managing flow variability process control a statement for quality goes here these sides and note...

Managing Flow VariabilityProcess Control

A Statement for Quality Goes Here

These sides and note were prepared using 1. Managing Business Flow processes. Anupindi, Chopra, Deshmukh, Van

Mieghem, and Zemel.Pearson Prentice Hall. 2. Few of the graphs of the slides of Prentice Hall for this book, originally

prepared by professor Deshmukh.

2Ardavan Asef-Vaziri Jan-2012Quality – Process Control

Introduction ~ The Garage Door ManufacturerAccording to the sales manager of a high-tech

manufacturer of garage doors, while the company has 15% of market share, customers are not satisfied Door Quality in terms of safety, durability, and ease of use High Price compared competitors’ process Not on-time orders Poor After Sales Service

We can not rely of subjective statements and opinions Collect and analyze concrete data –facts- on

performance measures that drive customer satisfaction Identify, correct, and prevent sources of future problems


9.1 Performance Variability

All internal and external performance measures display vary from tome to time. External Measurements - customer satisfaction, product

rankings, customer complaints. Internal Measurements - flow units cost, quality, and

time.

No two cars rolling off an assembly line have identical cost. No two customers for identical transaction spend the same time in a bank. The same meal you have had in two different occasions in a restaurant do not taste exactly the same.

Sources of Variability Internal: imprecise equipment, untrained workers, and

lack of standard operating procedures. External: inconsistent raw materials, supplier delays,

consumer taste change, and changing economic conditions.


9.1 Performance Variability

A discrepancy between the actual and the expected performance often leads to cost↑, flow time↑, quality↓ dissatisfied customers.

Processes with greater variability are judged less satisfactory than those with consistent, predictable performance.

What is the base of the customer judgment the exact unit of product or service s/he gets, not how the average product performs. Customers perceive any variation in their product or service from what they expected as a loss in value.

In general, a product is classified as defective if its cost, quality, availability or flow time differ significantly from their expected values, leading to dissatisfied customers.


Quality Management Terms

Quality of Design. How well product specifications aim to meet customer requirements (what we promise consumers ~ in terms of what the product can do). Quality Function Deployment (QFD) is a conceptual framework for translating customers’ functional requirements (such as ease of operation of a door or its durability) into concrete design specifications (such as the door weight should be between 75 and 85 kg.)

Quality of Conformance. How closely the actual product conforms to the chosen design specifications. Ex. # defects per car, fraction of output that meets specifications. Ex. irline conformance can be measured in terms of the percentage of flights delayed for more than 15 minutes OR the number of reservation errors made in a specific period of time.


9.2 Analysis of Variability

To analyze and improve variability there are diagnostic tools to help us:

1. Monitor the actual process performance over time2. Analyze variability in the process3. Uncover root causes4. Eliminate those causes5. Prevent them from recurring in the future


9.2.1 Check Sheets

check Sheet is simply a tally of the types and frequency of problems with a product or a service experienced by customers.

Pareto Chart is a bar chart of frequencies of occurrences in non-increasing order. The 80-20 Pareto principle states that 20% of problem types account for 80% of all occurrences.

Type of Complaint Number of Complaints

Cost IIII IIII

Response Time IIII

Customization IIII

Service Quality IIII IIII IIII

Door Quality IIII IIII IIII IIII IIII 0

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Door Quality Service Quality Cost Response Time Customization


9.2.3 Histograms

Collect data on door weight – Ex. one door, five times a day, 20 days, total of 100 door weight.

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Freq

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Weight (kg)

Histogram is a bar plot that displays the frequency distribution of an observed performance characteristic. Ex. 14% of the doors weighed about 83 kg, 8% weighed about 81 kg, and so forth.

Time\ Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

9 a.m. 81 82 80 74 75 81 83 86 88 82 86 86 88 72 84 76 74 85 82 8911 a.m. 73 87 83 81 86 86 82 83 79 84 84 83 79 86 85 82 86 85 84 801 p.m. 85 88 76 91 82 83 76 82 86 89 81 78 83 80 81 83 83 82 83 903 p.m. 90 78 84 75 84 88 77 79 84 84 81 80 83 79 88 84 89 77 92 835 p.m. 80 84 82 83 75 81 78 85 85 80 87 83 82 87 81 79 83 77 84 77


9.2.4 Run Charts

Run chart is a plot of some measure of process performance monitored over time.

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9.2.5 Multi-Vari Charts

Multi-vari chart is a plot of high-average-low values of performance measurement sampled over time.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time\ Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

9 a.m. 81 82 80 74 75 81 83 86 88 82 86 86 88 72 84 76 74 85 82 8911 a.m. 73 87 83 81 86 86 82 83 79 84 84 83 79 86 85 82 86 85 84 801 p.m. 85 88 76 91 82 83 76 82 86 89 81 78 83 80 81 83 83 82 83 903 p.m. 90 78 84 75 84 88 77 79 84 84 81 80 83 79 88 84 89 77 92 835 p.m. 80 84 82 83 75 81 78 85 85 80 87 83 82 87 81 79 83 77 84 77Average 81.8 83.8 81.0 80.8 80.4 83.8 79.2 83.0 84.4 83.8 83.8 82.0 83.0 80.8 83.8 80.8 83.0 81.2 85.0 83.8

High 90 88 84 91 86 88 83 86 88 89 87 86 88 87 88 84 89 85 92 90

Low 73 78 76 74 75 81 76 79 79 80 81 78 79 72 81 76 74 77 82 77

Range 17 10 8 17 11 7 7 7 9 9 6 8 9 15 7 8 15 8 10 13


Comparison

Pareto Chart. The importance of each item. Quality was the most important item. Quality was then defined as finish, ease of use, and durability. Ease of use and durability which are subjective, must be translated into some thing measurable. We translate them into weight. If weight is high, it cannot operate easily, if weight is low, it will not be durable. A high quality door, based on engineering design must weight 82.5 lbs.

Histogram. Shows the tendency (mean) and the standard deviation. Ex. For door weight.

Run Chart. Can show trend. Multi-Vari Chart. Shows average and variability inside

the samples and among the samples.


Process Management

Two aspects to process management; Process planning’s goal is to produce and deliver

products that satisfy targeted customer needs. Structuring the process Designing operating procedures Developing key competencies such as process capability,

flexibility, capacity, and cost efficiency Process control’s goal is to ensure that actual

performance conforms to the planned performance. Tracking deviations between the actual and the planned

performance and taking corrective actions to identify and eliminate sources of these variations.

There could be various reasons behind variation in performance.


9.3.1 The Feedback Control PrincipleProcess performance management is based on the general principle of feedback control of dynamical systems.

Applying the feedback control principle to process control.“involves periodically monitoring the actual process performance (in terms of cost, quality, availability, and response time), comparing it to the planned levels of performance, identifying causes of the observed discrepancy between the two, and taking corrective actions to eliminate those causes.”


Plan-Do-Check-Act (PDCA)

Process planning and process control are similar to the Plan-Do-Check-Act (PDCA) cycle. Performed continuously to monitor and improve the process performance.

Problems in Process Control Performance variances are determined by

comparison of the current and previous period’s performances.

Decisions are based on results of this comparison. Some variances may be due to factors beyond a

worker’s control. According to W. Edward Deming, incentives based

on factors that are beyond a worker’s control is like rewarding or punishing workers according to a lottery.


Two categories of performance variability

Normal Variability. Is statistically predictable and includes both structural variability and stochastic variability. Cannot be removed easily. Is not in worker’s control. Can be removed only by process re-design, more precise equipment, skilled workers, better material, etc.

Abnormal variability. Unpredictable and disturbs the state of statistical equilibrium of the process by changing parameters of its distribution in an unexpected way. Implies that one or more performance affecting factors may have changed due to external causes or process tampering. Can be identified and removed easily therefore is worker’s responsibility.


Process Control

If observed performance variability is Normal - due to random causes - process is in

control Abnormal - due to assignable causes - process is

out of control The short run goal is:

1. Estimate normal stochastic variability.2. Accept it as an inevitable and avoid tampering3. Detect presence of abnormal variability4. Identify and eliminate its sources

The long run goal is to reduce normal variability by improving process.


9.3.3 Control Limit Policy

How to decide whether observed variability is normal or abnormal?

Control Limit Policy Control band - A range within which any variation in

performance is interpreted as normal due to causes that cannot be identified or eliminated in short run.

Variability outside this range is abnormal. Lower limit of acceptable mileage, control band for

house temperature.


Process Control

Process control is useful to control any type of process.

Application of control limit policy Managing inventory, process capacity and flow

time. Cash management - liquidate some assets if

cash falls below a certain level. Stock trading - purchase a stock if and when its

price drops to a specific level.Control limit policy has usage in a wide

variety of business in form of critical threshold for taking action


9.3.4 Statistical Process Control

Statistical process control involves setting a “range of acceptable variations” in the performance of the process, around its mean.

If the observed values are within this range: Accept the variations as “normal” Don’t make any adjustments to the process

If the observed values are outside this range: The process is out of control Need to investigate what’s causing the problems –

the assignable cause


9.3.4 Process Control Charts

Let be the expected value and be the standard deviation of the performance. Set up an Upper Control Limit (UCL) and a Lower Control Limit (LCL).

LCL = - z UCL = + z

Decide how tightly to monitor and control the process. The smaller the z, the tighter the control


9.3.4 Process Control Charts

If observed data within the control limits and does not show any systematic pattern Performance variability is normal . Otherwise Process is out of control

Type I error ( error). Process is in control, its statistical parameters have not changed, but data falls outside the limits.

Type II error ( error) Process is out of control, its statistical parameters have changed, but data falls inside the limits.


9.3.4 Control Charts … Continued

Optimal Degree of Control depends on 2 things: How much variability in the performance measure we

consider acceptable How frequently we monitor the process performance.

Optimal frequency of monitoring is a balance between the costs and benefits

If we set ‘z’ to be too small: We’ll end up doing unnecessary investigation. Incur additional costs.

If we set ‘z’ to be too large: We’ll accept a lot more variations as normal. We wouldn’t look for problems in the process – less costly


9.3.4 Control Charts … Continued

In practice, a value of z = 3 is used. 99.73% of all measurements will fall within the “normal” range


We have collected 20 samples, each of size 5, n=5, of our variable of interest X – the door weight in our example. We have 100 pieces of data. We can simple use excel to compute the average and standard deviation of this data.

Overall average weight

5.82X

Variance 64.172 sStandard deviation 2.4s

A higher value of the average indicates a shift in the entire distribution to the right, so that all doors produced are consistently heavier. An increase in the value of the standard deviation means a wider spread of the distribution around the mean, implying that many doors are much heavier or lighter than the overall average weight.


X Bar Chart

Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

n

XX :sampleeach in t Door Weigh Average

88.15

2.4 :tDoor Weigh Average ofDeviation Standard

n

ssX

5.82 :t Door Weigh Average of Average X

If we compute the average of the random variable X, in each sample of n, in our example 5, and show it by

n ofDeviation Standard and Mean on with dostributi Normal has

ofDeviation Standard and Mean on with dostributiany has

X

X


X Bar Chart


Therefore, if we compute the average weight door68.26% of all doors will weigh within 82.5 + (1)(1.88), 95.44% of doors will weight within 82.5 + (2)(1.88), and 99.73% of door weights will be within 82.5 + (3)(1.88), or between and 76.86 and 88.14 .

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Avera

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LCL


R Chart


: Size of Sample ain Range Rn

Rn : Size of Sample ain Range Average

RsRS : ofDeviation tandard1.10R5.3Rs

UCL = 10.1+3(3.5) = 20.6 , LCL = 10.1-3(3.5) = -0.4 = 0

Time\ Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Range 17 10 8 17 11 7 7 7 9 9 6 8 9 15 7 8 15 8 10 13

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LCL

Process Is “In Control” (i.e., variation is stable)


Instead of analysis of Average, Range, etc. we may choose to classify each flow unit as defective or nondefective.

If we take a single flow unit, probability of being defective is p and not being defective is (1-p).

If we take a random sample of n flow units, then the number of defectives D in the sample will have binomial distribution , which has mean np and variance np(1 – p).

The fraction defective of this sample P = D/n will then have mean np/n = p and variance np(1 – p)/n2. = p(1 – p)/n.

To estimate the true fraction defective pbar, we take N samples, each containing n flow units, observe proportion defective in each and compute the average fraction defective . The fraction defective (or p) chart shows control limits on the observed fraction of defective units

Fraction Defective - P Chart


nppzpUCL /)1( nppzpLCL /)1(

we classify each garage door as defective or good, depending on its overall quality such as fit and finish, dimensions, weight.

Based on 20 samples of 5 doors each, the number of defective doors D in each sample is 1, 0, 0, 2, 1, 1, 0, 1, 2, 1, 2, 1, 1, 2, 1, 0, 3, 0, 1, 0. Dividing each by 5 gives fraction defective in each sample as 0.2, 0, 0, 0.4, 0.2, 0.2, 0, 0.2, 0.4, 0.2, 0.4, 0.2, 0.2, 0.4, 0.2, 0, 0.6, 0, 0.2, 0. The average proportion defective is then = 0.2. With z = 3,

07366.05/)8.0(2.02.0 zUCL

01366.05/)8.0(2.02.0 zLCL

If the observed fraction defective is less than 0.7366, we conclude the process is in control, as is the case above.


Number of Defects - c Chart

n =# of opportunities for defects/errors in a single flow unitp = Probability of a defect/error occurrence in eachm = Number of defects/errors per flow unit. Number of typos/page, equipment breakdowns/shift, power outages/year, customer complaints/month, defects/car, accounting errors/thousand transactions, bags lost/thousand flown,.m follows Binomial (n, p) with mean np, variance np(1-p) If n is large and p is small, then we can assume m follows Poisson distribution with cbar = np. cbar is mean and also variance.


czcUCL czcUCL If the observed number of errors exceeds the UCL, it indicates degradation in performance. If it is less than the LCL, it indicates better‑than‑expected performance.


Number of Defects - c Chart

Consider the number of order processing errors that occur per month at Garage Door Operations. If they process several orders per month and the chance of making an error on each order is small, then the number of errors per month follows Poisson distribution. Suppose they have tracked order processing errors over the past 12 months and found them to be 3, 1, 0, 4, 6, 2, 1, 2, 0, 1, 3, and 2. Then the average number of errors per month is 2.083


Since all observed processing errors are less than 6.413 (even though we made 6 order processing errors in month 5), we conclude that the order processing process is in control.

6.413083.23083.2 UCL 02.247 -083.23083.2 UCL


Performance Variation


Stable

Unstable

Trend Cyclical

Shift


Process Control and Improvement

LCL

UCL

Out of Control In Control Improved



Continuous Variables: Garage Door Weights, Costs, Waiting Time

Use Normal distribution

Discrete Variables: number of customer complaints, whether a flow unit is defective, number of defects per flow unit produced

Use Binomial or Poisson distribution

Control Chart


Cause – Effect Analysis: 5 Why

Why are these doors so heavy?

Because the Sheet Metal was too ‘thick’.

Why was the sheet metal too thick?

Because the rollers at the steel mill were set incorrectly.

Why were the rollers set incorrectly?

Because the supplier is not able to meet our specifications.

Why did we select this supplier?

Because our Project Supervisor was too busy getting the product out – didn’t have time to research other vendors.

Why did he get himself in this situation?

Because he gets paid by meeting the production quotas.


Cause – Effect Analysis: Fish Bone Diagram


9.3.6 Scatter Plots

The Thickness of the Sheet Metals

Change Settings on Rollers

Measure the Weight of the Garage Doors

Determine Relationship between the two

Plot the results on a graph:

Roller Settings & Garage Door Weights

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Roller Setting (mm)

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Scatter Plot

managing flow variability process control a statement for quality goes here these sides and note...

Documents

door quality

quality of conformance

quality dissatisfied

product specifications

performance variability

flow time

flow variability process

actual product