- Email: [email protected]
Reliability learning model: Application to color TV
A,Ftcroe~ctro,/c~ and Re//ab//ffy, VoI.19,pp. 73-80(1979) lha-gamon Press. Printed in the U.S.A.
0026-2714/79/0101-00735(~.00/0 Copyright © 1978 Pexgamon Press Ltd.
RELIABILITY LEARNING MODEL: APPLICATION TO COLOR TV
J. Imai, H. Karasawa and H. Machida TV and Consumer Video Group, Sony Corporation, Tokyo, Japan
141
ABSTRACT This paper discusses reliability learning for consumer color TV receivers, categorizing learning b y p r o d u c t model. Each product model has a hierarchical construction involving various levels, and learning occurs at each level. The characteristics of the convergence point for a chassis category are studied. Application of this learning model to practical reliability activity is explained, methods related to this application are indicated, and the process of total reliability learning is explained. Particularly, the B.M.B. method, which indicates inherent reliability capability, and the idea of design review to implement this method at the present level of theoretical understanding is indicated.
INTRODUCTION For an enterprise in the field of consumer goods, high product reliability means not only profitability but also consolidation of its business foundation by establishing a good brand reputation. A high level of reliability can only be achieved through effective management. In reliability management, rational target setting is highly important. A well defined and persuasive target results in gaining cooperation among people directly and indirectly involved. Reliability learning models are useful in establishing appropriate targets. In general, consumer products are complex entities, being constructed from a variety of components in complex assembly operations, and undergoing constant changes to new models. There are successive design changes of the chassis of color TV receivers, and newly produced models are constantly being placed on the market. When a new CRT (picture tube) size is adopted, it is normally accompanied by a newly developed chassis. In this case, a hierarchical structure is created with each receiver belonging to a certain chassis category and each chassis belonging to a certain CRT size category. All consumer products undergo the repeated process of planningdesign-production-sale. This work presents a reliability learning model, which is the first such model to explain the growth of reliability by comparing the field failure rates of new models with those of past products. Many applications of the learning model of J.T. Duane and others (1-4) have involved industrial or institutional product systems in the burn-in phase, or the design-
73
74
J. Imai,
H. Karasawa
and H. Machida
test-redesign cycle in the d e v e l o p m e n t a l phase. On the other hand, this model has not been p r e v i o u s l y applied to studies of product models of consumer products. The man power learning technique has been developed in the field of few-product-model, small-quantity m a n u f a c t u r e r s such as aircraft companies. It has only recently been applied in the field of mass p r o d u c t i o n industries. As an example, we refer to the work of S. Shimomura (5) who proposes a useful graphical model of m a n power learning in this field. The m o t i v a t i o n s for color TV model changes at Sony Corporation are to incorporate new features into a model, try to reduce cost, and to increase product performance. This hopefully results in both consumer satisfaction and business success. At Sony, reliability has always occupied animportant p o s i t i o n as one of the foundations of m a n a g e m e n t policy (6). In this paper scientific methods are proposed by means of the reliability learning model, and the optimum strategy for reaching this goal is described.
LEARNING
MODEL
The p r o p o s e d learning model was obtained by analysis of T r i n i t r o n receiver field failure rate data. It expresses the relationship b e t w e e n field failure rate and the elapsed time from the i n t r o d u c t i o n of the original model (the first model of a category) until the next model becomes available. The field failure rate is the average rate per m o n t h w i t h i n three m o n t h s after the i n t r o d u c t i o n of a new model, and is p l o t t e d as a linear ordinate. The time elapsed since the introduction of the original model in months is normally p l o t t e d as the abscissa on a logarithmic scale. Such a p l o t d e m o n s t r a t e s a g r a p h i c a l learning model, in which a newer p r o d u c t model has a lower failure rate. This learning model is q u a n t i t a t i v e l y d e s c r i b e d by the following: Fj(t i) = aj - bj log t i Inthis
(log t i >
aj/bj).
(i)
expression, Fj(ti)
is the failure rate of the product i which belongs to the j-th category; t i is the duration time of the i-th product: the number of months elapsed from the introduction of the original model of a category until the sale time of the i-th p r o d u c t model. (t I = i, t i > i, i = 2,3,...,I); aj is the initial p a r a m e t e r value of j-th category (aj = Fj(tl) > 0); bj is the learning p a r a m e t e r value of j-th category (bj > 0). The p r e s e n t learning model appears to contain only the time elapsed since the introduction of the original model of a category (t i) as a parameter. This parameter, however, is related to the number of m a n u f a c t u r e d products, the number of p r o d u c t models w h i c h have been sold, the total operating p e r i o d in the user stage, and the frequency of failure occurence. All these factors contribute to the learning model. The failure rate of a p a r t i c u l a r p r o d u c t whose m a r k e t i n g p e r i o d is k times longer than that of an arbitrarily chosen product can be w r i t t e n as the following: F(ti-k)
= a - b log ti-k.
(2)
Combining Eqs. (i) and (2), the learning is e x p r e s s e d as F(ti) - F(ti.k ) = b log k. In this learning model, when the time is increased by a factor of k, the failure rate is improved by b log k. For instance w h e n k = 2, the improvement is b log 2 0.35. Verification
of the Learning
Model
In order to test the validity of the present learning model, two basic learning models which have frequently been employed are selected for comparison. These two m o d e l s contain failure rates F' and F", and duration times T' and T". They are described by the following equations:
Reliability Type I
Learning Model:
Application
: log F' = a' - b' log T',
Type II : log F" = a" - b" T".
to Color TV
75 (3) (4)
With the addition of our present model, F = a - b log T (Type III), these three equations are employed in analyzing our field failure data (Table i). All the figures mentioned hereafter are expressed in terms of the ratio of failure rate of a particular model to that of the initial original model which indicates the maximum value. Prior to this analysis, the past product models are classified into CRT size and chassis categories, and the failure rate is plotted as described above. Sometimes it is necessary to reject obviously deviant data. From the results of the analysis indicated in Table i, the Type III Learning Model represents the best fit. Table 1 shows the results from analysis of four chassis categories and seven CRT size categories, respectively. The linear model shown in Fig. 1 is obtained by plotting the failure rate by CRT size category. The C i in the figure symbolize decreasing CRT size in the order CI, C2, C3, C 4. In Fig. 2 a learning curve by chassis category is shown. From this graph it is seen that the classification by chassis category is more suitable in describing the learning model than the CRT size classification.
Learning
Classified According
to CRT Size Category
Figure 3 shows the relationship between the marketing period and failure rate among the CRT size categories. It is rather difficult to find a definite analytical expression for the learning among CRT size categories. The general tendencies of a high failure rate for the original product model of the C 4 size category (which is the oldest and smallest type), and the decrease of failure rate for newer models can be seen in Fig. 3. On the other hand, the latest data show the tendency of smaller size CRT models to have higher reliability than ones employing larger tubes. The reason for this is that beside the inherently low reliability of the larger size category, additional reliability decreases may originate in the fact that larger size models are equipped with a variety of features which require a greater number of components as well as higher power consumption. From the fact that even if the new product model has a large CRT size, the original model has a lower failure rate than the original model of every preceding size category, it is clear that the learning depends on the duration time.
Learning Classified According
to Chassis Category
From detailed analysis of each linear model within a CRT size category, the growth of learning among chassis categories can be observed. Extracting the straight line of the C 4 size category, which has the largest number of chassis subcategories, the variation among chassis for each product model is replotted in Fig. 4. a. All points fall approximately on the straight line in Fig. 4. a, with slightly curved trends noticable in the same chassis category . Once again, replotting the data concerning the original product model and each of its derived chassis categories, the straight line relationships are easier to see, as indicated in Fig. 4. b. The newer chassis models have increased Reliability compared to the older chassis, but from a macroscopic point of view it is influenced by the original product model's learning characteristics in each size category. There is an occasional case where the reliability of original product model with a newer chassis decreases compared with an older chassis, in spite of the above mentioned tendency. In this case, the successive chassis show a rapid improvement of the reliability, and the linear model also becomes evident. The Converqence
Point
76
J. Imai,
H. K a r a s a w a and H. M a c h i d a
The m o s t p r o m i n e n t feature of Fig. 2 is the n e a r - i n t e r s e c t i o n p o i n t of the straight lines d e s c r i b i n g each chassis r e l i a b i l i t y growth. A s s u m i n g an exact i n t e r s e c t i o n exists, we m a y treat this c o n v e r g e n c e as follows. In order to discuss the nature of the intersection, Fig. 5 illustrates a simple example. Suppose two a r b i t r a r y lines F~ and F2 intersect at a certain point; then F 1 = F2 = al - bl log t = a2 - b2 log t, and it follows that: (al - a2)/(bl If the two lines indeed relations:
- b2) = log t = CONST.
intersect
at
(t c, Fc),
then Eq.
(5) (i) yields
the following
F c = a - b log tc, .'. a
= F c + b log t c,
and
b =
[F(t I) - F c ] / l o g
t c.
Figure 6 shows the results of using the actual a and b values of each chassis gory. R e g r e s s i o n analysis on Eq. (6) gives a = 0.0542
+ 2.219 b,
and
b =
[F(tl) - 0.0542]/2.219.
(6) cate-
(7)
The above analysis shows the tendency for the learning rate to d e c r e a s e w i t h decreasing failure rate of the original p r o d u c t model. W h e n the failure rate of the original p r o d u c t m o d e l of a c e r t a i n chassis category is equal to F c, the learning rate is equal to zero and convergence occurs. For older, w e l l - e s t a b l i s h e d chassis, the learning w o u l d never be lower than F c. The c o n v e r g e n c e level of learning b e c o m e s F c. It follows that if a c o n v e r g e n c e p o i n t exists, the e x p r e s s i o n for our learning model can be w r i t t e n as the following: a - b log t,
(log t <
(a - Fc)/b)
(8)
Fc
(log t ~
(a - Fc)/b)
(9)
F(t) ,
The d i s c o n t i n u i t y at the c o n v e r g e n c e p o i n t may seem to c o n t r a d i c t the smooth b e h a v i o r of m o d e l s p r o p o s e d in m a n y p r e v i o u s papers. This m a y be due to the fact that our data have not yet a p p r o a c h e d the time tc, w h e n actual c o n v e r g e n c e takes place. Since c o n v e r g e n c e of learning is only a t h e o r e t i c a l prediction, it m u s t be checked against future data.
APPLICATIONS
Reliability Management
for M i d - R a n g e
Planning
The m a i n p u r p o s e of the m i d - r a n g e p l a n in b u s i n e s s is to achieve a p p r o p r i a t e sales and profits. I n c r e a s e d p r o d u c t r e l i a b i l i t y n a t u r a l l y results in a steady increase of sales, as w e l l as in i n c r e a s e d p r o f i t s by saving the expense of field service calls. T h e r e f o r e the r e l i a b i l i t y in the field i.e., service call rate, as well as the ratio of service cost to total sales should be taken as i m p o r t a n t parameters. They m u s t be i n c o r p o r a t e d at the stage of m i d - r a n g e planning, and have d e f i n i t e target values. At the same stage, line-up e x p a n s i o n or d e v e l o p m e n t of new CRT size categories m a y also be required. F u r t h e r m o r e , new p r o d u c t i o n t e c h n i q u e s m a y have to be i n t r o d u c e d in order to p r o d u c e new features and to d e c r e a s e m a n u f a c t u r i n g costs. This may carry a s s o c i a t e d risks of d e c r e a s e d reliability. In this case, a conventional q u a l i t y control m e t h o d w o u l d not be e x p e c t e d to be a g o o d t e c h n i q u e to improve the r e l i a b i l i t y learning. On the other hand, top m a n a g e m e n t m a y r e a l i z e the fact that the r e l i a b i l i t y g r o w t h follows an o r d i n a r y learning pattern. A c c e p t a n c e of the s i t u a t i o n does not follow, however, and d r a s t i c i m p r o v e m e n t of the learning p a t t e r n may be r e q u e s t e d during the m i d - r a n g e p l a n n i n g period. R e l i a b i l i t y staff m u s t c o n t r i b u t e in setting r a t i o n a l
Reliability Learning Model: Application to Color TV
77
targets by estimating the present reliability level as well as the inherent reliability level. In addition to an application of effective learning models to this subject, the best mixed block (B.M.B.) method (to be described later) must be employed in reliability capability analysis. In order to obtain the understanding and cooperation of all personnel involved, the target i) must be easily understood, 2) must bear a clear relation to past achievements, 3) must be able to indicate differences from the present situation clearly, and 4) must also be able to show any deviation from projected values as time progresses. For management of reliability targets, it is useful to plot the target on a graph in which the calendar time is plotted along the horizontal axis and the failure rate is plotted along the vertical axis. A superior reliability program must be deduced from the target set by the above mentioned means. The set target manifests itself in each category of the hierarchy in accordance with size, chassis, and product model during every fiscal term. Moreover, it affects each division, e.g. design, purchasing, manufacturing, and it must be supported as all the activity items are organized for scheduling. In the process of attempting to reach these targets, the selection of activity theme and the method of laying emphasis etc. in each division are clarified. Follow-up and evaluation must be easily implementable. Since the inherent reliability of a product is essentially fixed at the design stage, critical design review is very important. Efforts to systematize and grade up the design procedure are also desirable. The present learning model, which is the consequence of systematization of Sony's historical manufacturing data, plays an important role in planning a mid-range program.
Development of the Basic Chassis In order to achieve the multipurpose target of mid-range planning, the development of chassis which contain new technologies is an important mission. This is due to the need to decrease manufacturing costs and to add new features. It has a great influence on development projects of new basic chassis, even though merely making minor changes of a conventional chassis is regarded as a better precedure for achieving reliability. The learning model shows that "a new chassis always yields the better reliability", which is supported by the management belief that "in order to obtain the better reliability, new chassis must be developed." Whether the target of service cost vs. selling ratio is accomplished or not in the mid-range planning depends upon the success of development of the basic chassis. New basic chassis have the characteristics of essentially good reliability. On the other hand, since development projects always bring up new problems, it is quite possible that the reliability of original product models for new basic chassis may deteriorate. The fundamental reason for this is the fact that past experience is not completely utilized in the design of the new structural part of the chassis. Since the main portion of reliability learning is acquired at this development and design stage, design review plays an important role here. The learning model shows that a reliability program must be incorporated in the basic structural design of the chassis in order to increase efficiency in this phase. The model also shows that it is necessary for the reliability engineer to be able to influence the developmental planning stage. Management decides the apportionment of resources and priorities for various aspects of the development of the chassis, and merges past know-how in reviewing the structure and design.
Minor Model Changes In the earlier period of a new chassis category the learning effectiveness is high. While applying the learning model, it is more effective to increase the reliability level by making partial improvements based on previously accumulated know-how. In
78
J. Imai, H. Karasawa and H. Machida
this phase, the learning model is useful for target decisions. In addition, the B.M.B. method plays an important role. The B.M.B. method involves the following process. First, a reliability block diagram is made for the chassis, subdividing it into subunit blocks which perform circuitry functions and include active devices. Subsequently a conceptual highest reliability block diagram is constructed, which only includes the highest reliability blocks among conventional chassis. This conceptual product model is named the "Best Mixed Model". Its reliability is expressed by the following: R = ~max m 1
(Rlm).
(i0)
In this formula, R is the reliability of the best mixed model, and Rlm is the reliability of the m-th block in the l-th product model. Generally, the best mixed model shows a much higher reliability than that of the learning model. The reliability obtained by the B.M.B. method shows the best possible presently achievable reliability. In case of a minor assembly change, the B.M.B. method serves as a rational foundation for increasing the reliability. This is because it is possible to isolate the effect of each block, and to determine where the major differences of failure rate occur between the usual learning model and the B.M.B. model. Analysis of the problem and its mechanism is based on these results. Moreover, adopting an effective acceleration test and proper derating methods, the reliability can be improved (8). The development of these methods is also important, and the results influence product design and design reviews. The learning model and B.M.B. methods, which are comprehensive analyses of data from the field, form the learning process mechanism of product reliability. They combine with each other through product design and design reviews, and form the basis for processes to increase product reliability.
CONCLUSIONS In this paper, a simple reliability learning model for color TV was applied. This model can graphically and concisely express the learning process for each stage of the color TV hierarchical structure. It is also shown that rational reliability management is possible by employing this model. This paper could not clarify the origin of the learning mechanism. Naturally, it is impossible that a single convergence point exists in the electronic industry, which is undergoing day-by-day improvements. Even if such a convergence point should exist, it is bound to be improved as time passes. More advanced reliability improvement techniques must be developed in order to manage a reliability problem when a situation approaches this particular convergence level. This subject also includes decisions concerning under what circumstances a new chassis should be developed from reliability considerations.
ACKNOWLEDGEMENT The authors wish to express their gratitude for the guidance and encouragement received from Mr. Y. Kato (Director, Computer Division, Sony) during the course of this work.
79
Reliability Learning Model: A p p l i c a t i o n to Color TV
o .2
~
o
I
I
IO DURATION TIME
I
IOO
I
10 DURATION
100 TIME
Fig. 2 Linear models of chassis category
Fig. 1 Linear m o d e l s of CRT size category
o
~
C4
C3
"
C2 xx
~.,
~, :CI X : C2
CI ~'x
xx
xx
•
"x
:C3
0 :C4
"x
© \,,
\\\
x
x
xx
©
© o
I
I
.69
I
.70
.71
I
I
72
I
73
,74
CALENDER YEAR
Fig.
3 Historical
c+
--
~
~ ]st chassis (~ : 2nd chasszs ~ : 3rd chassis [] o~hers
C4 fine
O--
~_
field failure data of CRT size category
0
-2
x
[]
C4 line
~
o
[
,~ DURATION
TIME
, I
,~0
Fig. 4. a Reliability learning model of C 4 CRT size category
10 D U R A T I O N TIME
Fig. 4. b Reliability each
chassis
r I00
learning models of of
C4 category
80
J. Imai, H. Karasawa and H. Machida
~:,,~
o2_ ......
,. . . . point
~;--
Fc
I
r
I
DURATION TIME (log U
tc
Fig. 5 Convergence point and level
Ol
I
02
I
03
I
04
VALUE OF b
05
Fig. 6 Regression line of aj, bj
Table i. Test data of Regression Analysis Category of data
data cas(
Type I r s
6.883 0.2656 CRT Size 5 6 7 8 9 i0 ii
Chassis
0.814 0.862 0.752 0.928 0.918 0.796 0.971 0.974 0.881 0.895
0.0510 0.0893 0.0424 0.2870 0.0279 0.0071 0.0242 0.0086 0.0469 0.0732
Type II Type III r r s 0.870 0.1592 0.958 0.0765 13 0.844 0.0627 0.908 0.0486 8 0.909 0.0837 0.949 0.0608 15 0.773 0.0431 0.784 7 0.0413 0.963 0.1781 0.965 0.0932 0.832 0.0630 0.958 0.0261 0.496 0.0117 0.818 0.0073 0.862 0.0974 0.975 0.0304 0.714 0.0385 0.945 0.0149 0.833 0.0526 0.900 0.0328 0.981 0.0364 0.918 0.0414
where r: Correlation coefficient. s: Standard error, square root of mean square of deviations between observed and estimated values. n: Number of observations. REFERENCES (1) J.T. Duane, Learning curve approach to reliability monitoring, IEEE Trans. Aerospace, 2, 563 (1964). (2) A.J. Gross and M. Kamins, Reliability assessment in the presence of reliability growth, Annual S~mposium on Reli.~bility, 406 (1968). (3) A. Bezat, V. Norquist and L. Montague, Growth modeling improves reliability predictions, Annual Reliability and Maintainability Symposium, 317 (1975). (4) B.L. Amstadter, (1971) Reliability Mathematics, McGraw-Hill, New York. (5) S. Shimomura and H. Karasawa, A study of stand-up model in mass production, Japan Industrial Management Association, 253 (1972). (6) Y. Kato, New products development and quality assurance of electronics industry, Factory Management, 13, 24 (1967). (7) C. Meade, T. Cox and J. Lavery, Reliability growth management in USAMC, Annual Reliability and Maintainability Symposium, 432 (1975). (8) Y. Kato and H. Karasawa, Some approachs to reliability physics, Annual Symposium on Reliability, 607 (1968).
0026-2714/79/0101-00735(~.00/0 Copyright © 1978 Pexgamon Press Ltd.
RELIABILITY LEARNING MODEL: APPLICATION TO COLOR TV
J. Imai, H. Karasawa and H. Machida TV and Consumer Video Group, Sony Corporation, Tokyo, Japan
141
ABSTRACT This paper discusses reliability learning for consumer color TV receivers, categorizing learning b y p r o d u c t model. Each product model has a hierarchical construction involving various levels, and learning occurs at each level. The characteristics of the convergence point for a chassis category are studied. Application of this learning model to practical reliability activity is explained, methods related to this application are indicated, and the process of total reliability learning is explained. Particularly, the B.M.B. method, which indicates inherent reliability capability, and the idea of design review to implement this method at the present level of theoretical understanding is indicated.
INTRODUCTION For an enterprise in the field of consumer goods, high product reliability means not only profitability but also consolidation of its business foundation by establishing a good brand reputation. A high level of reliability can only be achieved through effective management. In reliability management, rational target setting is highly important. A well defined and persuasive target results in gaining cooperation among people directly and indirectly involved. Reliability learning models are useful in establishing appropriate targets. In general, consumer products are complex entities, being constructed from a variety of components in complex assembly operations, and undergoing constant changes to new models. There are successive design changes of the chassis of color TV receivers, and newly produced models are constantly being placed on the market. When a new CRT (picture tube) size is adopted, it is normally accompanied by a newly developed chassis. In this case, a hierarchical structure is created with each receiver belonging to a certain chassis category and each chassis belonging to a certain CRT size category. All consumer products undergo the repeated process of planningdesign-production-sale. This work presents a reliability learning model, which is the first such model to explain the growth of reliability by comparing the field failure rates of new models with those of past products. Many applications of the learning model of J.T. Duane and others (1-4) have involved industrial or institutional product systems in the burn-in phase, or the design-
73
74
J. Imai,
H. Karasawa
and H. Machida
test-redesign cycle in the d e v e l o p m e n t a l phase. On the other hand, this model has not been p r e v i o u s l y applied to studies of product models of consumer products. The man power learning technique has been developed in the field of few-product-model, small-quantity m a n u f a c t u r e r s such as aircraft companies. It has only recently been applied in the field of mass p r o d u c t i o n industries. As an example, we refer to the work of S. Shimomura (5) who proposes a useful graphical model of m a n power learning in this field. The m o t i v a t i o n s for color TV model changes at Sony Corporation are to incorporate new features into a model, try to reduce cost, and to increase product performance. This hopefully results in both consumer satisfaction and business success. At Sony, reliability has always occupied animportant p o s i t i o n as one of the foundations of m a n a g e m e n t policy (6). In this paper scientific methods are proposed by means of the reliability learning model, and the optimum strategy for reaching this goal is described.
LEARNING
MODEL
The p r o p o s e d learning model was obtained by analysis of T r i n i t r o n receiver field failure rate data. It expresses the relationship b e t w e e n field failure rate and the elapsed time from the i n t r o d u c t i o n of the original model (the first model of a category) until the next model becomes available. The field failure rate is the average rate per m o n t h w i t h i n three m o n t h s after the i n t r o d u c t i o n of a new model, and is p l o t t e d as a linear ordinate. The time elapsed since the introduction of the original model in months is normally p l o t t e d as the abscissa on a logarithmic scale. Such a p l o t d e m o n s t r a t e s a g r a p h i c a l learning model, in which a newer p r o d u c t model has a lower failure rate. This learning model is q u a n t i t a t i v e l y d e s c r i b e d by the following: Fj(t i) = aj - bj log t i Inthis
(log t i >
aj/bj).
(i)
expression, Fj(ti)
is the failure rate of the product i which belongs to the j-th category; t i is the duration time of the i-th product: the number of months elapsed from the introduction of the original model of a category until the sale time of the i-th p r o d u c t model. (t I = i, t i > i, i = 2,3,...,I); aj is the initial p a r a m e t e r value of j-th category (aj = Fj(tl) > 0); bj is the learning p a r a m e t e r value of j-th category (bj > 0). The p r e s e n t learning model appears to contain only the time elapsed since the introduction of the original model of a category (t i) as a parameter. This parameter, however, is related to the number of m a n u f a c t u r e d products, the number of p r o d u c t models w h i c h have been sold, the total operating p e r i o d in the user stage, and the frequency of failure occurence. All these factors contribute to the learning model. The failure rate of a p a r t i c u l a r p r o d u c t whose m a r k e t i n g p e r i o d is k times longer than that of an arbitrarily chosen product can be w r i t t e n as the following: F(ti-k)
= a - b log ti-k.
(2)
Combining Eqs. (i) and (2), the learning is e x p r e s s e d as F(ti) - F(ti.k ) = b log k. In this learning model, when the time is increased by a factor of k, the failure rate is improved by b log k. For instance w h e n k = 2, the improvement is b log 2 0.35. Verification
of the Learning
Model
In order to test the validity of the present learning model, two basic learning models which have frequently been employed are selected for comparison. These two m o d e l s contain failure rates F' and F", and duration times T' and T". They are described by the following equations:
Reliability Type I
Learning Model:
Application
: log F' = a' - b' log T',
Type II : log F" = a" - b" T".
to Color TV
75 (3) (4)
With the addition of our present model, F = a - b log T (Type III), these three equations are employed in analyzing our field failure data (Table i). All the figures mentioned hereafter are expressed in terms of the ratio of failure rate of a particular model to that of the initial original model which indicates the maximum value. Prior to this analysis, the past product models are classified into CRT size and chassis categories, and the failure rate is plotted as described above. Sometimes it is necessary to reject obviously deviant data. From the results of the analysis indicated in Table i, the Type III Learning Model represents the best fit. Table 1 shows the results from analysis of four chassis categories and seven CRT size categories, respectively. The linear model shown in Fig. 1 is obtained by plotting the failure rate by CRT size category. The C i in the figure symbolize decreasing CRT size in the order CI, C2, C3, C 4. In Fig. 2 a learning curve by chassis category is shown. From this graph it is seen that the classification by chassis category is more suitable in describing the learning model than the CRT size classification.
Learning
Classified According
to CRT Size Category
Figure 3 shows the relationship between the marketing period and failure rate among the CRT size categories. It is rather difficult to find a definite analytical expression for the learning among CRT size categories. The general tendencies of a high failure rate for the original product model of the C 4 size category (which is the oldest and smallest type), and the decrease of failure rate for newer models can be seen in Fig. 3. On the other hand, the latest data show the tendency of smaller size CRT models to have higher reliability than ones employing larger tubes. The reason for this is that beside the inherently low reliability of the larger size category, additional reliability decreases may originate in the fact that larger size models are equipped with a variety of features which require a greater number of components as well as higher power consumption. From the fact that even if the new product model has a large CRT size, the original model has a lower failure rate than the original model of every preceding size category, it is clear that the learning depends on the duration time.
Learning Classified According
to Chassis Category
From detailed analysis of each linear model within a CRT size category, the growth of learning among chassis categories can be observed. Extracting the straight line of the C 4 size category, which has the largest number of chassis subcategories, the variation among chassis for each product model is replotted in Fig. 4. a. All points fall approximately on the straight line in Fig. 4. a, with slightly curved trends noticable in the same chassis category . Once again, replotting the data concerning the original product model and each of its derived chassis categories, the straight line relationships are easier to see, as indicated in Fig. 4. b. The newer chassis models have increased Reliability compared to the older chassis, but from a macroscopic point of view it is influenced by the original product model's learning characteristics in each size category. There is an occasional case where the reliability of original product model with a newer chassis decreases compared with an older chassis, in spite of the above mentioned tendency. In this case, the successive chassis show a rapid improvement of the reliability, and the linear model also becomes evident. The Converqence
Point
76
J. Imai,
H. K a r a s a w a and H. M a c h i d a
The m o s t p r o m i n e n t feature of Fig. 2 is the n e a r - i n t e r s e c t i o n p o i n t of the straight lines d e s c r i b i n g each chassis r e l i a b i l i t y growth. A s s u m i n g an exact i n t e r s e c t i o n exists, we m a y treat this c o n v e r g e n c e as follows. In order to discuss the nature of the intersection, Fig. 5 illustrates a simple example. Suppose two a r b i t r a r y lines F~ and F2 intersect at a certain point; then F 1 = F2 = al - bl log t = a2 - b2 log t, and it follows that: (al - a2)/(bl If the two lines indeed relations:
- b2) = log t = CONST.
intersect
at
(t c, Fc),
then Eq.
(5) (i) yields
the following
F c = a - b log tc, .'. a
= F c + b log t c,
and
b =
[F(t I) - F c ] / l o g
t c.
Figure 6 shows the results of using the actual a and b values of each chassis gory. R e g r e s s i o n analysis on Eq. (6) gives a = 0.0542
+ 2.219 b,
and
b =
[F(tl) - 0.0542]/2.219.
(6) cate-
(7)
The above analysis shows the tendency for the learning rate to d e c r e a s e w i t h decreasing failure rate of the original p r o d u c t model. W h e n the failure rate of the original p r o d u c t m o d e l of a c e r t a i n chassis category is equal to F c, the learning rate is equal to zero and convergence occurs. For older, w e l l - e s t a b l i s h e d chassis, the learning w o u l d never be lower than F c. The c o n v e r g e n c e level of learning b e c o m e s F c. It follows that if a c o n v e r g e n c e p o i n t exists, the e x p r e s s i o n for our learning model can be w r i t t e n as the following: a - b log t,
(log t <
(a - Fc)/b)
(8)
Fc
(log t ~
(a - Fc)/b)
(9)
F(t) ,
The d i s c o n t i n u i t y at the c o n v e r g e n c e p o i n t may seem to c o n t r a d i c t the smooth b e h a v i o r of m o d e l s p r o p o s e d in m a n y p r e v i o u s papers. This m a y be due to the fact that our data have not yet a p p r o a c h e d the time tc, w h e n actual c o n v e r g e n c e takes place. Since c o n v e r g e n c e of learning is only a t h e o r e t i c a l prediction, it m u s t be checked against future data.
APPLICATIONS
Reliability Management
for M i d - R a n g e
Planning
The m a i n p u r p o s e of the m i d - r a n g e p l a n in b u s i n e s s is to achieve a p p r o p r i a t e sales and profits. I n c r e a s e d p r o d u c t r e l i a b i l i t y n a t u r a l l y results in a steady increase of sales, as w e l l as in i n c r e a s e d p r o f i t s by saving the expense of field service calls. T h e r e f o r e the r e l i a b i l i t y in the field i.e., service call rate, as well as the ratio of service cost to total sales should be taken as i m p o r t a n t parameters. They m u s t be i n c o r p o r a t e d at the stage of m i d - r a n g e planning, and have d e f i n i t e target values. At the same stage, line-up e x p a n s i o n or d e v e l o p m e n t of new CRT size categories m a y also be required. F u r t h e r m o r e , new p r o d u c t i o n t e c h n i q u e s m a y have to be i n t r o d u c e d in order to p r o d u c e new features and to d e c r e a s e m a n u f a c t u r i n g costs. This may carry a s s o c i a t e d risks of d e c r e a s e d reliability. In this case, a conventional q u a l i t y control m e t h o d w o u l d not be e x p e c t e d to be a g o o d t e c h n i q u e to improve the r e l i a b i l i t y learning. On the other hand, top m a n a g e m e n t m a y r e a l i z e the fact that the r e l i a b i l i t y g r o w t h follows an o r d i n a r y learning pattern. A c c e p t a n c e of the s i t u a t i o n does not follow, however, and d r a s t i c i m p r o v e m e n t of the learning p a t t e r n may be r e q u e s t e d during the m i d - r a n g e p l a n n i n g period. R e l i a b i l i t y staff m u s t c o n t r i b u t e in setting r a t i o n a l
Reliability Learning Model: Application to Color TV
77
targets by estimating the present reliability level as well as the inherent reliability level. In addition to an application of effective learning models to this subject, the best mixed block (B.M.B.) method (to be described later) must be employed in reliability capability analysis. In order to obtain the understanding and cooperation of all personnel involved, the target i) must be easily understood, 2) must bear a clear relation to past achievements, 3) must be able to indicate differences from the present situation clearly, and 4) must also be able to show any deviation from projected values as time progresses. For management of reliability targets, it is useful to plot the target on a graph in which the calendar time is plotted along the horizontal axis and the failure rate is plotted along the vertical axis. A superior reliability program must be deduced from the target set by the above mentioned means. The set target manifests itself in each category of the hierarchy in accordance with size, chassis, and product model during every fiscal term. Moreover, it affects each division, e.g. design, purchasing, manufacturing, and it must be supported as all the activity items are organized for scheduling. In the process of attempting to reach these targets, the selection of activity theme and the method of laying emphasis etc. in each division are clarified. Follow-up and evaluation must be easily implementable. Since the inherent reliability of a product is essentially fixed at the design stage, critical design review is very important. Efforts to systematize and grade up the design procedure are also desirable. The present learning model, which is the consequence of systematization of Sony's historical manufacturing data, plays an important role in planning a mid-range program.
Development of the Basic Chassis In order to achieve the multipurpose target of mid-range planning, the development of chassis which contain new technologies is an important mission. This is due to the need to decrease manufacturing costs and to add new features. It has a great influence on development projects of new basic chassis, even though merely making minor changes of a conventional chassis is regarded as a better precedure for achieving reliability. The learning model shows that "a new chassis always yields the better reliability", which is supported by the management belief that "in order to obtain the better reliability, new chassis must be developed." Whether the target of service cost vs. selling ratio is accomplished or not in the mid-range planning depends upon the success of development of the basic chassis. New basic chassis have the characteristics of essentially good reliability. On the other hand, since development projects always bring up new problems, it is quite possible that the reliability of original product models for new basic chassis may deteriorate. The fundamental reason for this is the fact that past experience is not completely utilized in the design of the new structural part of the chassis. Since the main portion of reliability learning is acquired at this development and design stage, design review plays an important role here. The learning model shows that a reliability program must be incorporated in the basic structural design of the chassis in order to increase efficiency in this phase. The model also shows that it is necessary for the reliability engineer to be able to influence the developmental planning stage. Management decides the apportionment of resources and priorities for various aspects of the development of the chassis, and merges past know-how in reviewing the structure and design.
Minor Model Changes In the earlier period of a new chassis category the learning effectiveness is high. While applying the learning model, it is more effective to increase the reliability level by making partial improvements based on previously accumulated know-how. In
78
J. Imai, H. Karasawa and H. Machida
this phase, the learning model is useful for target decisions. In addition, the B.M.B. method plays an important role. The B.M.B. method involves the following process. First, a reliability block diagram is made for the chassis, subdividing it into subunit blocks which perform circuitry functions and include active devices. Subsequently a conceptual highest reliability block diagram is constructed, which only includes the highest reliability blocks among conventional chassis. This conceptual product model is named the "Best Mixed Model". Its reliability is expressed by the following: R = ~max m 1
(Rlm).
(i0)
In this formula, R is the reliability of the best mixed model, and Rlm is the reliability of the m-th block in the l-th product model. Generally, the best mixed model shows a much higher reliability than that of the learning model. The reliability obtained by the B.M.B. method shows the best possible presently achievable reliability. In case of a minor assembly change, the B.M.B. method serves as a rational foundation for increasing the reliability. This is because it is possible to isolate the effect of each block, and to determine where the major differences of failure rate occur between the usual learning model and the B.M.B. model. Analysis of the problem and its mechanism is based on these results. Moreover, adopting an effective acceleration test and proper derating methods, the reliability can be improved (8). The development of these methods is also important, and the results influence product design and design reviews. The learning model and B.M.B. methods, which are comprehensive analyses of data from the field, form the learning process mechanism of product reliability. They combine with each other through product design and design reviews, and form the basis for processes to increase product reliability.
CONCLUSIONS In this paper, a simple reliability learning model for color TV was applied. This model can graphically and concisely express the learning process for each stage of the color TV hierarchical structure. It is also shown that rational reliability management is possible by employing this model. This paper could not clarify the origin of the learning mechanism. Naturally, it is impossible that a single convergence point exists in the electronic industry, which is undergoing day-by-day improvements. Even if such a convergence point should exist, it is bound to be improved as time passes. More advanced reliability improvement techniques must be developed in order to manage a reliability problem when a situation approaches this particular convergence level. This subject also includes decisions concerning under what circumstances a new chassis should be developed from reliability considerations.
ACKNOWLEDGEMENT The authors wish to express their gratitude for the guidance and encouragement received from Mr. Y. Kato (Director, Computer Division, Sony) during the course of this work.
79
Reliability Learning Model: A p p l i c a t i o n to Color TV
o .2
~
o
I
I
IO DURATION TIME
I
IOO
I
10 DURATION
100 TIME
Fig. 2 Linear models of chassis category
Fig. 1 Linear m o d e l s of CRT size category
o
~
C4
C3
"
C2 xx
~.,
~, :CI X : C2
CI ~'x
xx
xx
•
"x
:C3
0 :C4
"x
© \,,
\\\
x
x
xx
©
© o
I
I
.69
I
.70
.71
I
I
72
I
73
,74
CALENDER YEAR
Fig.
3 Historical
c+
--
~
~ ]st chassis (~ : 2nd chasszs ~ : 3rd chassis [] o~hers
C4 fine
O--
~_
field failure data of CRT size category
0
-2
x
[]
C4 line
~
o
[
,~ DURATION
TIME
, I
,~0
Fig. 4. a Reliability learning model of C 4 CRT size category
10 D U R A T I O N TIME
Fig. 4. b Reliability each
chassis
r I00
learning models of of
C4 category
80
J. Imai, H. Karasawa and H. Machida
~:,,~
o2_ ......
,. . . . point
~;--
Fc
I
r
I
DURATION TIME (log U
tc
Fig. 5 Convergence point and level
Ol
I
02
I
03
I
04
VALUE OF b
05
Fig. 6 Regression line of aj, bj
Table i. Test data of Regression Analysis Category of data
data cas(
Type I r s
6.883 0.2656 CRT Size 5 6 7 8 9 i0 ii
Chassis
0.814 0.862 0.752 0.928 0.918 0.796 0.971 0.974 0.881 0.895
0.0510 0.0893 0.0424 0.2870 0.0279 0.0071 0.0242 0.0086 0.0469 0.0732
Type II Type III r r s 0.870 0.1592 0.958 0.0765 13 0.844 0.0627 0.908 0.0486 8 0.909 0.0837 0.949 0.0608 15 0.773 0.0431 0.784 7 0.0413 0.963 0.1781 0.965 0.0932 0.832 0.0630 0.958 0.0261 0.496 0.0117 0.818 0.0073 0.862 0.0974 0.975 0.0304 0.714 0.0385 0.945 0.0149 0.833 0.0526 0.900 0.0328 0.981 0.0364 0.918 0.0414
where r: Correlation coefficient. s: Standard error, square root of mean square of deviations between observed and estimated values. n: Number of observations. REFERENCES (1) J.T. Duane, Learning curve approach to reliability monitoring, IEEE Trans. Aerospace, 2, 563 (1964). (2) A.J. Gross and M. Kamins, Reliability assessment in the presence of reliability growth, Annual S~mposium on Reli.~bility, 406 (1968). (3) A. Bezat, V. Norquist and L. Montague, Growth modeling improves reliability predictions, Annual Reliability and Maintainability Symposium, 317 (1975). (4) B.L. Amstadter, (1971) Reliability Mathematics, McGraw-Hill, New York. (5) S. Shimomura and H. Karasawa, A study of stand-up model in mass production, Japan Industrial Management Association, 253 (1972). (6) Y. Kato, New products development and quality assurance of electronics industry, Factory Management, 13, 24 (1967). (7) C. Meade, T. Cox and J. Lavery, Reliability growth management in USAMC, Annual Reliability and Maintainability Symposium, 432 (1975). (8) Y. Kato and H. Karasawa, Some approachs to reliability physics, Annual Symposium on Reliability, 607 (1968).