on the process output; calculate mean and standard deviation of the distribution.
Step 2: Use data from the process distribution to compute process control charts.
Step 3: Take a series of random samples from the process and plot results on the control charts.
Step 4: Calculate the process capability index, Cpk, and the process capability ratio, Cp, if necessary. If results are acceptable, document any changes made to the process and continue to monitor output. If the results are unacceptable, further explore assignable causes.
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Intensive Care Lab
= 1.35 minutes
The intensive care unit lab process has an average turnaround time of 26.2 minutes and a standard deviation of 1.35 minutes.
The nominal value for this service is 25 minutes with an upper specification limit of 30 minutes and a lower specification limit of 20 minutes.
The administrator of the lab wants to have four-sigma performance for her lab. Is the lab process capable of this level of performance?
33
= 0.94
Average service = 26.2 minutes
After Process Modification
Average service = 26.1 minutes
Intensive Care Lab
Assessing Process Capability
Example 6.5